arXiv subjects

Eric Neuscamman

Publications and source records attributed to Eric Neuscamman.

At least 37 records · Page 2Linked to original sources

arXiv2022

Applying generalized variational principles to excited-state-specific complete active space self-consistent field theory

We employ a generalized variational principle to improve the stability, reliability, and precision of fully excited-state-specific complete active space self-consistent field theory. Compared to previous approaches that similarly seek to tailor this ansatz's orbitals and configuration interaction expansion for an individual excited state, we find the present approach to be more resistant to root flipping and better at achieving tight convergence to an energy stationary point. Unlike state-averaging, this approach allows orbital shapes to be optimal for individual excited states, which is especially important for charge transfer states and some doubly excited states. We demonstrate the convergence and state-targeting abilities of this method in LiH, ozone, and MgO, showing in the latter that it is capable of finding three excited state energy stationary points that no previous method has been able to locate.

physics.chem-ph↗

arXiv2020

A hybrid approach to excited-state-specific variational Monte Carlo and doubly excited states

We extend our hybrid linear-method/accelerated-descent variational Monte Carlo optimization approach to excited states and investigate its efficacy in double excitations. In addition to showing a superior statistical efficiency when compared to the linear method, our tests on the carbon dimer and cyclopentadiene show good energetic agreement with benchmark methods and experiment, respectively. We also demonstrate the ability to treat double excitations in systems that are too large for a full treatment by selective configuration interaction methods via an application to 4-aminobenzonitrile. Finally, we investigate the stability of state-specific variance optimization against collapse to other states' variance minima and find that symmetry, ansatz quality, and sample size all have roles to play in achieving stability.

physics.chem-ph↗

arXiv2020

A Self Consistent Field Formulation of Excited State Mean Field Theory

We show that, as in Hartree Fock theory, the orbitals for excited state mean field theory can be optimized via a self-consistent one-electron equation in which electron-electron repulsion is accounted for through mean field operators. In addition to showing that this excited state ansatz is sufficiently close to a mean field product state to admit a one-electron formulation, this approach brings the orbital optimization speed to within roughly a factor of two of ground state mean field theory. The approach parallels Hartree Fock theory in multiple ways, including the presence of a commutator condition, a one-electron mean-field working equation, and acceleration via direct inversion in the iterative subspace. When combined with a configuration interaction singles Davidson solver for the excitation coefficients, the self consistent field formulation dramatically reduces the cost of the theory compared to previous approaches based on quasi-Newton descent.

physics.chem-ph↗

arXiv2020

An N$^5$-scaling excited-state-specific perturbation theory

We show that by working in a basis similar to that of the natural transition orbitals and using a modified zeroth order Hamiltonian, the cost of a recently-introduced perturbative correction to excited state mean field theory can be reduced from seventh to fifth order in the system size. The (occupied)$^2$(virtual)$^3$ asymptotic scaling matches that of ground state second order Møller-Plesset theory, but with a significantly higher prefactor because the bottleneck is iterative: it appears in the Krylov-subspace-based solution of the linear equation that yields the first order wave function. Here we discuss the details of the modified zeroth order Hamiltonian we use to reduce the cost as well as the automatic code generation process we used to derive and verify the cost scaling of the different terms. Overall, we find that our modifications have little impact on the method's accuracy, which remains competitive with singles and doubles equation-of-motion coupled cluster.

physics.chem-ph↗

arXiv2020

A variational Monte Carlo approach for core excitations

We present a systematically-improvable approach to core excitations in variational Monte Carlo. Building on recent work in excited-state-specific Monte Carlo, we show how a straightforward protocol, starting from a quantum chemistry guess, is able to capture core state's strong orbital relaxations, maintain accuracy in the near-nuclear region during these relaxations, and explicitly balance accuracy between ground and core excited states. In water, ammonia, and methane, which serve as prototypical representatives for oxygen, nitrogen, and carbon core states, respectively, this approach delivers accuracies on par with the best available theoretical methods even when using relatively small wave function expansions.

