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• Hugh G. A. Burton

Hugh G. A. Burton University of Cambridge | Cam  ·  Department of Chemistry

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Hugh G. A. Burton

I am the Kim and Julianna Silverman Research Fellow at Downing College, Cambridge and an early-career researcher in the Yusuf Hamied Department of Chemistry, University of Cambridge . My primary research involves understanding the breakdown of electronic structure approximations in the presence of strongly coupled electrons and developing new theoretical methods to accurately predict the properties of electrons in molecules using emerging technology such as quantum computing . I am particularly interested in understanding the energy landscape of electronic structure approximations and how the existence of multiple stationary points is controlled by the presence of strong correlation or electronic excited states. I am also involved in collaborative projects investigating how to exploit nonorthogonal many-electron basis states to predict molecular potential energy surfaces, and exploring the exotic molecular properties and quantum phenomena using complex-valued non-Hermitian quantum physics .

• Introducing a global optimisation algorithm for quantum electronic structure approximations
• Deriving the properties of the exact electronic energy landscape
• Characterising the higher-energy solutions in CASSCF theory
• Developing efficient computational methods for nonorthogonal matrix elements
• Identifying the first example of mean-field symmetry-breaking in the complete basis set limit

In the summer of 2020, I was a postdoctoral research associate with Prof. David Wales at the University of Cambridge. I developed the electronic structure energy landscape framework where ground and excited states exist as stationary points of a high-dimensional energy surface. This approach allows the properties and connectivity of multiple electronic states to be systematically investigated, providing guiding principles for the development of high-accuracy excited-state methods .

I completed my PhD under the supervision of Dr Alex Thom at the University of Cambridge in 2020. During this period, I pioneered the holomorphic Hartree-Fock approach that allows complex analytic continuations of multiple Hartree–Fock solutions to be constructed across all structures of a molecule. My thesis showed that a linear combination of these solutions can provide numerically accurate predictions of bond-breaking processes and molecular binding curves.

In the summer of 2018, I undertook a two-month research internship at Q-Chem Inc. , an electronic structure software company based in Pleasanton CA, USA. At Q-Chem, I developed a new dedicated library for running nonorthogonal configuration interaction calcuations on molecules. This library is now available in the latest public release of the Q-Chem software package.

Prior to my PhD, I studied chemistry at the University of Cambridge. I completed a research project with Prof. Daan Frenkel , investigating the thermophoretic flow of atoms under the influence of temperature gradients at liquid-liquid interfaces.

I am a theoretical physicist and Senior Lecturer in Physics at Bristol University. My work concerns the theory of quantum matter. I tend to work on phenomena which involve interesting shapes and patterns (geometry and topology).

Until 2023 I was a Lecturer in Physics at Cardiff University. Before that I held the Astor Junior Research Fellowship at New College, Oxford, and a Lindemann Trust Fellowship of the English Speaking Union , which sent me to the University of California, Berkeley. I completed my PhD at the University of Bristol. I was on the Perimeter Institute's Perimeter Scholars International programme. I was an undergraduate at St. Catherine's College, Oxford.

Please see the Publications tab for papers, theses etc. , the Research , and Talks tabs for more information on both my scientific and outreach work, and Students for projects I have supervised.

The Teaching tab contains some resources I have produced.

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Felix Flicker

He previously held the Astor Junior Research Fellowship at New College, Oxford, and a Lindemann Trust Fellowship of the English Speaking Union, which sent him to the University of California, Berkeley. He completed his PhD at the University of Bristol. He was on the Perimeter Institute's Perimeter Scholars International programme. He was an undergraduate at St. Catherine's College, Oxford.

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I. INTRODUCTION

Ii. two-electron atomic hamiltonian, iii. computational details, iv. results, a. spin-symmetry breaking critical point, b. closed-shell critical point, c. fractional spin error, v. concluding remarks, supplementary material, acknowledgments, data availability, hartree–fock critical nuclear charge in two-electron atoms.

Note: This paper is part of the 2021 JCP Emerging Investigators Special Collection.

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Hugh G. A. Burton; Hartree–Fock critical nuclear charge in two-electron atoms. J. Chem. Phys. 21 March 2021; 154 (11): 111103. https://doi.org/10.1063/5.0043105

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Electron correlation effects play a key role in stabilizing two-electron atoms near the critical nuclear charge, representing the smallest charge required to bind two electrons. However, deciphering the importance of these effects relies on fully understanding the uncorrelated Hartree–Fock description. We investigate the properties of the ground state wave function in the small nuclear charge limit using various symmetry-restricted Hartree–Fock formalisms. We identify the nuclear charge where spin-symmetry breaking occurs to give an unrestricted wave function that predicts an inner and outer electron. We also identify closed-shell and unrestricted critical nuclear charges where the highest occupied orbital energy becomes zero and the electron density detaches from the nucleus. Finally, we identify the importance of fractional spin errors and static correlation for small nuclear charges.

How much positive charge is required to bind two electrons to a nucleus? This simple question has been subject to intense research and debate ever since the early 1930s. 1–9 High-precision calculations have only recently converged on a critical nuclear charge for binding two electrons of Z c = 0.911 028 224 077 255 73(4). 7–10 For Z > Z c , the two-electron atom ( Z e e) is bound and stable, with an energy lower than the ionized system ( Z e + e). However, for Z < Z c , the energy of the bound atom becomes higher than the ionized system, causing an electron to spontaneously detach from the nucleus. As a result, the critical charge marks the threshold for stability in the three-body problem 6,11,12 and can be interpreted as a quantum phase transition. 13  

While the critical nuclear charge is fascinating in its own right, the two-electron atom also provides an essential model for testing electronic structure methods. For example, recent studies have used the two-electron atom to understand the performance of different approximate density functionals. 10,14–16 It is also the simplest chemical system with electron correlation, which is thought to be essential in binding the two electrons near Z c . 3,17,18 Indeed, comparing the closed-shell Hartree–Fock (HF) energy to the exact energy of the ionized system suggests that HF theory fails to predict a stable two-electron atom with Z c < Z < 1.031 177 528, 14,17 including H − . 19,20 However, interpreting exactly how correlation influences the stability of the two-electron atom is made difficult by an incomplete understanding of the HF approximation for small Z .

In many ways, placing artificial restrictions on the wave function makes HF theory more complicated to interpret than the exact result. For example, the restricted HF (RHF) formalism can only predict doubly occupied orbitals, 21 and one might ask if comparing the RHF energy to the exact one-electron energy is a fair way to identify a critical nuclear charge. Alternatively, the nuclear charge at which the occupied HF orbital energy becomes zero can also be interpreted as a critical threshold for bound single-particle orbitals. 14 On the other hand, the unrestricted HF (UHF) approach allows the spin-up and spin-down electrons to occupy different spatial orbitals, 21 leading to the dissociation of a single electron in H − at the expense of broken spin-symmetry. 19,20 The onset of symmetry breaking in HF is marked by instability thresholds in the orbital Hessian, 22 which have also been interpreted as critical charges in closed-shell atoms. 23 These sudden qualitative changes in the HF wave function can be further probed using the average radial electronic positions, providing an indicator for ionization that does not rely on energetic properties. However, to the best of our knowledge, the exact nuclear charge for UHF symmetry breaking, and the qualitative properties of HF wave functions near this point, remains unknown.

Previous studies on the two-electron atom using HF theory have primarily focused on the large Z , or “high-density,” limit (see Ref. 24 ). In this limit, the closed-shell RHF wave function provides a good approximation to the exact result, creating a model for understanding dynamic electron correlation. 24,25 However, the small- Z “low-density” limit, where static correlation becomes significant, remains far less explored. The primary challenges of small Z include the presence of HF symmetry-breaking and convergence issues that occur with diffuse basis functions. One recent study has been unable to reliably converge the RHF approximation for Z < 0.85, 17 hindering attempts to understand HF theory for smaller Z . Consequently, the small- Z limit also provides a model for understanding how to predict strong static correlation, 14,26 which remains a major computational challenge.

In this contribution, we investigate the properties of the RHF and UHF ground-state wave functions in the small Z limit. We use numerical Laguerre-based HF calculations to compute the exact location of the UHF symmetry-breaking threshold, and the critical charge for bound single-particle orbitals. By investigating the average radial positions in the RHF and UHF wave functions, we assess how each HF formalism predicts electron detachment near these critical charges. We find that the UHF symmetry-breaking threshold represents the onset of electron detachment and forms a branch point singularity in the complex Z plane. Alternatively, RHF theory predicts a closed-shell critical point where half the electron density becomes ionized, leading to strong static correlation.

