We present a new method for modeling electronically excited states that overcomes a key failing of linear response theory by allowing the underlying ground state ansatz to relax in the presence of an excitation. The method is variational, has a cost similar to ground state variational Monte Carlo, and admits both open and periodic boundary conditions. We present preliminary numerical results showing that, when paired with the Jastrow antisymmetric geminal power ansatz, the variation-after-response formalism delivers accuracies for valence and charge transfer single excitations on par with equation of motion coupled cluster, while surpassing coupled cluster's accuracy for excitations with significant doubly excited character.
We present a new method for modeling electronically excited states that overcomes a key failing of linear response theory by allowing the underlying ground state ansatz to relax in the presence of an excitation. The method is variational, has a cost similar to ground state variational Monte Carlo, and admits both open and periodic boundary conditions. We present preliminary numerical results showing that, when paired with the Jastrow antisymmetric geminal power ansatz, the variation-after-response formalism delivers accuracies for valence and charge transfer single excitations on par with equation of motion coupled cluster, while surpassing coupled cluster's accuracy for excitations with significant doubly excited character.
We present a variational function that targets excited states directly based on their position in the energy spectrum, along with a Monte Carlo method for its evaluation and minimization whose cost scales polynomially for a wide class of approximate wave functions. Being compatible with both real and Fock space and open and periodic boundary conditions, the method has the potential to impact many areas of chemistry, physics, and materials science. Initial tests on doubly excited states show that using this method, the Hilbert space Jastrow antisymmetric geminal power ansatz can deliver order-of-magnitude improvements in accuracy relative to equation of motion coupled cluster theory, while a very modest real space multi-Slater Jastrow expansion can achieve accuracies within 0.1 eV of the best theoretical benchmarks for the carbon dimer.
Abstract We present a discussion of recent progress in excited‐state‐specific quantum chemistry and quantum Monte Carlo alongside a demonstration of how a combination of methods from these two fields can offer reliably accurate excited state predictions across singly excited, doubly excited, and charge transfer states. Both of these fields have seen important advances supporting excited state simulation in recent years, including the introduction of more effective excited‐state‐specific optimization methods, improved handling of complicated wave function forms, and ways of explicitly balancing the quality of wave functions for ground and excited states. To emphasize the promise that exists at this intersection, we provide demonstrations using a combination of excited‐state‐specific complete active space self‐consistent field theory, selected configuration interaction, and state‐specific variance minimization. These demonstrations show that combining excited‐state‐specific quantum chemistry and variational Monte Carlo can be more reliably accurate than either equation of motion coupled cluster theory or multi‐reference perturbation theory, and that it can offer new clarity in cases where existing high‐level methods do not agree. This article is categorized under: Electronic Structure Theory > Ab Initio Electronic Structure Methods Software > Quantum Chemistry
We study the ionization energy, electron affinity, and the π → π(∗) ((1)La) excitation energy of the anthracene molecule, by means of variational quantum Monte Carlo (QMC) methods based on a Jastrow correlated antisymmetrized geminal power (JAGP) wave function, developed on molecular orbitals (MOs). The MO-based JAGP ansatz allows one to rigorously treat electron transitions, such as the HOMO → LUMO one, which underlies the (1)La excited state. We present a QMC optimization scheme able to preserve the rank of the antisymmetrized geminal power matrix, thanks to a constrained minimization with projectors built upon symmetry selected MOs. We show that this approach leads to stable energy minimization and geometry relaxation of both ground and excited states, performed consistently within the correlated QMC framework. Geometry optimization of excited states is needed to make a reliable and direct comparison with experimental adiabatic excitation energies. This is particularly important in π-conjugated and polycyclic aromatic hydrocarbons, where there is a strong interplay between low-lying energy excitations and structural modifications, playing a functional role in many photochemical processes. Anthracene is an ideal benchmark to test these effects. Its geometry relaxation energies upon electron excitation are of up to 0.3 eV in the neutral (1)La excited state, while they are of the order of 0.1 eV in electron addition and removal processes. Significant modifications of the ground state bond length alternation are revealed in the QMC excited state geometry optimizations. Our QMC study yields benchmark results for both geometries and energies, with values below chemical accuracy if compared to experiments, once zero point energy effects are taken into account.
We present a simple and efficient wave function ansatz for the treatment of excited charge-transfer states in real-space quantum Monte Carlo methods. Using the recently introduced variation-after-response method [E. Neuscamman, J. Chem. Phys. 145, 081103 (2016)], this ansatz allows a crucial orbital optimization step to be performed beyond a configuration interaction singles expansion, while only requiring calculation of two Slater determinant objects. We demonstrate this ansatz for the illustrative example of the stretched LiF molecule, for a range of excited states of formaldehyde, and finally for the more challenging ethylene-tetrafluoroethylene molecule.
We present a modification to variational Monte Carlo's linear method optimization scheme that addresses a critical memory bottleneck while maintaining compatibility with both the traditional ground state variational principle and our recently introduced variational principle for excited states. For wave function ansatzes with tens of thousands of variables, our modification reduces the required memory per parallel process from tens of gigabytes to hundreds of megabytes, making the methodology a much better fit for modern supercomputer architectures in which data communication and per-process memory consumption are primary concerns. We verify the efficacy of the new optimization scheme in small molecule tests involving both the Hilbert space Jastrow antisymmetric geminal power ansatz and real space multi-Slater Jastrow expansions. Satisfied with its performance, we have added the optimizer to the QMCPACK software package, with which we test a systematically convergent, nonperturbative approach to excitation energies on the example of a Mott-insulating hydrogen ring.
Describing the electronic structure of molecules using computational methods is of central importance in many areas of chemical research and industry. To this day, the variational quantum Monte Carlo (VMC) algorithm, which utilizes the variational principle of quantum mechanics to optimize an ansatz towards the true electronic wave function, is one of the lesser employed of such computational methods. While it is generally applicable, and provides direct access to the wave function, its accuracy has been limited by insufficiently expressive ansatzes. This barrier was recently lifted with the introduction of deep-learning-based ansatzes, providing unprecedented flexibility and corresponding accuracy, at the cost of increased computational requirements. In this thesis, our implementation of the VMC algorithm with deep-learning ansatzes is described, along with a number of developments facilitating the computation of electronic excited states, extraction of various observables, and characterization of potential energy surfaces, at a reduced computational cost. The method is implemented as open-source software, employing a common framework to encompass most ansatzes present in the literature. Utilizing the direct wave function access granted by VMC, an approach is developed to extract one-electron reduced densities, that are free from Gaussian basis set effects. Significant advances in the methodology of computing electronic excited states via the ladder-of-states approach are made, including an improved form of the overlap penalty term with an automatically determined prefactor, and a new loss term with which the total spin of the solution can be selected. The efficiency of computing excited potential energy surfaces are enhanced by optimizing a single ansatz for a range of molecular configurations. To enable such transferable training in the presence of state crossings, a dynamic, geometry-wise ordering in the ladder of states is introduced. Geometry-optimization-based tasks are identified as natural fits for such transferable ansatzes, and a transferability-native approach for extracting the necessary information from VMC data is devised. Finally, transferable training is employed to simultaneously model different chemical species, resulting in a foundation model predicting bond breaking at a cost-accuracy ratio competitive with mature multi-reference methods. The work presented here contributes significantly to the development of a practically useful deep-learning-based VMC method. The described approaches have the potential to become tools for a wide community of computational chemists, as a source of accurate data, describing strong correlation in both ground and excited states.