arXiv subjects

Diptarka Hait

Publications and source records attributed to Diptarka Hait.

At least 37 records · Page 2Linked to original sources

arXiv2021

Exploring Spin Symmetry-Breaking Effects for Static Field Ionization of Atoms: Is There an Analog to the Coulson-Fischer Point in Bond Dissociation?

Löwdin's symmetry dilemma is an ubiquitous issue in approximate quantum chemistry. In the context of Hartree-Fock (HF) theory, the use of Slater determinants with some imposed constraints to preserve symmetries of the exact problem may lead to physically unreasonable potential energy surfaces. On the other hand, lifting these constraints leads to the so-called broken symmetry solutions that usually provide better energetics, at the cost of losing information about good quantum numbers that describe the state of the system. This behavior has been previously extensively studied in the context of bond dissociation. This paper studies the behavior of different classes of Hartree-Fock spin polarized solutions (restricted, unrestricted, generalized) in the context of ionization by strong static electric fields. We find that, for simple two-electron systems, UHF is able to provide a qualitatively good description of states involved during the ionization process (neutral, singly-ionized and doubly ionized states), whereas RHF fails to describe the singly ionized state. For more complex systems, even though UHF is able to capture some of the expected characteristics of the ionized states, it is constrained to a single $M_s$ (diabatic) manifold in the energy surface as a function of field intensity. In this case a better qualitative picture can be painted by GHF as it is able to explore different spin manifolds and follow the lowest solution due to lack of collinearity constraints on the spin quantization axis.

physics.chem-ph↗

arXiv2021

Real time evolution for ultracompact Hamiltonian eigenstates on quantum hardware

In this work we present a detailed analysis of variational quantum phase estimation (VQPE), a method based on real-time evolution for ground and excited state estimation on near-term hardware. We derive the theoretical ground on which the approach stands, and demonstrate that it provides one of the most compact variational expansions to date for solving strongly correlated Hamiltonians. At the center of VQPE lies a set of equations, with a simple geometrical interpretation, which provides conditions for the time evolution grid in order to decouple eigenstates out of the set of time evolved expansion states, and connects the method to the classical filter diagonalization algorithm. Further, we introduce what we call the unitary formulation of VQPE, in which the number of matrix elements that need to be measured scales linearly with the number of expansion states, and we provide an analysis of the effects of noise which substantially improves previous considerations. The unitary formulation allows for a direct comparison to iterative phase estimation. Our results mark VQPE as both a natural and highly efficient quantum algorithm for ground and excited state calculations of general many-body systems. We demonstrate a hardware implementation of VQPE for the transverse field Ising model. Further, we illustrate its power on a paradigmatic example of strong correlation (Cr2 in the SVP basis set), and show that it is possible to reach chemical accuracy with as few as ~50 timesteps.

quant-ph↗

arXiv2021

Orbital Optimized Density Functional Theory for Electronic Excited States

Density functional theory (DFT) based modeling of electronic excited states is of importance for investigation of the photophysical/photochemical properties and spectroscopic characterization of large systems. The widely used linear response time-dependent DFT (TDDFT) approach is however not effective at modeling many types of excited states, including (but not limited to) charge-transfer states, doubly excited states and core-level excitations. In this perspective, we discuss state-specific orbital optimized (OO) DFT approaches as an alterative to TDDFT for electronic excited states. We motivate the use of OO-DFT methods and discuss reasons behind their relatively restricted historical usage (vs TDDFT). We subsequently highlight modern developments that address these factors and allow efficient and reliable OO-DFT computations. Several successful applications of OO-DFT for challenging electronic excitations are also presented, indicating their practical efficacy. OO-DFT approaches are thus increasingly becoming a useful route for computing excited states of large chemical systems. We conclude by discussing the limitations and challenges still facing OO-DFT methods, as well as some potential avenues for addressing them.

physics.chem-ph↗

arXiv2021

Too big, too small or just right? A benchmark assessment of density functional theory for predicting the spatial extent of the electron density of small chemical systems