The Z -scaled Hamiltonian for the two-electron atom with an infinite nuclear mass is 1  

where ρ i = r i / Z is the scaled distance of electron i from the nucleus, ρ 12 = | ρ 1 − ρ 2 | is the scaled inter-electronic distance, and the unscaled distances have atomic units a 0 . Nuclear charges are given in atomic units e . The exact wave function is defined by the time-independent Schrödinger equation

with the spin-spatial coordinate x i = ( ρ i , σ i ) and the scaled energy E ̃ = E / Z 2 ⁠ . The electron–electron repulsion can be considered as a perturbation to the independent-particle model with the coupling strength λ = 1/ Z , 1 giving the power series expansions E ̃ ( λ ) = ∑ k = 0 ∞ E ̃ ( k ) λ k and Ψ ( λ ) = ∑ k = 0 ∞ Ψ ( k ) λ k ⁠ . The critical nuclear charge Z c can then be identified from the radius of convergence of these series, 2,4,5,27 defined by the distance of the closest singularity to the origin in the complex λ plane. 28 Both E ̃ ( λ ) and |Ψ( λ )| 2 have complicated singularities on the positive real axis at λ c = 1/ Z c , 5 which have been interpreted as a quantum phase transition in the complete-basis-set limit. 13  

The HF wave function is a single Slater determinant Ψ HF ( x 1 , x 2 ) built from the antisymmetrized product of the occupied spin-orbitals ψ i ( x ). These orbitals are self-consistent eigenfunctions of the one-electron Fock operator f ^ ( x ) ⁠ , with the corresponding eigenvalues ϵ i defining orbital energies. The Z -scaled Fock operator is

with the one-electron Hamiltonian

and the Coulomb and exchange operators denoted as Ĵ i ( x ) and K ^ i ( x ) ⁠ , respectively (see Ref. 21 ). The total Z -scaled HF energy is

with the matrix elements h i = ψ i | ĥ | ψ i and f i = ψ i | f ^ | ψ i ⁠ .

The self-consistent two-electron component of the Fock operator can be considered as a perturbation with the coupling strength λ = 1/ Z . For large Z ( λ → 0), only the one-electron component remains and the HF wave function is exact. 24 As Z becomes smaller and λ grows, the self-consistent repulsion becomes increasingly dominant over the one-electron nuclear attraction. Eventually, it becomes energetically favorable for a pair of lower-energy UHF solutions to emerge where either the spin-up or spin-down electron becomes detached from the nucleus. 19,20 This phenomenon is analogous to the Coulson–Fischer point in stretched H 2 , where the spin-up and spin-down electrons localize on opposite atoms, 29 and is closely related to Wigner crystallisation. 30 By analytically continuing an equivalent two-electron coupling parameter to complex values, we have recently shown that the UHF wave functions form a non-Hermitian square-root branch point at the symmetry-breaking threshold. 28,31 Remarkably, following a complex-valued contour around this point leads to the interconversion of the degenerate solutions, and allows a ground-state wave function to be smoothly evolved into an excited-state wave function. 31  

In the present work, we follow Ref. 17 and express the spatial component ϕ p ( r ) of the HF spin-orbital ψ p ( x ) using the spherically symmetric Laguerre-based functions 32  

Here, we employ the nonorthogonal tensor notation of Head–Gordon et al. 33 The non-linear parameter A controls the spatial extent of the basis functions and is optimized alongside the coefficients C ⋅ p μ ⋅ ⁠ . 17 In practice, this expansion is truncated at a finite basis set of size n . To avoid previous issues with iterative solutions to the HF equations for small Z , we optimize the C ⋅ p μ ⋅ coefficients for a fixed A value using the quasi-Newton Geometric Direct Minimization (GDM) algorithm. 34 The optimal A value is then identified through another quasi-Newton minimization with the orbital coefficients re-optimized on each step. All calculations were performed in a developmental version of Q-CHEM, 35 and analytic expressions for the Laguerre-based integrals are provided in the supplementary material (Sec. SI).

First, we identify the nuclear charge for HF symmetry-breaking Z sb UHF using a bisection method to locate the point where the lowest orbital Hessian eigenvalue of the RHF solution vanishes (see the supplementary material , Sec. SII). The convergence of Z sb UHF with respect to the basis set size is shown in Table I . The Z sb UHF values appear converged up to 10 decimal places for n ≥ 24, giving

with the energy converged to 8 decimal places,

Converged RHF energies for He and H − are also obtained for n ≥ 24 as

in agreement with the best variational benchmarks up to 10 decimal places. 17,36,37 We believe that this is the first numerically precise estimate of a symmetry-breaking threshold in the complete-basis-set HF limit, defining a new type of benchmark value within electronic structure theory. As expected, Z sb UHF > 1 ⁠ , making our result consistent with previous observations of UHF symmetry breaking in the hydride anion. 19,20

Convergence of the UHF symmetry-breaking threshold Z sb UHF and the associated energy E UHF ( Z sb UHF ) with respect to the basis set size. Best estimates for the exact values are obtained using the converged decimal places for n ≥ 24.

Figure 1 (top panel) compares the Z -scaled RHF energy (red line) and the symmetry-broken UHF energy (blue dashed line) as functions of Z −1 with n = 26. We also consider the exact one-electron energy (black line) that corresponds to the ionized atom, the exact two-electron energy (gray dashed line; reproduced from Ref. 8 ), and a fractional spin RHF calculation (orange dashed line) with half a spin-up and half spin-down electron (see Sec. IV C ). The UHF symmetry-breaking threshold Z sb UHF (black dotted line) occurs below the exact one-electron energy, and is therefore greater than the HF critical nuclear charge previously identified using energetic arguments. 17 This suggests that the RHF approximation is already an inadequate representation of the exact wave function before it becomes degenerate with the one-electron atom. Beyond this point, the RHF energy continues to increase, while the UHF energy rapidly flattens toward the exact one-electron result. There is, therefore, a small relaxation region where the UHF approximation approaches a qualitative representation of the one-electron atom.

Z -scaled energy (top) using various HF formalisms and the exact one- and two-electron results. Exact two-electron data are reproduced from Ref. 8 . The onset of UHF symmetry breaking Z sb UHF is indicated by the black dot and vertical line and corresponds to the lowest RHF Hessian eigenvalue becoming zero (bottom).

While Z sb UHF marks the onset of symmetry-breaking, both electrons remain in bound orbitals with negative eigenvalues. Alternatively, the charge where the outer orbital eigenvalue becomes zero can be considered as the critical charge Z c UHF for stability under the UHF approximation. We have located the nuclear charge associated with this zero orbital eigenvalue up to n = 50 (see the supplementary material , Sec. SIII), but have not reached convergence with respect to the available basis set size. Assuming that the basis set truncation error decays exponentially, an extrapolation based on the Shanks transformation 38,39 leads to the first five digits

with energy

This value suggests that the threshold for UHF stability lies remarkably close to the charge of the hydride anion, and we direct the reader to the supplementary material (Sec. SIV) for in-depth analysis. As a result, we find Z c UHF < Z sb UHF ⁠ , and the UHF wave function is symmetry-broken but bound for Z c UHF < Z < Z sb UHF ⁠ .

Radial electron position expectation values ⟨ r ⟩ provide further insights into the properties of the two-electron atom close to electron detachment ( Fig. 2 ). 8,18,40 The exact wave function yields an “inner” and “outer” electron, with repulsive interactions pushing the inner electron closer to the nucleus than in the corresponding hydrogenic system. 40 For Z > Z sb UHF ⁠ , the RHF radial electron position (red line) closely matches the averaged exact two-electron result (gray dashed line). However, the RHF result starts to deviate from the two-electron value as electron correlation effects become significant for Z < Z sb UHF ⁠ . In contrast, the additional flexibility of the UHF wave function correctly predicts the separation of an inner and outer electron (dashed and solid blue lines, respectively). Ionization begins almost immediately for Z < Z sb UHF ⁠ , as indicated by a sudden increase in ⟨ r ⟩ for the outer electron, while the inner electron tends toward the exact one-electron result.

Average radial position ⟨ r ⟩ using various HF formalisms and exact one- and two-electron results. Exact two-electron data are reproduced from Ref. 8 . UHF yields different orbitals for different spins, giving an inner and outer electron.

Figure 2 also indicates that the dissociation of the outer electron for the UHF approximation is relatively sudden, mirroring the behavior at the exact critical nuclear charge. 8 The outer electron becomes fully ionized near Z ≈ Z c UHF ⁠ , suggesting that the UHF solution for Z c UHF < Z < Z sb UHF represents a weakly bound wave function that smoothly evolves from the closed-shell two-electron atom to the ionized system. The exact two-electron system has a shape resonance as the nuclear charge goes through Z c , with the outer electron remaining at a finite distance from the nucleus. 7,41 The region Z c UHF < Z < Z sb UHF can therefore be interpreted as an unrestricted mean-field approximation of this resonant stability.