physics.chem-ph↗

arXiv2020

Core Excitations with Excited State Mean Field and Perturbation Theory

We test the efficacy of excited state mean field theory and its excited-state-specific perturbation theory on the prediction of K-edge positions and X-ray peak separations. We find that the mean field theory is surprisingly accurate, even though it contains no accounting of differential electron correlation effects. In the perturbation theory, we test multiple core-valence separation schemes and find that, with the mean field theory already so accurate, electron-counting biases in one popular separation scheme become a dominant error when predicting K-edges. Happily, these appear to be relatively easy to correct for, leading to a perturbation theory for K-edge positions that is lower scaling and more accurate than coupled cluster theory and competitive in accuracy with recent high-accuracy results from restricted open-shell Kohn Sham theory. For peak separations, our preliminary data show excited state mean field theory to be exceptionally accurate, but more extensive testing will be needed to see how it and its perturbation theory compare to coupled cluster peak separations more broadly.

physics.chem-ph↗

arXiv2020

Improving excited state potential energy surfaces via optimal orbital shapes

We demonstrate that, rather than resorting to high-cost dynamic correlation methods, qualitative failures in excited-state potential energy surface predictions can often be remedied at no additional cost by ensuring that optimal molecular orbitals are used for each individual excited state. This approach also avoids the weighting choices required by state-averaging and dynamic weighting and obviates their need for expensive wave function response calculations when relaxing excited state geometries. Although multi-state approaches are of course preferred near conical intersections, other features of excited-state potential energy surfaces can benefit significantly from our single state approach. In three different systems, including a double bond dissociation, a biologically relevant amino hydrogen dissociation, and an amino-to-ring intramolecular charge transfer, we show that state-specific orbitals offer qualitative improvements over the state-averaged status quo.

physics.chem-ph↗

arXiv2020

QMCPACK: Advances in the development, efficiency, and application of auxiliary field and real-space variational and diffusion Quantum Monte Carlo

We review recent advances in the capabilities of the open source ab initio Quantum Monte Carlo (QMC) package QMCPACK and the workflow tool Nexus used for greater efficiency and reproducibility. The auxiliary field QMC (AFQMC) implementation has been greatly expanded to include k-point symmetries, tensor-hypercontraction, and accelerated graphical processing unit (GPU) support. These scaling and memory reductions greatly increase the number of orbitals that can practically be included in AFQMC calculations, increasing accuracy. Advances in real space methods include techniques for accurate computation of band gaps and for systematically improving the nodal surface of ground state wavefunctions. Results of these calculations can be used to validate application of more approximate electronic structure methods including GW and density functional based techniques. To provide an improved foundation for these calculations we utilize a new set of correlation-consistent effective core potentials (pseudopotentials) that are more accurate than previous sets; these can also be applied in quantum-chemical and other many-body applications, not only QMC. These advances increase the efficiency, accuracy, and range of properties that can be studied in both molecules and materials with QMC and QMCPACK.

physics.comp-ph↗

arXiv2020

Excited State Mean-Field Theory without Automatic Differentiation

We present a formulation of excited state mean-field theory in which the derivatives with respect to the wave function parameters needed for wave function optimization (not to be confused with nuclear derivatives) are expressed analytically in terms of a collection of Fock-like matrices. By avoiding the use of automatic differentiation and grouping Fock builds together, we find that the number of times we must access the memory-intensive two-electron integrals can be greatly reduced. Furthermore, the new formulation allows the theory to exploit existing strategies for efficient Fock matrix construction. We demonstrate this advantage explicitly via the shell-pair screening strategy, with which we achieve a cubic overall cost scaling. Using this more efficient implementation, we also examine the theory's ability to predict charge redistribution during charge transfer excitations. Using coupled cluster as a benchmark, we find that by capturing orbital relaxation effects and avoiding self-interaction errors, excited state mean field theory out-performs other low-cost methods when predicting the charge density changes of charge transfer excitations.