Multipole moments are the first order responses of the energy to spatial derivatives of the electric field strength. The quality of density functional theory (DFT) prediction of molecular multipole moments thus characterizes errors in modeling the electron density itself, as well as the performance in describing molecules interacting with external electric fields. However, only the lowest non-zero moment is translationally invariant, making the higher order moments origin-dependent. Therefore, instead of using the $3 \times 3$ quadrupole moment matrix, we utilize the translationally invariant $3 \times 3$ matrix of second cumulants (or spatial variances) of the electron density as the quantity of interest (denoted by $\mathcal{K}$). The principal components of ${\mathcal{K}}$ are the square of the spatial extent of the electron density along each axis. A benchmark dataset of the prinicpal components of ${\mathcal{K}}$ for 100 small molecules at the coupled cluster singles and doubles with perturbative triples (CCSD(T)) at the complete basis set (CBS) limit is developed, resulting in 213 independent ${\mathcal{K}}$ components. The performance of 47 popular and recent density functionals is assessed against this Var213 dataset. Several functionals, especially double hybrids, and also SCAN and SCAN0 yield reliable second cumulants, although some modern, empirically parameterized functionals yield more disappointing performance. The H and Be atoms in particular are challenging for nearly all methods, indicating that future functional development could benefit from inclusion of their density information in training or testing protocols.

physics.chem-ph↗

arXiv2021

Third order Møller-Plesset theory made more useful? The role of density functional theory orbitals

The practical utility of Møller-Plesset (MP) perturbation theory is severely constrained by the use of Hartree-Fock (HF) orbitals. It has recently been shown that use of regularized orbital-optimized MP2 orbitals and scaling of MP3 energy could lead to a significant reduction in MP3 error (J. Phys. Chem. Lett. 10, 4170, 2019). In this work we examine whether density functional theory (DFT) optimized orbitals can be similarly employed to improve the performance of MP theory at both the MP2 and MP3 levels. We find that use of DFT orbitals leads to significantly improved performance for prediction of thermochemistry, barrier heights, non-covalent interactions, and dipole moments relative to standard HF based MP theory. Indeed MP3 (with or without scaling) with DFT orbitals is found to surpass the accuracy of coupled cluster singles and doubles (CCSD) for several datasets. We also found that the results are not particularly functional sensitive in most cases, (although range-separated hybrid functionals with low delocalization error perform the best). MP3 based on DFT orbitals thus appears to be an efficient, non-iterative $O(N^6)$ scaling wave function approach for single-reference electronic structure computations. Scaled MP2 with DFT orbitals is also found to be quite accurate in many cases, although modern double hybrid functionals are likely to be considerably more accurate.

physics.chem-ph↗

arXiv2020

The Ground State Electronic Energy of Benzene

We report on the findings of a blind challenge devoted to determining the frozen-core, full configuration interaction (FCI) ground state energy of the benzene molecule in a standard correlation-consistent basis set of double-$ζ$ quality. As a broad international endeavour, our suite of wave function-based correlation methods collectively represents a diverse view of the high-accuracy repertoire offered by modern electronic structure theory. In our assessment, the evaluated high-level methods are all found to qualitatively agree on a final correlation energy, with most methods yielding an estimate of the FCI value around $-863$ m$E_{\text{H}}$. However, we find the root-mean-square deviation of the energies from the studied methods to be considerable (1.3 m$E_{\text{H}}$), which in light of the acclaimed performance of each of the methods for smaller molecular systems clearly displays the challenges faced in extending reliable, near-exact correlation methods to larger systems. While the discrepancies exposed by our study thus emphasize the fact that the current state-of-the-art approaches leave room for improvement, we still expect the present assessment to provide a valuable community resource for benchmark and calibration purposes going forward.

physics.chem-ph↗

arXiv2020

Accurate prediction of core-level spectra of radicals at density functional theory cost via square gradient minimization and recoupling of mixed configurations

State-specific orbital optimized approaches are more accurate at predicting core-level spectra than traditional linear-response protocols, but their utility had been restricted on account of the risk of `variational collapse' down to the ground state. We employ the recently developed square gradient minimization (SGM, J. Chem. Theory Comput. 16, 1699-1710, 2020) algorithm to reliably avoid variational collapse and study the effectiveness of orbital optimized density functional theory (DFT) at predicting second period element 1s core-level spectra of open-shell systems. Several density functionals (including SCAN, B3LYP and $ω$B97X-D3) are found to predict excitation energies from the core to singly occupied levels to high accuracy ($\le 0.3$ eV RMS error), against available experimental data. Higher excited states are however more challenging by virtue of being intrinsically multiconfigurational. We thus present a CI inspired route to self-consistently recouple single determinant mixed configurations obtained from DFT, in order to obtain approximate doublet states. This recoupling scheme is used to predict the C K-edge spectra of the allyl radical, the O K-edge spectra of CO$^+$ and the N K-edge of NO$_2$ to high accuracy relative to experiment, indicating substantial promise in using this approach for computation of core-level spectra for doublet species (vs more traditional time dependent DFT, EOM-CCSD or using unrecoupled mixed configurations). We also present general guidelines for computing core-excited states from orbital optimized DFT.