Comparing the radial distribution functions P ( r ) = r 2 | ψ ( r )| 2 for each electronic orbital at Z = 1 ( Fig. 3 ), we find that the inner UHF orbital closely matches the one-electron H atom, which is also the case for the exact wave function. 40 However, at Z = 1, the outer electron has essentially ionized from the atom in the UHF approximation, but remains closely bound to the nucleus in the fully correlated description. This result suggests that UHF overlocalizes the electron density between Z c < Z < Z sb UHF (including H − ), as previously observed for two-electrons on concentric spheres, 42 and fails to capture the correlation effects required to describe the bound two-electron atom near Z c .

Radial distribution functions for different HF orbitals compared to the exact one-electron wave function at Z = 1. UHF yields different orbitals for different spins, giving an inner and outer electron.

For Z < Z c , the exact wave function is an equal combination of two configurations where either the spin-up or spin-down electron remains bound to the nucleus. In contrast, the single-determinant nature of the UHF wave function means that only one of these configurations can be represented: the UHF orbitals are “pinned” to one resonance form. 43 Therefore, there must be a wave function singularity at Z sb UHF where the UHF approximation branches into a form with either the spin-up or spin-down electron remaining bound. The mathematical structure of this point can be revealed by following a continuous pathway around Z sb UHF in the complex Z plane. When Z is analytically continued to complex values, the Fock operator becomes non-Hermitian and we must consider the holomorphic HF approach. 44–46 In the remainder of this section, we fix the non-linear A parameter to its value at Z sb UHF as the non-Hermitian energy is complex-valued and cannot be variationally optimized.

Figure 4 shows the real component of ⟨ r ⟩ for the (initial) inner electron along a pathway that spirals in toward Z sb UHF ⁠ , parameterized as

Remarkably, after one complete rotation ( ξ = 2 π ), the inner and outer electrons have swapped, indicating that the degenerate UHF solutions have been interconverted. A second full rotation is required to return the states to their original forms. The two degenerate UHF wave functions are, therefore, connected as a square-root branch point in the complex- Z plane, in agreement with our previous observations in analytically solvable models. 28,31 Furthermore, the branch point behaves as a quasi-exceptional point, where the two solutions become identical but remain normalized (see Ref. 31 ), providing the first example of this type of non-Hermitian HF degeneracy in the complete-basis-set limit.

Average radial position ⟨ r ⟩ of the inner electron along a spiral contour in the complex Z plane converging on Z sb UHF using n = 26. On each rotation, the UHF wave function transitions between the two degenerate solutions, as shown by the spin-up ( ⁠ α ⁠ ) and spin-down ( ⁠ β ⁠ ) radial positions (bottom).

Now consider the RHF ground state as Z continues to decrease below Z sb UHF ⁠ . Intuitively, one might expect that doubly occupied RHF orbitals would fail to describe the open-shell atom with an ionized electron. Indeed, King et al. have observed a smooth and finite ⟨ r ⟩ value for the RHF wave function as low as Z = 0.85, with erratic convergence for lower nuclear charges. 17 A similar nuclear charge Z = 0.84 was identified in Ref. 23 as a singlet instability threshold, where the orbital Hessian contains a zero eigenvalue with respect to symmetry-pure orbital rotations. These observations suggest that the RHF approximation somehow breaks down at Z ≈ 0.84, but we are not aware of any detailed insight into this behavior.

By using the gradient-based GDM algorithm, 34 we have accurately converged the RHF ground state for all nuclear charges and can now firmly establish its properties in the small- Z limit. Remarkably, we find a sudden increase in ⟨ r ⟩ at Z = 0.82 ( Fig. 2 ) suggesting that the RHF approximation can, to a certain extent, represent the ionized system. This feature closely mirrors the electron dissociation in the UHF wave function, but gives a less sudden increase. The smoother nature of the RHF dissociation indicates that the closed-shell restriction on the orbitals artificially attenuates the electron detachment, providing a less accurate representation of the exact critical charge than UHF.

The RHF electron detachment occurs when the occupied orbital energy becomes zero, representing a closed-shell critical point Z c RHF in the RHF approximation. Identifying the convergence of this critical charge with respect to the basis set size (see the supplementary material , Sec. SIII) yields the first 9 decimal places as

At this critical charge, the orbital radial density is expected to decay asymptotically as 14,41

The Laguerre-based functions allow the fitting of this asymptotic behavior up to a certain radial distance using a truncated basis set (see the supplementary material , Sec. SV), but ultimately fail to describe the r → ∞ limit.

The RHF critical nuclear charge is also accompanied by another zero eigenvalue in the orbital Hessian, as described in Ref. 23 , but we find that this zero eigenvalue persists for small Z ( Fig. 1 : bottom panel). Zero Hessian eigenvalues generally indicate a broken continuous symmetry in the wave function, such as a global spin-rotation, 47,48 and define the “Goldstone” manifold of degenerate states. 48,49 Here, the new zero-eigenvalue Hessian mode corresponds to a spin-symmetry-breaking orbital rotation that also leads to an “inner” and “outer” electron.

To further understand the electron positions in the vicinity of Z c RHF ⁠ , we consider the cumulative radial distribution function of the doubly occupied RHF orbital ψ RHF , defined as

as shown in Fig. 5 . Here, we integrate the RHF radial density over the range 0 < r ′ < r to obtain the total number of electrons within a shell of radius r from the nucleus.

Cumulative radial distribution function for the RHF wave function (Eq. 14 ) using n = 26, with different Z values indicated by distinct colors. For Z < Z c RHF ⁠ , this function adopts a double-step structure corresponding to an inner and outer peak in the radial electron density. At Z = 0.41, each peak contains half the electron density (dashed line).

The single-step structure at Z > Z c RHF is consistent with a single peak in the radial distribution function where both electrons are localized at a small radial distance (e.g., the red line in Fig. 3 ) and the electrons are closely bound to the nucleus. For Z < Z c RHF ⁠ , this cumulative density adopts a double-step structure corresponding to a peak in the radial density close to the nucleus, and another representing an unbound electron. The relative height of each step indicates the fraction of the total electron density contained within each peak. The magnitude of the second step continues to grow for smaller Z as the outer peak becomes increasingly unbound. At Z = 0.41 (dashed line), the steps in the cumulative radial density have equal heights and the inner and outer peaks both contain exactly one electron. This suggests that one electron becomes fully unbound at this point, while the remaining electron density becomes unbound for smaller Z . Remarkably, the RHF wave function for 0.41 < Z < Z c RHF is, therefore, providing a closed-shell representation of the ionized atom by delocalizing the electron density over the bound and unbound radial “sites.” This delocalization provides a qualitatively correct representation of the exact one-body density, but fails to capture any two-body correlation between the bound and unbound electrons.

Although the RHF radial density for Z < Z c RHF appears to approximate the exact result, the RHF energy remains consistently above the one-electron hydrogenic energy. The closed-shell nature of the RHF orbitals means that the spin-up and spin-down electrons are equally split between the inner and outer radial density peaks. As a result, the RHF electron distribution for small Z tends toward a description of the one-electron atom that also contains half a spin-up and half a spin-down electron. We have confirmed this limiting behavior by computing the RHF energy with a half-occupied orbital, also known as the “spin-unpolarized” atom with fractional spins. 50–52 Our implementation is described in the supplementary material (Sec. SVI). As expected, this half-occupied RHF solution becomes degenerate with the two-electron RHF energy at small Z ( Fig. 1 ).

Remarkably, even though a one-electron atom always has a bound ground state, the fractional spin RHF wave function predicts an additional critical nuclear charge Z c frac where the (half) electrons suddenly become unbound ( Fig. 2 ). This critical charge also matches the point where the corresponding occupied orbital eigenvalue becomes zero, and identifying the convergence with respect to the basis set size (see the supplementary material , Sec. SIII) gives the first 8 decimal places as

Note that since Z c RHF = 2 Z c frac ⁠ , twice as much nuclear charge is required to bind two electrons at the RHF level compared to the spin-unpolarized one-electron atom. Furthermore, at Z c frac ⁠ , exactly half the electron density has ionized from the nucleus in the conventional RHF approach (the dashed line in Fig. 5 ). It is well-known that RHF with fractional spins fails to predict the correct energy for one-electron atoms, despite the fact that HF theory should be exact in this limit, causing the static correlation error that leads to the RHF breakdown for stretched H 2 . 50,51 Therefore, we conclude that this static correlation also creates an artificial critical nuclear charge in one-electron atoms at Z c frac and is responsible for the failure of conventional RHF in the small Z limit.

