An efficient deterministic perturbation theory for selected configuration interaction methods

Abstract

The interplay between advances in stochastic and deterministic algorithms has recently led to development of interesting new selected configuration interaction (SCI) methods for solving the many-body Schrödinger equation. The performance of these SCI methods can be greatly improved with a second order perturbation theory (PT2) correction, for which stochastic and hybrid-stochastic methods have recently been proposed as new tools to perform such calculations. In this work, we present a highly efficient, fully deterministic PT2 algorithm for SCI methods and demonstrate that our approach is orders of magnitude faster than recent proposals for stochastic SCI+PT2. We also show that it is important to have a compact reference SCI wave function, in order to obtain optimal SCI+PT2 energies. This indicates that it advantageous to use accurate search algorithms such as 'ASCI search' rather than more approximate approaches. Our deterministic PT2 algorithm is based on sorting techniques that have been developed for modern computing architectures and is inherently straightforward to use on parallel computing architectures. Related architectures such as GPU implementations can be also used to further increase the efficiency. Overall, we demonstrate that the algorithms presented in this work allow for efficient evaluation of trillions of PT2 contributions with modest computing resources.

The Effect of Geometry, Spin and Orbital Optimization in Achieving Accurate, Fully-Correlated Results for Iron-Sulfur Cubanes

“…To study the low energy eigenstates of iron-sulfur clusters, we employ the ASCI [29][30][31] and DMRG [32][33][34] approaches, both for ground state calculations and as approximate solvers in CASSCF [35][36][37][38] orbital optimizations. ASCI and DMRG are complementary methods to treat strong correlation in many-body systems, based on different heuristics: the former finds the most relevant Slater determinants for a truncated ground state description exploiting perturbative estimates iteratively, whereas the latter leverages the simple orbital entanglement structure in ground state wave functions to determine a compact Matrix Product State (MPS) wave function.…”

“…less than 50) of correlated orbitals. Dynamical correlation within the active space can then be recovered perturbatively, [30] and ASCI has been shown to provide near FCI accuracy for the ground state energies and spectral functions for a wide variety of challenging, strongly correlated molecular and extended systems. [29-31, 37, 42-46] As is usual in SCI approaches, the orbital basis chosen to define the Hamiltonian has a critical effect on the convergence of ASCI, and simple choices such as the natural orbital basis [47][48][49][50] do not always assure rapid convergence.…”

SOiCI and iCISO: Combining iterative configuration interaction with spin-orbit coupling in two ways

“…(44) to (45). This reformulation avoids the expensive double check of the excited CSFs belonging to Q or P. The use of pre-ordered arrays [114] for Timsorting [149,150] the residues [122,151] involved in the constraint-based [121] ENPT2 allows allows a massive parallel implementation.…”

“…In this work, we extend the recently proposed iCIPT2 approach [113,114] to the relativistic domain within the 1C framework. iCIPT2 stems from the combination of iterative configuration interaction (iCI, an exact solver of full CI) [115] with configuration selection for static correlation and second-order perturbation theory for dynamic correlation, and belongs to the 'modern family' of selected CI methods [116][117][118][119][120][121][122][123][124][125][126][127][128][129][130][131][132][133] for strongly correlated systems of electrons. In particular, the use of configuration state functions (CSF) as the many-electron basis and the tabulated unitary group approach (TUGA) [113] for fast evaluation and reuse of the basic coupling coefficients between CSFs allows an easy extension of iCIPT2 to the treatment of SOC in two ways, one-step SOiCI and two-step iCISO, which are to be discussed in detail in Sec.…”

Near-Exact Nuclear Gradients of Complete Active Space Self-Consistent Field Wave Functions

“…This steep cost limits the size of active spaces that can be treated to roughly 22 electrons in 22 orbitals, which we abbreviate as (22e,22o). 4 A substantial amount of research in quantum chemistry is devoted to reducing the cost of configuration interaction (CI) methods through a variety of approximations: restricted active space, 3,5 generalized active space, 2,6,7 density matrix renormalization, selected configuration interaction (SCI), [30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49] FCI quantum monte carlo, [50][51][52][53] . The heat bath configuration interaction (HCI) is a particularly efficient implementation of the SCI method.…”