physics.chem-ph↗

arXiv2020

CASSCF with Extremely Large Active Spaces using the Adaptive Sampling Configuration Interaction Method

The complete active space self-consistent field (CASSCF) method is the principal approach employed for studying strongly correlated systems. However, exact CASSCF can only be performed on small active spaces of ~20 electrons in ~20 orbitals due to exponential growth in the computational cost. We show that employing the Adaptive Sampling Configuration Interaction (ASCI) method as an approximate Full CI solver in the active space allows CASSCF-like calculations within chemical accuracy (<1 kcal/mol for relative energies) in active spaces with more than ~50 active electrons in ~50 active orbitals, significantly increasing the sizes of systems amenable to accurate multiconfigurational treatment. The main challenge with using any selected CI-based approximate CASSCF is the orbital optimization problem; they tend to exhibit large numbers of local minima in orbital space due to their lack of invariance to active-active rotations (in addition to the local minima that exist in exact CASSCF). We highlight methods that can avoid spurious local extrema as a practical solution to the orbital optimization problem. We employ ASCI-SCF to demonstrate lack of polyradical character in moderately sized periacenes with up to 52 correlated electrons and compare against heat-bath CI on an iron porphyrin system with more than 40 correlated electrons.

physics.comp-ph↗

arXiv2020

Highly Accurate Prediction of Core Spectra of Molecules at Density Functional Theory Cost: Attaining sub eV Error from a Restricted Open-Shell Kohn-Sham Approach

We present the use of the recently developed Square Gradient Minimization (SGM) algorithm for excited state orbital optimization, to obtain spin-pure Restricted Open-Shell Kohn-Sham (ROKS) energies for core excited states of molecules. The SGM algorithm is robust against variational collapse, and offers a reliable route to converging orbitals for target excited states at only 2-3 times the cost of ground state orbital optimization (per iteration). ROKS/SGM with the modern SCAN/$ω$B97X-V functionals is found to predict the K edge of C,N,O and F to a root mean squared error of $\sim$0.3 eV. ROKS/SGM is equally effective at predicting L edge spectra of third period elements, provided a perturbative spin-orbit correction is employed. This high accuracy can be contrasted with traditional TDDFT, which typically has greater than 10 eV error and requires translation of computed spectra to align with experiment. ROKS is computationally affordable (having the same scaling as ground state DFT, and a slightly larger prefactor) and can be applied to geometry optimizations/ab-initio molecular dynamics of core excited states, as well as condensed phase simulations. ROKS can also model doubly excited/ionized states with one broken electron pair, which are beyond the ability of linear response based methods.

physics.chem-ph↗

arXiv2019

Modern Approaches to Exact Diagonalization and Selected Configuration Interaction with the Adaptive Sampling CI Method

Recent advances in selected CI, including the adaptive sampling configuration interaction (ASCI) algorithm and its heat bath extension, have made the ASCI approach competitive with the most accurate techniques available, and hence an increasingly powerful tool in solving quantum Hamiltonians. In this work, we show that a useful paradigm for generating efficient selected CI/exact diagonalization algorithms is driven by fast sorting algorithms, much in the same way iterative diagonalization is based on the paradigm of matrix vector multiplication. We present several new algorithms for all parts of performing a selected CI, which includes new ASCI search, dynamic bit masking, fast orbital rotations, fast diagonal matrix elements, and residue arrays. The algorithms presented here are fast and scalable, and we find that because they are built on fast sorting algorithms they are more efficient than all other approaches we considered. After introducing these techniques we present ASCI results applied to a large range of systems and basis sets in order to demonstrate the types of simulations that can be practically treated at the full-CI level with modern methods and hardware, presenting double- and triple-zeta benchmark data for the G1 dataset. The largest of these calculations is Si$_{2}$H$_{6}$ which is a simulation of 34 electrons in 152 orbitals. We also present some preliminary results for fast deterministic perturbation theory simulations that use hash functions to maintain high efficiency for treating large basis sets.

physics.comp-ph↗

arXiv2019

Excited state orbital optimization via minimizing the square of the gradient: General approach and application to singly and doubly excited states via density functional theory