In summary, we have presented an extensive investigation into the HF description of electron detachment near the critical nuclear in the two-electron atom. We have identified the exact charge Z sb UHF where spin-symmetry-breaking occurs in the UHF approximation, alongside critical nuclear charges where the highest occupied orbital energy becomes zero in the RHF, UHF, and unpolarized fractional-spin RHF methods. These threshold nuclear charges, summarized in Table II , suggest that closed-shell orbital restrictions artificially stabilize the two-electron atom for small- Z but with an energy above the ionized system ( Z e + e).

Summary of critical nuclear charges, and their energies, identified for different HF formalisms.

The presence of spin-symmetry-breaking and the RHF breakdown for Z < Z sb UHF highlight the importance of static correlation near the exact critical nuclear charge Z c . While the closed-shell RHF wave function correctly delocalizes each electron over the bound and unbound sites, it cannot capture instantaneous electron–electron correlations such that, when one electron is bound to the nucleus, the other becomes unbound. In contrast, the UHF description allows one electron to occupy a diffuse (or ionized) orbital, while the other electron remains bound to the nucleus. This symmetry breaking provides a frozen snapshot of the instantaneous correlations but fails to describe the resonance of each electron between the two sites. Ultimately, a combination of these correlation effects is essential for correctly describing the exact critical nuclear charge, but this panacea remains out of reach for HF wave functions.

Included in the supplementary material are analytic derivation of the Laguerre-based one- and two-electron integrals, details of the bisection root-finding method, convergence data for critical nuclear charges, extrapolation of UHF critical nuclear charge, analysis of the asymptotic density at the critical point, and implementation details for fractional-spin calculations.

H.G.A.B. was supported by New College, Oxford, through the Astor Junior Research Fellowship. The author is thankful to Hazel Cox for providing the exact two-electron numerical data from Ref. 8 , and Pierre-François Loos for countless inspiring conversations and critical comments on the manuscript.

The data that support the findings of this study are available from the author upon reasonable request.

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Incommensurate charge order in a low-dimensional superconductor

Z Shi, SJ Kuhn, F Flicker, T Helm, J Lee, W Steinhardt, S Dissanayake, D Graf, J Ruff, G Fabbris, D Haskel, and S Haravifard

A team lead by Sara Haravifard from Duke University has conclusively and directly identified the subtle charge density wave phase in TPT emerging below 12K. The CDW couples to the superconducting transition and is suppressed by pressure at a critical point that maximizes the superconducting Tc. The promise of engineered high temperature superconducting materials, which could revolutionize computing, energy, and transportation industries, drives ongoing fundamental research into the interplay between SC and CDW order.

Subtle superstructures at low temperatures in Ta 4 Pd 3 Te 16 : High dynamic range diffraction maps collected at T = 5K show a superlattice of weak, sharp features that are absent at high temperature. These are signatures of a coherent charge density wave modulation of the crystal structure. The map above displays the incommensurate K=4.21 plane. Two CDW peaks, labeled Q1 and Q2, appear in each Brillouin zone.

What is the new discovery? The ternary telluride Ta 4 Pd 3 Te 16 (TPT) was recently discovered to host a superconducting ground state. Signatures in NMR, transport, and Raman measurements previously inferred that a charge density wave (CDW) phase may also exist in this material, although the evidence was inconclusive and the reported transition temperatures varied widely (from 20K to 200K). Now, a team lead by Sara Haravifard from Duke University has conclusively and directly identified the subtle CDW phase in TPT  emerging below 12K. The CDW couples to the superconducting transition and is suppressed by pressure at a critical point that maximizes the superconducting Tc.

Why is it important? Understanding how superconductivity competes with other electronic ground states is a central challenge for quantum materials research. Electron-phonon coupling can render a metallic “normal” state unstable to both CDW formation and superconductivity, with a subtle interplay of competing interactions determining the ultimate material behavior. It is necessary to identify and quantify these competing phases, if we ever want to understand and control the mechanisms that promote or suppress superconductivity. 

Why CHEXS? The <QM>2 beamline at CHEXS is optimized for high dynamic range mapping measurements of quantum materials at very low temperatures. A core mission of this beamline is to hunt down and quantify subtle and “hidden” ordered states, like the multiply incommensurate CDW phase in Ta 4 Pd 3 Te 16 . 

What are the Broader Impacts? The surprising ubiquity of charge density wave phases in superconducting materials is a recurring theme over the past decade of materials research. To date, no conclusive explanation has been accepted for why these phenomena so often coexist. A core goal of quantum materials research is to understand quantum phenomena so that we can eventually learn to engineer useful properties. There is no quantum property more potentially useful, or more consistently confusing, than unconventional superconductivity, where materials conduct electricity without resistance. The promise of engineered high temperature superconducting materials, which could revolutionize computing, energy, and transportation industries, drives ongoing fundamental research into the interplay between SC and CDW order.  

How was the work funded? This work is based upon research conducted at CHESS and CHEXS, supported by the National Science Foundation under awards  DMR-1332208 and DMR-1829070. Work at Argonne was supported by the US DOE Office of Science, Office of Basic Energy Sciences, under Award DE-AC02-06CH11357. FF acknowledges the Astor Junior Research Fellowship of New College, Oxford. ZS, WS, SD, and SH acknowledge support from the Powe Junior Faculty Enhancement Award, and William M. Fairbank Chair in Physics at Duke University. A portion of this work was  performed at the National High Magnetic Field Laboratory, which is supported by National Science Foundation Cooperative Agreement DMR-1157490 and the State of Florida.

Reference:  Incommensurate two-dimensional checkerboard charge density wave in the low-dimensional superconductor Ta 4 Pd 3 Te 16 ;   Z Shi, SJ Kuhn, F Flicker, T Helm, J Lee, W Steinhardt, S Dissanayake, D Graf, J Ruff, G Fabbris, D Haskel, and S Haravifard;  Physical Review Research 2 , 042042(R) (2020);  https://doi.org/10.1103/PhysRevResearch.2.042042

New College

Official fellowship in classics.

The College proposes to elect, if a suitable candidate applies, a Fellow and Tutor in Greek and Latin Languages and Literature, with effect from 1 October 2000. The Fellowship is associated with a titular University Lecturership, which the University may at a later date convert into a stipendiary post; meanwhile the College will pay the full stipend. The College and University encourage applications from those interested in any aspects of Classical Literature and Languages. (The Faculty has some preference for candidates with expertise in the following: Latin Literature and Literary Theory and its applications to Classical Studies.)

Application forms and further particulars are available from the Senior Tutor, New College, Oxford, OX1 3BN (tel. 01865 279596, fax 01865 279590, e-mail [email protected]). The closing date for receipt of applications is 11 February 2000.

THREE JUNIOR RESEARCH FELLOWSHIPS

Applications are invited for the Todd-Bird Junior Research Fellowship, the Astor Junior Research Fellowship, and the Weston Junior Research Fellowship, each tenable for three years from 1 October 2000. The Todd-Bird Junior Research Fellowship is restricted to the fields of Medicine and Biochemistry. The Astor Junior Research Fellowship is restricted on this occasion to the field of Music. The Weston Junior Research Fellowship is restricted on this occasion to the field of Chemistry.

For all these Fellowships applicants must, at the time of taking up the post, have completed at least two years' study for an advanced degree. Each Fellowship carries a stipend of £12,372 a year (subject to review). In addition, the Fellows will be entitled to free rooms and meals in College, and to entertainment, research, and book allowances.

Application forms and further particulars are available from the Senior Tutor, New College, Oxford, OX1 3BN (tel. 01865 279596, fax 01865 279590, e-mail [email protected]). The closing date for receipt of applications is 18 February 2000.

The College is an equal opportunities employer.

Cambridge University Reporter, 12 January 2000 Copyright © 2000 The Chancellor, Masters and Scholars of the University of Cambridge.

Search NYU Steinhardt

Astor Fellows 2024

The astor international travel fellowship for new york city teachers, made possible through a generous gift from mrs. brooke astor, celebrates the accomplishments of full-time classroom teachers in the new york city public schools by awarding them a fully-sponsored, ten-day, educational fellowship with nyu steinhardt faculty., summer 2024 theme : finding joy engaging with the earth: biodiversity, fossils, and culturally sustaining pedagogy.

How can culturally-sustaining teaching practices be applied to the natural world? How can we build curricula that inspire students to find joy and wonder? The Summer 2024 Astor Fellows will travel to London, UK and England's Jurassic Coast to explore these questions. Participants will reflect on their teaching practices, develop their observational skills, and  consider how nature can be integrated into their work.

Following the Fellows' travels in Summer 2024, participants will present about their experiences at a Symposium event in late October 2024. This is an opportunity for the participants to reflect on their travels, share the impact of the program on their pedagogy and classroom practices, and promote innovation in teaching. The symposium is attended by the NYU community, teacher colleagues, and alumni of the program.

