arXiv subjects

Martin Head-Gordon

Publications and source records attributed to Martin Head-Gordon.

At least 73 records · Page 4Linked 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

Assessment of the Performance of Density Functionals for Predicting Potential Energy Curves in Hydrogen Storage Applications

The availability of accurate computational tools for modeling and simulation is vital to accelerate the discovery of materials capable of storing hydrogen (H2) under given parameters of pressure swing and temperature. Previously, we compiled the H2Bind275 dataset consisting of equilibrium geometries and assessed the performance of 55 density functionals over this dataset (Veccham, S. P.; Head-Gordon, M. J. Chem. Theory Comput., 2020, 16, 4963--4982). As it is crucial for computational tools to accurately model the entire potential energy curve (PEC), in addition to the equilibrium geometry, we have extended this dataset with 389 new data points to include two compressed and three elongated geometries along 78 PECs for H2 binding, forming the H2Bind78x7 dataset. Assessing the performance of 55 density functionals on this significantly larger and more comprehensive H2Bind78x7 dataset, we have identified the best performing density functionals for H2 binding applications: PBE0-DH, $ω$B97X-V, $ω$B97M-V, and DSD-PBEPBE-D3(BJ). Addition of Hartree Fock exchange improves the performance of density functionals, albeit not uniformly throughout the PEC. We recommend the usage of wB97X-V and wB97M-V density functionals as they give good performance for both geometries and energies. In addition, we have also identified B97M-V and B97M-rV as the best semi-local density functionals for predicting H2 binding energy at its equilibrium geometry.

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 Critical Role of Thermal Fluctuations for Electrocatalytic Metal Surface Properties and CO Binding Trends

This work addresses a longstanding theoretical discrepancy using Density Functional Theory (DFT) with experimental observations of CO binding trends on electrocatalytically relevant metals for the CO2 reduction reaction (CO2RR). By introducing thermal fluctuations using appropriate statistical mechanical NVT and NPT ensembles, we show that DFT with universal dispersion interactions yields qualitatively better metal surface strain trends and CO binding energetics, consistently predicts the correct site preference for all metals due to thermally induced surface distortions that preferentially exposes the undercoordinated atop site for Cu(111) and Pt(111), and for the weak binding Ag(111) and Au(111) surfaces at finite temperatures shows CO-metal interactions that are a mixture of chemisorbed and physisorbed species. This study better places theory as an equal partner to experimental heterogeneous catalysis by demonstrating the need to fully account for finite temperature fluctuations to make contact with surface science experiments.

physics.chem-ph↗

arXiv2020

A Non-Perturbative Pairwise-Additive Analysis of Charge Transfer Contributions to Intermolecular Interaction Energies

Energy decomposition analysis (EDA) based on absolutely localized molecular orbitals (ALMOs) decomposes the interaction energy between molecules into physically interpretable components like geometry distortion, frozen interactions, polarization, and charge transfer (CT, also sometimes called charge delocalization) interactions. In this work, a numerically exact scheme to decompose the CT interaction energy into pairwise additive terms is introduced for the ALMO-EDA using density functional theory. Unlike perturbative pairwise charge-decomposition analysis, the new approach does not break down for strongly interacting systems, or show significant exchange-correlation functional dependence in the decomposed energy components. Both the energy lowering and the charge flow associated with CT can be decomposed. Complementary occupied-virtual orbital pairs (COVPs) that capture the dominant donor and acceptor CT orbitals are obtained for the new decomposition. It is applied to systems with different types of interactions including DNA base-pairs, borane-ammonia adducts, and transition metal hexacarbonyls. While consistent with most existing understanding of the nature of CT in these systems, the results also reveal some new insights into the origin of trends in donor-acceptor interactions.

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

Polishing the Gold Standard: The Role of Orbital Choice in CCSD(T) Vibrational Frequency Prediction

While CCSD(T) with spin-restricted Hartree-Fock (RHF) orbitals has long been lauded for its ability to accurately describe closed-shell interactions, the performance of CCSD(T) on open-shell species is much more erratic, especially when using a spin-unrestricted HF (UHF) reference. Previous studies have shown improved treatment of open-shell systems when a non-HF set of molecular orbitals, like Brueckner or Kohn-Sham density functional theory (DFT) orbitals, is used as a reference. Inspired by the success of regularized orbital-optimized second-order Møller-Plesset perturbation theory ($κ$-OOMP2) orbitals as reference orbitals for MP3, we investigate the use of $κ$-OOMP2 orbitals and various DFT orbitals as reference orbitals for CCSD(T) calculations of the corrected ground-state harmonic vibrational frequencies of a set of 36 closed-shell (29 neutrals, 6 cations, 1 anion) and 59 open-shell diatomic species (38 neutrals, 15 cations, 6 anions). The use of $κ$-OOMP2 orbitals in this context alleviates difficult cases observed for both UHF orbitals and OOMP2 orbitals. Removing 2 multireference systems and 12 systems with ambiguous experimental data leaves a pruned data set. Overall performance on the pruned data set highlights CCSD(T) with a B97 orbital reference (CCSD(T):B97), CCSD(T) with a $κ$-OOMP2 orbital reference (CCSD(T):$κ$-OOMP2), and CCSD(T) with a B97M-rV orbital reference (CCSD(T):B97M-rV) with RMSDs of 8.48 cm$^{-1}$ and 8.50 cm$^{-1}$, and 8.75 cm$^{-1}$ respectively, outperforming CCSD(T):UHF by nearly a factor of 5. Moreover, the performance on the closed- and open-shell subsets show these methods are able to treat open-shell and closed-shell systems with comparable accuracy and robustness. The use of $κ$-OOMP2 orbitals has also proven useful in diagnosing multireference character that can hinder the reliability of CCSD(T).