We present a general approach to converge excited state solutions to any quantum chemistry orbital optimization process, without the risk of variational collapse. The resulting Square Gradient Minimization (SGM) approach only requires analytic energy/Lagrangian orbital gradients and merely costs 3 times as much as ground state orbital optimization (per iteration), when implemented via a finite difference approach. SGM is applied to both single determinant $Δ$SCF and spin-purified Restricted Open-Shell Kohn-Sham (ROKS) approaches to study the accuracy of orbital optimized DFT excited states. It is found that SGM can converge challenging states where the Maximum Overlap Method (MOM) or analogues either collapse to the ground state or fail to converge. We also report that $Δ$SCF/ROKS predict highly accurate excitation energies for doubly excited states (which are inaccessible via TDDFT). Singly excited states obtained via ROKS are also found to be quite accurate, especially for Rydberg states that frustrate (semi)local TDDFT. Our results suggest that orbital optimized excited state DFT methods can be used to push past the limitations of TDDFT to doubly excited, charge-transfer or Rydberg states, making them a useful tool for the practical quantum chemist's toolbox for studying excited states in large systems.

physics.chem-ph↗

arXiv2019

Beyond the Coulson-Fischer point: Characterizing single excitation CI and TDDFT for excited states in single bond dissociations

Linear response time dependent density functional theory (TDDFT), which builds upon configuration interaction singles (CIS) and TD-Hartree-Fock (TDHF), is the most widely used class of excited state quantum chemistry methods and is often employed to study photochemical processes. This paper studies the behavior of the resulting excited state potential energy surfaces beyond the Coulson-Fisher (CF) point in single bond dissociations, when the optimal reference determinant is spin-polarized. Many excited states exhibit sharp kinks at the CF point, and connect to different dissociation limits via a zone of unphysical concave curvature. In particular, the unrestricted M$_S=0$ lowest triplet T$_1$ state changes character, and does not dissociate into ground state fragments. The unrestricted $M_S=\pm 1$ T$_1$ CIS states better approximate the physical dissociation limit, but their degeneracy is broken beyond the CF point for most single bond dissociations. On the other hand, the $M_S=\pm 1$ T$_1$ TDHF states reach the asymptote too soon, by merging with the ground state from the CF point onwards. Use of local exchange-correlation functionals causes $M_S=\pm 1$ T$_1$ TDDFT states to resemble their unphysical $M_S= 0$ counterpart. The 2 orbital, 2-electron model system of minimal basis H$_2$ is analytically treated to understand the origin of these issues, revealing that the lack of double excitations is at the root of these remarkable observations. The behavior of excited state surfaces is also numerically examined for species like H$_2$, NH$_3$, C$_2$H$_6$ and LiH in extended basis sets.

physics.chem-ph↗

arXiv2018

Well-behaved versus ill-behaved density functionals for single bond dissociation: Separating success from disaster functional by functional for stretched H$_2$

Unrestricted DFT methods are typically expected to describe the homolytic dissociation of nonpolar single bonds in neutral species with qualitative accuracy, due to the lack of significant delocalization error. We however find that many widely used density functional approximations fail to describe features along the dissociation curve of the simple H$_2$ molecule. This is not an universal failure of DFT in the sense that many classic functionals like PBE and B3LYP give very reasonable results, as do some more modern methods like MS2. However, some other widely used functionals like B97-D (empirically fitted) and TPSS (non-empirically constrained) predict qualitatively wrong static polarizabilities, force constants and some even introduce an artificial barrier against association of independent H atoms to form H$_2$. The polarizability and force constant prediction failures appear to stem from incomplete spin localization into individual H atoms beyond the Coulson-Fisher point, resulting in `fractionally bonded' species where the ionic contributions to the Slater determinant are not completely eliminated, unlike the case of unrestricted Hartree-Fock. These errors therefore appear to be a consequence of poor self-consistent density prediction by the problematic functional. The same reasons could potentially lead to spurious barriers towards H atom association, indirectly also leading to incorrect forces. These unphysicalities suggest that the use of problematic functionals is probably unwise in \textit{ab initio} dynamics calculations, especially if strong electrostatic interactions are possible.

physics.chem-ph↗

arXiv2018

Postponing the orthogonality catastrophe: efficient state preparation for electronic structure simulations on quantum devices

Despite significant work on resource estimation for quantum simulation of electronic systems, the challenge of preparing states with sufficient ground state support has so far been largely neglected. In this work we investigate this issue in several systems of interest, including organic molecules, transition metal complexes, the uniform electron gas, Hubbard models, and quantum impurity models arising from embedding formalisms such as dynamical mean-field theory. Our approach uses a state-of-the-art classical technique for high-fidelity ground state approximation. We find that easy-to-prepare single Slater determinants such as the Hartree-Fock state often have surprisingly robust support on the ground state for many applications of interest. For the most difficult systems, single-determinant reference states may be insufficient, but low-complexity reference states may suffice. For this we introduce a method for preparation of multi-determinant states on quantum computers.