We seek to recruit a diverse cohort of Fellows teaching at all levels and across academic disciplines within the NYC public school system. Please note that Fellows do not receive NYU course credit or continuing education credit.

Location, Dates, & Faculty

The Summer 2024 edition of the Astor Fellows program will travel to London and the Jurassic Coast of England.

The group will depart New York City on July 31 and return on August 10. Fellows are asked to commit to attending 1-2 pre-travel events in Spring 2024 as well as a post-travel Symposium in late October 2024.

Catherine Milne , Professor of Science Education in the Department of Teaching and Learning

Tentative Visits and Activities

• 2-3 night trip to the Jurassic Coast; museum visits, walking the coast, and fossil hunting
• British Museum
• Natural History Museum
• Eastcheap & the Tower walking tour

Program Structure

NYU Steinhardt, through the generous support of the estate of Mrs. Brooke Astor, will cover the following participant expenses:

• Roundtrip, economy-class group airfare
• Single hotel accommodation during all program dates
• Ground transportation for official program activities
• Some daily meals
• Supplemental international health insurance

Participants are responsible for the following costs:

• Transportation to/from airports
• Obtaining or renewing a passport and any visa expenses
• Some meals and any personal incidental expenses
• Any independent activities, visits, or transportation outside of official program activities

Eligibility & Application Process

Who can participate:.

In order to be eligible to apply for this opportunity, you must:

• Be a current, fulltime classroom teacher in a New York City Public School
• Have completed at least three years of full-time teaching experience in NYC public schools as of the date of application
• Not be a previous recipient of the Astor Fellowship

Please note: School staff other than fulltime classroom teachers (i.e. substitute teachers, administrators, counselors, principals, etc.) are not eligible to apply.

Application Process:

Applicants must complete the Fellows Application form and request a recommendation from a colleague. Competitive applications should:

• Discuss how participating in the program will enhance your practice as a classroom teacher
• Demonstrate a critical reflection of your own cultural identity and its influence on classroom practice
• Show an interest in and commitment to issues of diversity, social justice, and antibias education; for example, through lessons or curricular choices

Recommendations should be from a fellow teacher or administrator who currently works (or has previously worked) with the applicant. Recommenders will be asked to confirm the applicant's years of work in NYC public school and their recommendation should speak to the applicant's background, current work, and service inside and outside of the classroom.

Application Links and Deadline:

Applications for the Summer 2024 edition of the program are now closed. The Summer 2025 program theme and location will be posted in the fall, and the application will open in early December 2024.

• Applicants must fill out the Astor Fellows Application Form
• Applicants should ask that their recommender complete the Astor Fellows Recommendation Form . Please do not request recommendations from multiple people. Only the first recommendation received for each applicant will be considered

All applications and recommendations must be submitted no later than 11:59 PM (EST) on January 31, 2024 . Top candidates will be invited to interview in February and the 2024 Fellows will be notified of their selection by the end of March.

For questions about the program or application process, please contact  [email protected] .

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U.S. Department of Treasury

Office of international affairs — junior fellowship.

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The U.S. Department of the Treasury’s Office of International Affairs (IA) seeks outstanding recent college graduates to help advance IA’s mission to support U.S. economic prosperity by strengthening the external environment for U.S. growth, preventing and mitigating global financial instability, and managing key global challenges.

About the Program: The Junior Fellowship program is a highly selective, fixed two-year program for new college graduates to work shaping international economic policy for the United States in Treasury’s Office of International Affairs. Throughout the Fellowship, junior fellows perform a variety of tasks that include developing policy proposals and conducting research and analysis on pressing international economic and financial developments . Fellows also support bilateral and multilateral meetings for senior Treasury officials engaging counterparts at the IMF, World Bank, G7, and G20 – to name a few. Junior fellows often participate in such meetings and may have opportunities to travel abroad. The program exposes fellows to multiple policy issues and provides opportunities to enhance their knowledge and skills including in writing, research, oral briefing, and economic policy and statecraft. Junior fellows will be placed in either a regional or functional office. Regional offices oversee Treasury’s engagement with counterpart finance ministries and treasuries across the world. Functional offices oversee Treasury’s engagement with international financial institutions and structure broader Treasury policy on issues ranging from climate change, to export credits, to foreign exchange. Junior fellows are usually hired at the GS-9 level and receive standard Treasury benefits.

Following the program, fellows have pursued a range of opportunities, including employment at Treasury and elsewhere in the U.S. government, work in the private sector, and graduate study (e.g., law, public policy, international relations, and finance and business).

Qualifications: Strong candidates will have recently received – or will soon receive – a bachelor’s degree with relevant coursework in economics, public policy, finance, international relations, regional studies, or related fields. IA is committed to attracting and developing a diverse and inclusive workforce. We recognize that different perspectives and experiences among our employees are workforce strengths and contribute to better policymaking. Please note that due to the structure of the program, preference is given to undergraduates.

The Astor Junior Research Fellowship in English

• Posted 2 years ago
• 30000 AED / Month

University of Oxford - New College

Description:

The College invites applications for this post, which is tenable for a fixed period of three years from 1 October 2023 based in New College, Oxford. The person appointed will be expected to undertake their own independent and original academic research in English. The Fellowship is open to those who have already acquired a first degree, and who at the time of appointment have completed at least two years’ study for a PhD/DPhil.

Candidates may not previously have held a Junior Research Fellowship or comparable appointment.

The Fellowship carries a stipend of (subject to review). The appointment will be pensionable under the USS scheme, details of which are available here: https://www.uss.co.uk/.

The appointment will be for a fixed period of three years without possibility of renewal.

Further particulars are available here:

https://isw.changeworknow.co.uk/new_college_oxford/vms/e/careers/search/new  or available from the Academic Registrar ( [email protected] ).

All enquiries should be in the first instance addressed to the Academic Registrar at [email protected] New College is committed to increasing diversity across all parts of the institution and to welcoming under-represented groups. It aims to provide an inclusive environment which promotes equality and maintains a working, learning and social context in which the rights and dignity of all its members are respected to assist them in reaching their full potential. The College is an equal opportunities employer and adheres to the University’s Equal Opportunities Policy and Code of Practice, a copy of which is available on request.

To apply for this job please visit www.jobs.ac.uk .

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Lectureship/Senior Lectureship in Structural Dynamics/Solid Mechanics – Grade 8-9

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Autumn 2024 Academic Year Part-Time Research Fellowship Opportunity: "Environmental interventions to improve maternal and child health in rural Bangladesh"

The  Stanford King Center on Global Development’s   Academic Year Part-Time Research Fellowship Program  connects King Center faculty affiliates and affiliated researchers with undergraduate students committed to providing approximately 10 hours per week (no more) of research support during autumn, winter, and spring quarters. 

Students have the opportunity to engage in world-class research that has real-world impact. Undergraduate student research fellows are paid* $19/hour, for 8-10 hours per week of research per quarter (max. $1,900/quarter).

* Awardees must submit an I-9 form to receive payment.

Students must be enrolled full-time to participate and must be able to commit to research 8-10 hours per week (likely excluding them from any other job). Students who cannot accept pay may be allowed to receive academic credit for this research. Students will be asked in the applications if they are eligible for Federal Work Study (FWS) .

Research Project Description :

We are currently conducting a series of studies in rural Bangladesh to investigate innovative environmental interventions to combat infectious diseases, antimicrobial resistance (AMR), and the health impacts of climate change. At the core of our current research is a randomized controlled trial investigating the impact of concrete flooring on child enteric infections in rural Bangladeshi households. This study seeks to provide rigorous evidence on whether a seemingly simple environmental modification – replacing soil floors with concrete – can significantly reduce the prevalence of soil-transmitted helminths and diarrheal diseases among young children. Beyond measuring direct health outcomes, we're also exploring how this intervention might improve maternal quality of life and reduce household stress. We're also investigating the complex issue of AMR in these communities, where factors such as dense populations, frequent human-animal contact, and inadequate sanitation create ideal conditions for the emergence and spread of resistant bacteria. The goal of this research is to identify novel interventions that address the intricate web of social and environmental factors contributing to AMR, with a focus on solutions that can be implemented at the household level. Simultaneously, we're confronting the looming threat of climate change on health in Bangladesh – a country uniquely vulnerable to its impacts. Our research in the Chauhali sub-district, an area prone to extreme heat, severe flooding, and river erosion, positions us to study and develop adaptive strategies for some of the world's most climate-vulnerable populations. We're particularly interested in interventions that can promote resilience of mothers and young children in the face of increasing climate-related health risks. The research assistant will have the opportunity to contribute to research that has the potential to inform public health policy and improve lives in some of the world's most vulnerable communities. This role offers a unique chance to engage with complex global health issues at the intersection of environmental health, infectious diseases, and climate change adaptation.