physics.chem-ph↗

arXiv2020

Density Functionals for Hydrogen Storage: Defining the H2Bind275 Test Set with Ab Initio Benchmarks and Assessment of 55 Functionals

Efficient and high capacity storage materials are indispensable for a hydrogen-based economy. In silico tools can accelerate the process of discovery of new adsorbent materials with optimal hydrogen adsorption enthalpies. Density functional theory is well-poised to become a very useful tool for enabling high-throughput screening of potential materials. In this work, we have identified density functional approximations that provide good performance for hydrogen binding applications following a two-pronged approach. First, we have compiled a dataset (H2Bind275) that comprehensively represents the hydrogen binding problem capturing the chemical and mechanistic diversity in the binding sites encountered in hydrogen storage materials. We have also computed reference interaction energies for this dataset using coupled cluster theory. Secondly, we have assessed the performance of 55 density functional approximations for predicting H$_2$ interaction energies and have identified two hybrid density functionals ($ω$B97X-V and $ω$B97M-V), two double hybrid density functionals (DSD-PBEPBE-D3(BJ) and PBE0-DH), and one semi-local density functional (B97M-V) as the best performing ones. We have recommended the addition of empirical dispersion corrections to systematically underbinding density functionals like revPBE, BLYP, and B3LYP for improvements in performance at negligible additional cost. We have also recommended the usage of the def2-TZVPP basis set as it represents a good compromise between accuracy and cost, limiting the finite basis set errors to less than 1kJ/mol.

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

Systematically Improvable Tensor Hypercontraction: Interpolative Separable Density-Fitting for Molecules Applied to Exact Exchange, Second- and Third-Order Møller-Plesset Perturbation Theory

We present a systematically improvable tensor hypercontraction (THC) factorization based on interpolative separable density fitting (ISDF). We illustrate algorithmic details to achieve this within the framework of Becke's atom-centered quadrature grid. A single ISDF parameter $c_\text{ISDF}$ controls the tradeoff between accuracy and cost. In particular, $c_\text{ISDF}$ sets the number of interpolation points used in THC, $N_\text{IP} = c_\text{ISDF}\times N_\text{X}$ with $N_\text{X}$ being the number of auxiliary basis functions. In conjunction with the resolution-of-the-identity (RI) technique, we develop and investigate the THC-RI algorithms for cubic-scaling exact exchange for Hartree-Fock and range-separated hybrids (e.g., $ω$B97X-V) and quartic-scaling second- and third-order Møller-Plesset theory (MP2 and MP3). These algorithms were evaluated over the W4-11 thermochemistry (atomization energy) set and A24 non-covalent interaction benchmark set with standard Dunning basis sets (cc-pVDZ, cc-pVTZ, aug-cc-pVDZ, and aug-cc-pVTZ). We demonstrate the convergence of THC-RI algorithms to numerically exact RI results using ISDF points. Based on these, we make recommendations on $c_\text{ISDF}$ for each basis set and method. We also demonstrate the utility of THC-RI exact exchange and MP2 for larger systems such as water clusters and $\text{C}_{20}$. We stress that more challenges await in obtaining accurate and numerically stable THC factorization for wavefunction amplitudes as well as the space spanned by virtual orbitals in large basis sets and implementing sparsity-aware THC-RI algorithms.

physics.chem-ph↗

arXiv2019

Making Many-Body Interactions Nearly Pairwise Additive: The Polarized Many-Body Expansion Approach

The Many-Body Expansion (MBE) is a useful tool to simulate condensed phase chemical systems, often avoiding the steep computational cost of usual electronic structure methods. However, it often requires higher than 2-body terms to achieve quantitative accuracy. In this work, we propose the Polarized MBE (PolBE) method where each MBE energy contribution is treated as an embedding problem. In each energy term, a smaller fragment is embedded into a larger, polarized environment and only a small region is treated at the high-level of theory using embedded mean-field theory. The role of polarized environment was found to be crucial in providing quantitative accuracy at the 2-body level. PolBE accurately predicts non-covalent interaction energies for a number of systems, including CO$_2$, water, and hydrated ion clusters, with a variety of interaction mechanisms, from weak dispersion to strong electrostatics considered in this work. We further demonstrate that the PolBE interaction energy is predominantly pairwise unlike the usual vacuum MBE which requires higher-order terms to achieve similar accuracy. We numerically show that PolBE often performs better than other widely used embedded MBE methods such as the electrostatically embedded MBE. Owing to the lack of expensive diagonalization of Fock matrices and its embarrassingly parallel nature, PolBE is a promising way to access condensed phase systems with hybrid density functionals that are difficult to treat with currently available methods.

physics.chem-ph↗