physics.chem-ph↗

arXiv2020

A generalized variational principle with applications to excited state mean field theory

We present a generalization of the variational principle that is compatible with any Hamiltonian eigenstate that can be specified uniquely by a list of properties. This variational principle appears to be compatible with a wide range of electronic structure methods, including mean-field theory, density functional theory, multi-reference theory, and quantum Monte Carlo. Like the standard variational principle, this generalized variational principle amounts to the optimization of a nonlinear function that, in the limit of an arbitrarily flexible wave function, has the desired Hamiltonian eigenstate as its global minimum. Unlike the standard variational principle, it can target excited states and select individual states in cases of degeneracy or near-degeneracy. As an initial demonstration of how this approach can be useful in practice, we employ it to improve the optimization efficiency of excited state mean field theory by an order of magnitude. With this improved optimization, we are able to demonstrate that the accuracy of the corresponding second-order perturbation theory rivals that of singles-and-doubles equation-of-motion coupled cluster in a substantially broader set of molecules than could be explored by our previous optimization methodology.

physics.chem-ph↗

arXiv2019

A Density Functional Extension to Excited State Mean-Field Theory

We investigate an extension of excited state mean-field theory in which the energy expression is augmented with density functional components in an effort to include the effects of weak electron correlations. The approach remains variational and entirely time-independent, allowing it to avoid some of the difficulties associated with linear response and the adiabatic approximation. In particular, all of the electrons' orbitals are relaxed state specifically and there is no reliance on Kohn-Sham orbital energy differences, both of which are important features in the context of charge transfer. Preliminary testing shows clear advantages for single-component charge transfer states, but the method, at least in its current form, is less reliable for states in which multiple particle-hole transitions contribute significantly.

physics.chem-ph↗

arXiv2019

Variational Excitations in Real Solids: Optical Gaps and Insights into Many-Body Perturbation Theory

We present an approach to studying optical band gaps in real solids in which quantum Monte Carlo methods allow for the application of a rigorous variational principle to both ground and excited state wave functions. In tests that include small, medium, and large band gap materials, optical gaps are predicted with a mean-absolute-deviation of 3.5% against experiment, less than half the equivalent errors for typical many-body perturbation theories. The approach is designed to be insensitive to the choice of density functional, a property we exploit in order to provide insight into how far different functionals are from satisfying the assumptions of many body perturbation theory. We explore this question most deeply in the challenging case of ZnO, where we show that although many commonly used functionals have shortcomings, there does exist a one particle basis in which perturbation theory's zeroth order picture is sound. Insights of this nature should be useful in guiding the future application and improvement of these widely used techniques.

cond-mat.str-el↗

arXiv2019

Complementary First and Second Derivative Methods for Ansatz Optimization in Variational Monte Carlo

We present a comparison between a number of recently introduced low-memory wave function optimization methods for variational Monte Carlo in which we find that first and second derivative methods possess strongly complementary relative advantages. While we find that low-memory variants of the linear method are vastly more efficient at bringing wave functions with disparate types of nonlinear parameters to the vicinity of the energy minimum, accelerated descent approaches are then able to locate the precise minimum with less bias and lower statistical uncertainty. By constructing a simple hybrid approach that combines these methodologies, we show that all of these advantages can be had at once when simultaneously optimizing large determinant expansions, molecular orbital shapes, traditional Jastrow correlation factors, and more nonlinear many-electron Jastrow factors.

cond-mat.str-el↗

arXiv2019

Tracking excited states in wave function optimization using density matrices and variational principles