Research Mentor : Jade Benjamin-Chung, SoM - Epidemiology and Population Health    

Stanford undergraduate students in good academic standing and enrolled full-time are eligible to apply.  Co-term students must have undergraduate student status - if they are in GR billing status (after 12 quarters) they will be ineligible. 

All majors are welcome! 

Student Responsibilities: 

- Create field report scripts in R for tracking enrollment,data collection, and intervention installation  - Create detailed maps of the study site to support field activities  - Process environmental spatial raster data for the study site  - Support quality control checks for data collection  - Support protocol and SOP development  - Conduct literature reviews and write literature summaries

Students qualifications:

• Experience in R and Excel
• Experience with Github desired but optional     

Time Commitment:    

The time commitment is defined as no more than 10 hours per week (equivalent to a 3-unit course) during autumn quarter with possible continuation in winter and spring quarters.  

These hours may be an average and be flexible across the 10-week quarter to accommodate your academic obligations, such as midterms or finals week.

Along with the application, applicants are asked to submit:

• a cover letter
• resume or CV
• unofficial Stanford transcript (first quarter frosh do not need to submit transcripts for autumn quarter applications)

Research Mentor Questions for Applicants:

• Do you have any experience in a research lab? If so, what activities did you do?
• Have you taken any chemistry courses with labs? If so, did you enjoy them?
• Please describe your experience conducting literature reviews.
• Please describe your experience coding in R. Which packages do you use most frequently? How comfortable are you with data processing and data visualization? 
• Please describe your experience using Excel.

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REVISED Junior Research Fellowships (JRF through CSIR-UGC NET) guidelines w.e.f. from 1st March 2023

a) The EMR Division under HRD Group of Council of Scientific & Industrial Research (CSIR) provide CSIR Research Fellowships and Associateships to bright young men and women for training in methods of research under the expert guidance of faculty members/scientists working in University Departments/Institutes of National Importance/National Laboratories and Institutes of CSIR in various fields of Science & Technology and Medical Sciences. List of CSIR Laboratories is at Annexture-I .

b) The CSIR Fellowships/Associateships are tenable in Universities/IITs/Post- Graduate Colleges/ Government Research Establishments including those of CSIR, R&D establishments of recognized public or private sector, industrial firms and other recognized institutions.

c) The CSIR Fellowships/Associateships are tenable in India. Only bonafide Indian citizens, residing in India are eligible for the award of research Fellowship/Associateships. The programme is aimed at National Human Resource Development for S&T.

d)  The award of CSIR Fellowship/Associateships is for fixed tenure and does not imply any assurance or guarantee for subsequent employment by CSIR to the beneficiary. The authority to award/ terminate vests with CSIR. The awardee shall not lay claim to permanent absorption in CSIR, after the expiry of Fellowship/ Associateship.

2. SUBJECT OF RESEARCH

Preference is given to a subject/topic of research relevant to the  research programme of CSIR laboratories and nationally important S&T areas.

3. ELIGIBILITY FOR CSIR JUNIOR RESEARCH FELLOWSHIP (JRF)

A large number of JRFs are awarded each year by CSIR to candidates holding BS-4 years program/BE/B.Tech/B. Pharma/MBBS/Integrated BS-MS/M.Sc. or Equivalent degree/BSc (Hons) or equivalent degree holders or students enrolled in integrated MS- Ph.D program with at least 55% marks for General & OBC (50% for SC/ST candidates, Divyangjan (PWD)) after qualifying the National Eligibility Test ( NET) conducted by CSIR normally twice a year in June and December.  

Candidates with bachelor’s degree, whether Science, engineering or any other discipline, will be eligible for fellowship only after getting registered/enrolled for Ph.D/integrated Ph.D. programme within the validity period of JRF-NET certificate which is two years from the effective date of fellowship as mentioned in the JRF- NET certificate.

Candidate enrolled for M.Sc. or having completed 10+2+3 years of the above qualifying examination are also eligible to apply in the above subject under the Result Awaited (RA).

4. APPLICATION PROCEDURE

On-line applications for JRF-NET are invited normally twice a year on all India basis. The information with respect to inviting applications is also made available on HRDG website :  www.csirhrdg.res.in .

5. AGE LIMIT

The upper age limit for applying for the award of JRF shall be 28 years, which is relaxed up to 5 years in the case of candidates belonging to Schedule Castes/Schedule Tribes/Divyangjan (PWD) and female applicants whereas 3 years in the case of OBCs (Non-creamy layer candidates).

6. SELECTION PROCEDURE

The Selection for award of JRF shall be made on the basis of a competitive written test called the National Eligibility Test (NET), conducted by CSIR at national level normally twice a year in the following areas (1) Chemical Sciences (2) Earth, Atmosphere, Ocean and Planetary Sciences (3) Life Sciences, (4) Mathematical Sciences, and (5) Physical Sciences. From June 2011, CSIR has introduced a Single MCQ (Multiple Choice Question) Paper based test comprising of three parts. Part-A shall be common to all subjects comprising question on General Science and Research Aptitude. Part-B shall contain subject-related conventional MCQ and Part-C shall contain higher value questions that may test the candidate’s knowledge of scientific concepts and/or application of the scientific concepts. Negative marking for wrong answers shall be done.

The Fellowship is awarded on receipt of necessary details of the qualifying degree examination, proposed place of research work, research topic, the name of supervisor and the concurrence of the Institution to provide all the necessary facilities. The validity of the JRF-NET certificate is two years from the effective date of fellowship as mentioned in the JRF-NET certificate and will not be extendable.

Application format of the undertaking by a Research Fellows/Associates on acceptance of the Award of Research Fellowship/Associateship is at Annexture-II .

7. PHD REGISTRATION AND TERMINATION OF FELLOWSHIP

  (a)   JRF-NET qualified Graduate Candidates  

Candidates with Bachelor’s degree, whether Science, Engineering or any other discipline, will be eligible for fellowship only after getting registered/enrolled for Ph.D/Integrated Ph.D. programme (Ph.D registration certificate is at Annexture-III  within the validity period of two years of JRF-NET Certificate from the effective date of fellowship as mentioned in the JRF-NET certificate.

  (b)  JRF-NET qualified Postgraduate Candidates  

CSIR Junior Research Fellows should register for PhD within a period of two year ( PhD registration certificate is at Annexure-III ) from the date of joining their fellowship, failing which they will not be upgraded to SRF on completion of two years. However, CSIR may consider giving extension for an additional period of one year as JRF-NET or the fellowship can be terminated based on the recommendations of Three Member Assessment Committee. The Committee may consist of the Guide, Head of the Department and External Member from outside the University/ Institution who is an expert in the relevant field, not below the rank of Professor/ Associate Professor. As far as possible the External Member should be the chairman of three members Committee. Further, where the guide happens to be the Head of the Department, the Dean, Faculty of Science or any senior member of the Department may be associated as the third member of the Committee. If prior to completion of third year, the fellow is not registered for PhD, the JRF-NET fellowship will be terminated on completion of third year.

(c) The Fellowship shall stand terminated from the date of PhD viva-voce or from  the date the Fellow resigns and his/her resignation has been accepted by CSIR or on completion of tenure. The fellowship may also be terminated if the institution where it is tenable refuses to provide facilities to the fellow on disciplinary grounds and so informs CSIR.

8. STIPEND & TENURE

(a) The stipend of a JRF selected through CSIR-UGC National Eligibility Test (NET) will be Rs 31,000/ p.m for the first two years. In addition, annual contingent grant of Rs. 20,000/- per fellow will also  be provided to the fellow .The guidelines for utilization of contingent grant are given in ( Annexure-IV ).

(b.I) If the Fellow is registered in PhD within the stipulated period of 2 years and  Progress is satisfactory:

   If the fellow is registered for PhD within the stipulated period of two years, then on completion of two years as JRF, he/she will be required to submit the work/progress report within six months for upgradation to SRF (NET). On the basis      of assessment of Fellows’ research progress/ achievements through interview by an Expert Committee consisting of the Guide, Head of the Department and External Member from outside the University/Institution who is an expert in the relevant field, not below the rank of Professor/Associate Professor and on the recommendation of the said expert committee, the JRF will be upgraded to the position of SRF on the monthly stipend of Rs. 35,000/- for the 3rd and subsequent years. As far as possible the External Member should be the chairman of three members Committee. Further, where the guide happens to be the Head of the Department, the Dean, Faculty of Science or any senior member of the Department may be associated as the third member of the Committee ( Annexure-V ) and ( Annexure-VI ).

