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We explore the performance of a recently-introduced $N^5$-scaling excited-state-specific second order perturbation theory (ESMP2) on the singlet excitations of the Thiel benchmarking set. We find that, without regularization, ESMP2 is quite sensitive to $\pi$ system size, performing well in molecules with small $\pi$ systems but poorly in those with larger $\pi$ systems. With regularization, ESMP2 is far less sensitive to $\pi$ system size and shows a higher overall accuracy on the Thiel set than CC2, EOM-CCSD, CC3, and a wide variety of time-dependent density functional approaches. Unsurprisingly, even regularized ESMP2 is less accurate than multi-reference perturbation theory on this test set, which can in part be explained by the set's inclusion of some doubly excited states but none of the strong charge transfer states that often pose challenges for state-averaging. Beyond energetics, we find that the ESMP2 doubles norm offers a relatively low-cost way to test for doubly excited character without the need to define an active space.

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 M{\o}ller-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., Comment: 11 pages, 2 figures, 7 tables, accepted by the Journal of Chemical Theory and Computation

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.

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., Comment: 13 pages, submitted to JCTC

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., Comment: 6 pages

QMCPACK is an open source quantum Monte Carlo package for ab-initio electronic structure calculations. It supports calculations of metallic and insulating solids, molecules, atoms, and some model Hamiltonians. Implemented real space quantum Monte Carlo algorithms include variational, diffusion, and reptation Monte Carlo. QMCPACK uses Slater-Jastrow type trial wave functions in conjunction with a sophisticated optimizer capable of optimizing tens of thousands of parameters. The orbital space auxiliary field quantum Monte Carlo method is also implemented, enabling cross validation between different highly accurate methods. The code is specifically optimized for calculations with large numbers of electrons on the latest high performance computing architectures, including multicore central processing unit (CPU) and graphical processing unit (GPU) systems. We detail the program's capabilities, outline its structure, and give examples of its use in current research calculations. The package is available at http://www.qmcpack.org .

We demonstrate that a broad class of excited state variational principles is not size consistent. In light of this difficulty, we develop and test an approach to excited state optimization that transforms between variational principles in order to achieve state selectivity, size consistency, and compatibility with quantum Monte Carlo. To complement our formal analysis, we provide numerical examples that confirm these properties and demonstrate how they contribute to a more black box approach to excited states in quantum Monte Carlo., Comment: 27 pages, 10 figures, 2 tables