We present a method for finding individual excited states' energy stationary points in complete active space self-consistent field theory that is compatible with standard optimization methods and highly effective at overcoming difficulties due to root flipping and near-degeneracies. Inspired by both the maximum overlap method and recent progress in excited state variational principles, our approach combines these ideas in order to track individual excited states throughout the orbital optimization process. In a series of tests involving root flipping, near-degeneracies, charge transfers, and double excitations, we show that this approach is more effective for state-specific optimization than either the naive selection of roots based on energy ordering or a more direct generalization of the maximum overlap method. Furthermore, we provide evidence that this state-specific approach improves the performance of complete active space perturbation theory. With a simple implementation, a low cost, and compatibility with large active space methods, the approach is designed to be useful in a wide range of excited state investigations.

cond-mat.str-el↗

arXiv2018

Excited-state diffusion Monte Carlo calculations: a simple and efficient two-determinant ansatz

We perform excited-state variational Monte Carlo and diffusion Monte Carlo calculations using a simple and efficient wave function ansatz. This ansatz follows the recent variation-after-response formalism, accurately approximating a configuration interaction singles wave function as a sum of only two non-orthogonal Slater determinants, and further including important orbital relaxation. The ansatz is used to perform diffusion Monte Carlo calculations with large augmented basis sets, comparing to benchmarks from near-exact quantum chemical methods. The significance of orbital optimization in excited-state diffusion Monte Carlo is demonstrated, and the excited-state optimization procedure is discussed in detail. Diffuse excited states in water and formaldehyde are studied, in addition to the formaldimine and benzonitrile molecules.

cond-mat.str-el↗

arXiv2018

Clean and Convenient Tessellations for Number Counting Jastrow Factors

We introduce a basis of counting functions that, by cleanly tessellating three dimensional space, allows real space number counting Jastrow factors to be straightforwardly applied to general molecular situations. By exerting direct control over electron populations in local regions of space and encoding pairwise correlations between these populations, these Jastrow factors allow even very simple reference wave functions to adopt nodal surfaces well suited to many strongly correlated settings. Being trivially compatible with traditional Jastrow factors and diffusion Monte Carlo and having the same cubic per-sample cost scaling as a single determinant trial function, these Jastrow factors thus offer a powerful new route to the simultaneous capture of weak and strong electron correlation effects in a wide variety of molecular and materials settings. In multiple strongly correlated molecular examples, we show that even when paired with the simplest possible single determinant reference, these Jastrow factors allow quantum Monte Carlo to out-perform coupled cluster theory and approach the accuracy of traditional multi-reference methods.

cond-mat.str-el↗

arXiv2018

Excited State Specific Multi-Slater Jastrow Wave Functions

We combine recent advances in excited state variational principles, fast multi-Slater Jastrow methods, and selective configuration interaction to create multi-Slater Jastrow wave function approximations that are optimized for individual excited states. In addition to the Jastrow variables and linear expansion coefficients, this optimization includes state-specific orbital relaxations in order to avoid the compromises necessary in state-averaged approaches. We demonstrate that, when combined with variance matching to help balance the quality of the approximation across different states, this approach delivers accurate excitation energies even when using very modest multi-Slater expansions. Intriguingly, this accuracy is maintained even when studying a difficult chlorine-anion-to-$π^{*}$ charge transfer in which traditional state-averaged multi-reference methods must contend with different states that require drastically different orbital relaxations.

cond-mat.str-el↗

arXiv2018

A Mean Field Platform for Excited State Quantum Chemistry

We present a mean field theory for excited states that is broadly analogous to ground state Hartree-Fock theory. Like Hartree-Fock, our approach is deterministic, state-specific, applies a variational principle to a minimally correlated ansatz, produces energy stationary points, relaxes the orbital basis, has a Fock-build cost-scaling, and can serve as the foundation for correlation methods such as perturbation theory and coupled cluster theory. To emphasize this last point, we pair our mean field approach with an excited state analogue of second order Moller-Plesset theory and demonstrate that in water, formaldehyde, neon, and stretched lithium fluoride, the resulting accuracy far exceeds that of configuration interaction singles and rivals that of equation of motion coupled cluster.

cond-mat.str-el↗