  (b.II) If the Fellow is registered in PhD within the stipulated period of 2 years and Progress is not satisfactory:

If the fellow is registered for PhD within the stipulated period of two years and submits his/her work report within six months of completion of the sanctioned tenure but his/her work/progress report is not found satisfactory by the Three Member Assessment Committee, the Committee may recommend him/her to continue as JRF for third year on the monthly stipend of Rs. 31,000/- or may recommend the termination of fellowship. If the fellow continues as JRF for third year, the progress of research work of JRF will be assessed again by duly constituted three-member assessment committee at the end of third year for upgradation. If the work of JRF is still not found satisfactory for upgradation by the Committee, then the fellowship will be terminated.

  (b.III)  Fellows and host institutions are strongly advised to complete the Assessment and  submit the report timely to avoid delays. Nonetheless, to minimize the hardship to students, fellows are given six months from the time of completion of the second year of JRF to submit the Assessment Evaluation Report. During this period (six months) he/she shall be getting fellowship of JRF, subject to submission of online attendance certification by Host Institute on the portal as usual procedure for fellowship. Once the Assessment committee recommends for SRF upgradation they may receive SRF fellowship and arrears if any. However, it may be noted that      in the event of the non receipt of Assessment Evaluation Report within six months period upon completion of two years of JRF fellowship from the host institute, the stipend of fellow shall automatically be stopped and resumed only when the requirements are fulfilled. However, in the case of non-receipt of the three-member assessment committee report even after completion of Two years and six months, the tenure of the JRF may be continued further for six months on the condition that an undertaking by the concerned institution assuring that they would conduct the three-member assessment committee and submit the report in the next six months. In case assessment report is not received till the end of the third year, the fellowship shall stand terminated without further notice. The decision of CSIR in  this regard shall be final.

  (b.IV) If the Fellow is not registered in PhD within the stipulated period of 2 years:

In the event of non-registration for PhD by the fellow within the stipulated period of two years, he/she will not be eligible for upgradation to SRF but the fellow can be recommended to continue as JRF for the third year by the assessment committee. The progress of research work of JRF and PhD registration status will be assessed again by duly constituted three-member assessment committee as described above at the end of third year for upgradation. If the fellow is still not registered for PhD and/or work of JRF is not found satisfactory for continuation into third year as JRF, the fellowship will be terminated.

(c)  Extension of tenure for the fourth and fifth year extension of SRF (NET) will be on the basis of the progress report ( Annexure-VI ) and recommendation of the guide.

The annual progress report for continuation from third to fourth and from fourth to fifth year may be maintained by the Host Institute. After confirmation of the submission of the requisite reports on the portal by the Maker/Checker, HRDG shall process the fellowship for the fourth and the fifth year.

The fellows and host institutions are strongly advised to submit the reports in advance such that no delays in fellowships are encountered. However, the fellows and host institutions will be given an additional six months from the last date of the third and fourth year respectively for submission of the requisite report. During this six months fellowship may continue pending the submission of the requisite reports. After six months, if the confirmation of receipt of the report is not received on the portal, the fellowship to all such fellows will not be released.

The confirmation of the receipt of the report both for continuation to fourth and fifth year on the portal by the Maker/Checker shall be full and final and the Host Institute is fully accountable for correctness of the details. In case of any discrepancy/incorrect information submission by the Host Institutions leading to  any undue payment etc., the entire responsibility shall be with the Host Institutions to refund the related amount, with interest, to CSIR.

Non-compliance of CSIR norms for submission of annual progress report along with other requisite documents within six months after completion of yearly tenure may result in termination of fellowship/associateship .

(d) The total tenure as JRF plus SRF(NET) will not exceed five years. This will include the tenure of Fellowship awarded by UGC/DST/DBT/ICMR/ICAR etc. or any other funding agency/Institution. The order for continuation at the same rate of stipend as SRF(NET), continuation at the same rate of stipend as JRF or otherwise will be issued by the EMR Division of HRDG, CSIR. Extension may also not be granted if the fellow does not acknowledge the support of CSIR in his/her research publication(s).

(e)  A Research Fellow who joins on the first day of the month, his/her tenure will be completed on the last day of the previous month. In other cases the, tenure will be completed on the last day of the same month of joining the Fellowship. 

   9. AWARD OF FELLOWSHIP AND RELEASE OF GRANTS

(a)  The Fellowship will be awarded to the selected applicants by a formal letter giving details of the grant and the conditions governing it, under intimation to the University/Institution, which forwarded their applications. The tenability of JRF-NET certificate is two years from the effective date of fellowship as mentioned in the JRFNET certificate and a NET qualified JRF-NET should avail the fellowship within two years i.e. within the validity period of JRF-NET certificate. The fellowship grant money is payable on monthly basis whereas the contingency will be reimbursed annually directly to the research fellow based on submission of the online claim.

The first payment (monthly stipend) will be made after the issue of formal award letter by EMR through the portal. The Maker/Checker/Authorized Officer at the Host Institute shall obtain the Attendance Certificate of the respective fellows of their institutions and based on the same shall certify the attendance on the portal and uploading of attendance certificate is discontinued henceforth. The attendance details submitted by the Maker/Checker on the CSIR portal shall be final and the bill shall be generated and processed by HRDG accordingly. The submission of the attendance details on the portal by the Maker/Checker shall be full and final and the host institute is fully accountable for correctness of the details. In case of any discrepancy/incorrect information submission by Host Institutions leading to any undue payment etc., the entire responsibility shall be with the Host Institutions to refund the related amount with interest, to CSIR. The Host Institutes shall maintain the requisite records of attendance submitted through CSIR portal at their level.

(b)  The contingency grant will be reimbursed to the fellows subject to submission of the claim online on the CSIR portal through Maker/Checker on annual basis. The Fellows are required to submit the original bills to Host Institute and Host Institute shall verify the expenditure and ensure that all expenditure should be as per CSIR guidelines. The accounts should be maintained by the grantee institution for the research fellow on ledger type system as per Annexure-VII . The host Institute shall be responsible for compliance of CSIR-HRDG guidelines issued on contingency grant from time to time. CSIR reserve the right to inspect or call for the Bills/Vouchers as and when required. 

   10. CONTINGENT GRANT

An annual contingent grant of Rs.20,000/- per fellow is provided to the  Research Fellow on reimbursement basis . For less than one year, the contingent grant will be admissible on pro-rata basis. The grant may be utilized in the interest of research work. The maximum amount of contingency admissible to a fellow shall be restricted to maximum Rs. 20000/- in a year. Further, request (claim) for reimbursement of contingency grant of the previous financial year(s) will not be entertained. The guidelines for utilization of the contingent grant are given in Annexure-IV  and reimbursement claim form at Annexure-VIII .

   11. PROGRESS REPORT

The preparation of annual progress report on the research work done shall be essential part of the Fellow’s work. Each Research Fellow shall submit his/her annual research report in the prescribed proforma ( Annexure-VI ) within a period of six months after completion of one-year tenure to its Host Institute. It is essential to give up to-date and full information against all the columns of Annexure-VI . The results should be presented quantitatively in Tables/Figures and discussed in terms of the objectives and conclusions drawn should also be given. Fragmentary reports shall not be entertained. The progress report should be always accompanied by copies of published papers, re- prints and pre-prints of papers accepted for publication, manuscripts of papers communicated for publication duly acknowledging financial assistance of CSIR. The publishing of research papers is only desirable and not mandatory. Fellows should be discouraged from publishing in predatory journals. Noncompliance of CSIR norms for submission of annual progress report along with other requisite documents within six months after completion of yearly tenure may result in termination of fellowship/associateship. The Host Institutes shall maintain at their level the requisite records of Report (Annual Progress Report for continuation to fourth year and Annual Progress Report for continuation to fifth year) . CSIR reserve the right to inspect or call for the reports as and when required.

   12. PUBLICATION/PATENT

(a)   Publication:   The results of Fellow's research work may be published in standard refereed journals at the discretion of the Guide. IT SHOULD BE ENSURED THAT THE ASSISTANCE PROVIDED BY CSIR is ALWAYS ACKNOWLEDGED IN ALL SUCH PUBLICATIONS. One copy of the published research papers may be submitted on the portal.

(b)   Patent:  The commercial exploitation of the results and ownership of patent rights pertaining to investigations concerning the intellectual work of the CSIR research fellows/associates will be as follows:

(i) Public funded educational/research institution, to which a fellow is associated, may seek patent right at their own cost and/or commercial exploitation of the results of the investigation concerning the Intellectual work of the fellow and all rights would vest exclusively with the Institution concerned. All matters concerning ownership of IP and its licensing/exploitation would be governed by the IP policy of the concerned institutions.

