Heat-Bath Configuration Interaction: An Efficient Selected Configuration Interaction Algorithm Inspired by Heat-Bath Sampling

237

209

In the past two decades, the density matrix renormalization group (DMRG) has emerged as an innovative new method in quantum chemistry relying on a theoretical framework very different from that of traditional electronic structure approaches. The development of the quantum chemical DMRG has been remarkably fast: it has already become one of the reference approaches for large-scale multiconfigurational calculations. This perspective discusses the major features of DMRG, highlighting its strengths and weaknesses also in comparison to other novel approaches. The method is presented following its historical development, starting from its original formulation up to its most recent applications. Possible routes to recover dynamical correlation are discussed in detail. Emerging new fields of applications of DMRG are explored, in particular its time-dependent formulation and the application to vibrational spectroscopy.

“…116 Another issue associated with DMRG[S&I] is the selection of the operator H for Eq. (6). Choosing H to be the full Hamiltonian of the system would require explicit inversion of MPOs.…”

Section: Targeting Excited States With Dmrgmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The density matrix renormalization group in chemistry and molecular physics: Recent developments and new challenges

Baiardi

Reiher

2020

237

209

“…1. The use of an effective Hamiltonian that reduces the cost of the local energy calculation from O(N 4 ) to O(N 2 ); inspired by the Heat-bath Configuration Interaction (HCI) algorithm [20].…”

Section: A Variational Monte Carlo Frameworkmentioning

confidence: 99%

An accelerated linear method for optimizing non-linear wavefunctions in variational Monte Carlo

Sabzevari

Mahajan

Sharma

2020

Although the linear method is one of the most robust algorithms for optimizing non-linearly parametrized wavefunctions in variational Monte Carlo, it suffers from a memory bottleneck due to the fact at each optimization step a generalized eigenvalue problem is solved in which the Hamiltonian and overlap matrices are stored in memory. Here we demonstrate that by applying the Jacobi-Davidson algorithm, one can solve the generalized eigenvalue problem iteratively without having to build and store the matrices in question. The resulting direct linear method greatly lowers the cost and improves the scaling of the algorithm with respect to the number of parameters. To further improve the efficiency of optimization for wavefunctions with a large number of parameters, we use the first order method AMSGrad far from the minimum as it is very inexpensive, and only switch to the direct linear method near the end of the optimization where methods such as AMSGrad have long convergence tails. We apply this improved optimizer to various wavefunctions with both real and orbital space Jastrow factors for atomic systems such as Beryllium and Neon, molecular systems such as the Carbon dimer and Iron(II) Porphyrin, and model systems such as the Hubbard model and Hydrogen chains.I.

“…The use and development of CI-based theories continues today [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] despite their central shortcoming of having to choose between being size-inconsistent (in truncated forms) or having a cost that scales factorially with system size (in full (FCI) or complete active space (CAS) forms). Indeed, many researchers are willing to live with this flaw in light of the stability and robustness that arise from CI's variational nature and straightforward systematic improvability.…”

Section: Introductionmentioning

confidence: 99%

“…sCI methods were originally developed [17][18][19][20][21][22] at a time when high-accuracy treatments of weak correlation were being sought, a role that has now been more or less filled by coupled cluster theory. [23] More recently, there has been much renewed interest in sCI [2,3,8,[10][11][12][13][14][15][16], especially in the context of treating strong correlation. While these approaches have made impressive progress, they do not remove the fundamental challenge that any CI, selective or otherwise, will lose its ability to systematically converge as system size increases and the number of determinants needed for a given level of accuracy quickly overwhelms available computing resources.…”

Section: Introductionmentioning

confidence: 99%

Excitation variance matching with limited configuration interaction expansions in variational Monte Carlo

Robinson

Flores

Neuscamman

2017

In the regime where traditional approaches to electronic structure cannot afford to achieve accurate energy differences via exhaustive wave function flexibility, rigorous approaches to balancing different states' accuracies become desirable. As a direct measure of a wave function's accuracy, the energy variance offers one route to achieving such a balance. Here, we develop and test a variance matching approach for predicting excitation energies within the context of variational Monte Carlo and selective configuration interaction. In a series of tests on small but difficult molecules, we demonstrate that the approach it is effective at delivering accurate excitation energies when the wave function is far from the exhaustive flexibility limit. Results in C3, where we combine this approach with variational Monte Carlo orbital optimization, are especially encouraging.