quant-ph↗

arXiv2018

Delocalization errors in density functional theory are essentially quadratic in fractional occupation number

Approximate functionals used in practical density functional theory (DFT) deviate from the piecewise linear behavior of the exact functional for fractional charges. This deviation causes excess charge delocalization, which leads to incorrect densities, molecular properties, barrier heights, band gaps and excitation energies. We present a simple delocalization function for characterizing this error and find it to be almost perfectly linear vs the fractional electron number for systems spanning in size from the H atom to the C$_{12}$H$_{14}$ polyene. This causes the delocalization energy error to be a quadratic polynomial in the fractional electron number, which permits us to assess the comparative performance of 47 popular and recent functionals through the curvature. The quadratic form further suggests that information about a single fractional charge is sufficient to eliminate the principal source of delocalization error. Generalizing traditional two-point information like ionization potentials or electron affinities to account for a third, fractional charge based data point could therefore permit fitting/tuning of functionals with lower delocalization error.

physics.chem-ph↗

arXiv2018

An efficient deterministic perturbation theory for selected configuration interaction methods

The interplay between advances in stochastic and deterministic algorithms has recently led to development of interesting new selected configuration interaction (SCI) methods for solving the many body Schrödinger equation. The performance of these SCI methods can be greatly improved with a second order perturbation theory (PT2) correction, which is often evaluated in a stochastic or hybrid-stochastic manner. In this work, we present a highly efficient, fully deterministic PT2 algorithm for SCI methods and demonstrate that our approach is orders of magnitude faster than recent proposals for stochastic SCI+PT2. We also show that it is important to have a compact reference SCI wave function, in order to obtain optimal SCI+PT2 energies. This indicates that it advantageous to use accurate search algorithms such as 'ASCI search' rather than more approximate approaches. Our deterministic PT2 algorithm is based on sorting techniques that have been developed for modern computing architectures and is inherently straightforward to use on parallel computing architectures. Related architectures such as GPU implementations can be also used to further increase the efficiency. Overall, we demonstrate that the algorithms presented in this work allow for efficient evaluation of trillions of PT2 contributions with modest computing resources.

cond-mat.str-el↗

arXiv2018

xDH double hybrid functionals can be qualitatively incorrect for non-equilibrium geometries: Dipole moment inversion and barriers to radical-radical association using XYG3 and XYGJ-OS

Double hybrid (DH) density functionals are amongst the most accurate density functional approximations developed so far, largely due to incorporation of correlation effects from unoccupied orbitals via second order perturbation theory (PT2). The xDH family of DH functionals calculate energy directly from orbitals optimized by a lower level approach like B3LYP, without self-consistent optimization. XYG3 and XYGJ-OS are two widely used xDH functionals that are known to be quite accurate at equilibrium geometries. Here, we show that the XYG3 and XYGJ-OS functionals can be ill behaved for stretched bonds well beyond the Coulson-Fischer point, predicting unphysical dipole moments and humps in potential energy curves for some simple systems like the HF molecule. Numerical experiments and analysis show these failures are not due to PT2. Instead, a large mismatch at stretched bond-lengths between the reference B3LYP orbitals and the optimized orbitals associated with the non-PT2 part of XYG3 lead to an unphysically large non-Hellman-Feynman contribution to first order properties like forces and electron densities.

physics.chem-ph↗

arXiv2018

How accurate is density functional theory at predicting dipole moments? An assessment using a new database of 200 benchmark values

Dipole moments are a simple, global measure of the accuracy of the electron density of a polar molecule. Dipole moments also affect the interactions of a molecule with other molecules as well as electric fields. To directly assess the accuracy of modern density functionals for calculating dipole moments, we have developed a database of 200 benchmark dipole moments, using coupled cluster theory through triple excitations, extrapolated to the complete basis set limit. This new database is used to assess the performance of 88 popular or recently developed density functionals. The results suggest that double hybrid functionals perform the best, yielding dipole moments within about 3.6-4.5% regularized RMS error versus the reference values---which is not very different from the 4% regularized RMS error produced by coupled cluster singles and doubles. Many hybrid functionals also perform quite well, generating regularized RMS errors in the 5-6% range. Some functionals however exhibit large outliers and local functionals in general perform less well than hybrids or double hybrids.

physics.chem-ph↗