(ii) In case an institution, to which a fellow is associated, is not in a position to seek patent rights and/or commercial exploitation of      the results of the investigation concerning the intellectual work of the fellow, CSIR at its own cost may seek the patent rights and/or commercial exploitation of the results of the intellectual work of the fellow and all rights would vest exclusively with CSIR. (Issued vide CSIR OM NO. F.No. 6/IPR/2011/EMR-I dated 29th July 2011)

   13. OBLIGATIONS OF RESEARCH FELLOW

a)  He/She has to be a full time researcher and submit himself/herself to the disciplinary regulations of the University/ Institute/ Laboratory where he/she is working. Regular attendance of the fellow may be ensured by the department by keeping an attendance register.

b)  In case a fellow decides to appear for competitive examination, he/she would invariably seek permission from the guide and this information may be kept with the Host Institute.

c) The Research Fellow is not to take any assignment other than related to his/her approved research programme, paid or unpaid. However, if required, the fellow may assist the host institute in its academic work/other activities, as per guidelines of its PhD programme, provided such assignments should not hamper the progress of research work of the fellow.

d) Once a Research Fellow accepts the Fellowship and joins, it is incumbent on him/her to continue the research for the normal tenure of the fellowship or for such lesser duration in which the original objectives of the research problem have been achieved.

e)  No Fellow shall discontinue his/her Fellowship without prior approval of CSIR. In case he/she wishes to discontinue the fellowship prior to completion of the tenure on attainment of original objectives of research, he/she must submit the resignation to CSIR through the Guide one month in advance, indicating specific reasons for not continuing the Fellowship. The Fellowship shall cease from the date stipulated in the CSIR letter approving the resignation.

f) The research Fellow must send a detailed consolidated report of the research work done during the entire period of Fellowship on completion of the tenure/resignation of the Fellowship through the Guide to CSIR, in the prescribed proforma ( Annexure-IX ), within one month.

g)  During the tenure of the Fellowship, the Fellow shall correspond with CSIR only through the Guide with the approval of the Head of the Institution.

h)  The Research Fellow shall keep CSIR informed about his/her getting the higher degree, submission of thesis for Ph.D., MD, MDS, MS, MPhil, ME etc. and submission/acceptance/publication of any research paper arising out of the research work done during the tenure of the fellowship. He/She must acknowledge the support of CSIR in the publication(s). One copy each of all the research papers published must be submitted to the host institute and uploaded on CSIR portal at each stage of publication/ manuscript/reprint.  

   14. TEMPORARY TEACHING & RESEARCH JOB

A Research Fellow on the recommendation of Guide, and provided that his/her University/ Institute has no objection, may be permitted by CSIR to take up temporary paid lectureship/research job in a recognized R&D Institution/University, College/Institute of repute/Recognized R & D Institution/ PDF studies in India & abroad for a period not exceeding one year during the entire tenure of the Fellowship (JRF & SRF together). The Research Fellow will not be entitled to any extension of the Fellowship for such periods. The Fellow will not be entitled to stipend and contingency grant during such leave. Such leave period will be counted in the tenure. Such leave can be taken only after joining and working as Research Scholar at least for one year. Fellow has to report for duty at the same place from where he proceeded on leave.

    15. LEAVE

a) Leave with stipend not exceeding 30 days for each completed year of tenure may be allowed by the Guide after the request has been communicated to CSIR. The leave will be treated as part of the Fellow’s tenure. The leave due can be carried over to the next year, however not more than 90 days can be accumulated at any time during the tenure. Of this not more than 30 days can be availed in a calendar year with stipend and beyond that any leave will be treated as “Leave Without Stipend”. During the first year of Fellowship or any uncompleted year, leave may be granted on pro-rata basis. Sanction of leave without stipend may be considered by CSIR under special circumstances. In case a Fellow proceeds on leave before expiry of Fellowship tenure, he/she must join back before the expiry of tenure; failing which the tenure will be deemed to have terminated with effect from the date he/she proceeded on leave. The fact of joining back from leave should be communicated to CSIR immediately. As the CSIR releases the grant in advance, therefore, the amount on account of “Leave Without Stipend” has to be refunded to CSIR at the end of a financial year or adjusted against the fresh claim, if any.

b) The Guide can grant leave to a Fellow in his/her charge with the concurrence of the Head of the Institution/Department if the leave is due as prescribed in para 15(a) above. If leave is not due, such cases will be decided by CSIR only. The Fellow should not be allowed to proceed on leave to visit abroad for attending conferences/seminars etc. without prior approval of the CSIR well in advance. The entire duration of such foreign visits if funded by any national/international agency, whether partially or fully, would be treated as leave without stipend.

c) Women Fellows with less than two surviving children are entitled to full stipend plus HRA, during the period of absence180 days on grounds of maternity. Such leave shall be sanctioned by the Guide under  intimation to CSIR. The Fellowship amount for leave period will be paid after the fellow resumes duty and submits a medical certificate in support of actual confinement. It is expected that the Fellow will make up for the research work during the remaining tenure.

d) Male Fellows of CSIR with less than two surviving children are entitled for 15 days paternity leave during confinement of his wife on submission of relevant documentary proof.

   16. TRANSFER OF FELLOWSHIP

The fellow should carefully choose the host institution, guide/supervisor, availability of necessary infrastructural and other research facilities etc. to carry out his/her research before joining. Request for transfer of fellowship will not be entertained except on compelling circumstances for which the fellow & his/her guide should submit proper justification. The No Objection Certificate should be produced by the Fellow/ Associate from supervisor and Head of Department of University/Institute from where transfer is sought and consent of the Guide/Host Institute where Fellowships is sought to be transferred by giving reasons of transfer. No fellow will be allowed to join another institute without seeking prior approval from CSIR for "transfer of fellowship" and if he/she joins elsewhere without approval of CSIR, his/her fellowship will be terminated. Fellowship/Associateship will stand terminated from the date of resignation. Further, no transfers will be allowed in the last six months of the tenure of fellowships & also after submission of Ph.D. thesis.

    17. TERMINATION OF FELLOWSHIP

(a) Junior Research Fellowship /Senior Research Fellowship will be terminated from the date of viva-voce of PhD or on completion of fellowship tenure, whichever is earlier. The fellowship shall also stand terminated from the date the Fellow resigns and his/her resignation has been accepted by CSIR. The Fellowship may be terminated by the CSIR on the recommendation of the Supervisor and Head  of the Department/Institution. The fellowship may also be terminated if the institution where it refuses to continue to provide facilities to the fellow on disciplinary grounds and so informs CSIR.

(b)  If a fellow leaves without permission, stipend due at any time shall not be paid to him/her. The Universities/ Host Institutions must not raise any claim of Fellowship in r/o those fellows who resign or whose termination of fellowship is under consideration at any stage. The entire onus of raising such claims lie upon the Host Institutes and any extra payment made to the fellow due to such undue claims received from the Host institutes are recoverable in full along with interest from the Host institute.

  (c)  The unspent balance of grant lying with the Institution at any time due to termination/resignation/transfer of fellowship of a Fellow/Leave sanctioned without stipend/interest earned on grants released by CSIR must be refunded to CSIR immediately by online payment mode i.e. NEFT/RTGS.

(d)  Research Fellows must settle their fellowship claims within one year of leaving the Fellowship. No claim will be admitted by CSIR after the time admissible under the rules.

18. ACCOMMODATION / HRA

All Research Fellows may be allowed hostel accommodation wherever available and those residing in hostel provided by University/Institute will not be eligible for HRA. Reimbursement of hostel fee is not permissible. Where this is not possible, house rent allowance will be allowed as per the rules of the host institutions. In no case it should exceed the rates payable to Central Government Employees in that area. The basis for calculating HRA will be the actual stipend of the Research Fellow.

   19. MEDICAL BENEFITS

(a)  No separate/fixed medical assistance should be provided. However, the fellow may avail of the medical facilities available in the institution/university/college, without any financial liability on CSIR. This will be limited to the fellow only and not to his/her family members/dependents.

(b)  The host institute may get the fellows/associates medically examined at the time of joining or thereafter.

   20. OTHER TERMS AND CONDITIONS

(a)  CSIR may send whenever considered necessary its officers for reviewing the work of the fellows and Associates, inspection of accounts, attendance, etc, in Universities/Institutes where the Research Fellows/Associates are placed.

(b)  Any kind of paid or honorary, part-or-full-time employment or private practice even in honorary capacity is not permissible during the tenure of Fellowship/ Associateship.  

(c)  The stipend of research fellow/associate is exempt from the payment of income tax under10(16) of IT Act.

(d)  These terms and conditions supersede all previous instructions issued in regard to JRF/SRF/RA. However, any relaxation would require approval of DG, CSIR. In all matters decision taken by CSIR shall be final.