Many-Body Expanded Full Configuration Interaction. I. Weakly Correlated Regime

Over the course of the past few decades, the field of computational chemistry has managed to manifest itself as a key complement to more traditional lab-oriented chemistry. This is particularly true in the wake of the recent renaissance of full configuration interaction (FCI)-level methodologies, albeit only if these can prove themselves sufficiently robust and versatile to be routinely applied to a variety of chemical problems of interest. In the present series of works, performance and feature enhancements of one such avenue towards FCI-level results for medium to large one-electron basis sets, the recently introduced many-body expanded full configuration interaction (MBE-FCI) formalism [J. Phys. Chem. Lett., 8, 4633 (2017)], will be presented. Specifically, in this opening part of the series, the capabilities of the MBE-FCI method in producing near-exact ground state energies for weakly correlated molecules of any spin multiplicity will be demonstrated.Comment: 38 pages, 7 tables, 3 figures, 1 SI attached as an ancillary fil

Many-Body Expanded Full Configuration Interaction. II. Strongly Correlated Regime

In this second part of our series on the recently proposed many-body expanded full configuration interaction (MBE-FCI) method, we introduce the concept of multideterminantal expansion references. Through theoretical arguments and numerical validations, the use of this class of starting points is shown to result in a focussed compression of the MBE decomposition of the FCI energy, thus allowing chemical problems dominated by strong correlation to be addressed by the method. The general applicability and performance enhancements of MBE-FCI are verified for standard stress tests such as the bond dissociations in H$_2$O, N$_2$, C$_2$, and a linear H$_{10}$ chain. Furthermore, the benefits of employing a multideterminantal expansion reference in accelerating calculations of high accuracy are discussed, with an emphasis on calculations in extended basis sets. As an illustration of this latter quality of the MBE-FCI method, results for H$_2$O and C$_2$ in basis sets ranging from double- to pentuple-$\zeta$ quality are presented, demonstrating near-ideal parallel scaling on up to almost $25000$ processing units.Comment: 41 pages, 4 tables, 10 figures, 1 SI attached as an ancillary fil

Virtual orbital many-body expansions: A possible route towards the full configuration interaction limit

In the present letter, it is demonstrated how full configuration interaction (FCI) results in extended basis sets may be obtained to within sub-kJ/mol accuracy by decomposing the energy in terms of many-body expansions in the virtual orbitals of the molecular system at hand. This extension of the FCI application range lends itself to two unique features of the current approach, namely that the total energy calculation can be performed entirely within considerably reduced orbital subspaces and may be so by means of embarrassingly parallel programming. Facilitated by a rigorous and methodical screening protocol and further aided by expansion points different from the Hartree-Fock solution, all-electron numerical results are reported for H$_2$O in polarized core-valence basis sets ranging from double-$\zeta$ (10 $e$, 28 $o$) to quadruple-$\zeta$ (10 $e$, 144 $o$) quality.Comment: 20 pages, 3 figures, 1 table. * With respect to the original arXiv version (v1), the present version of the letter contains updated results. The original TZ and QZ values were unfortunately in error due to a subtle PySCF bug, which has since then been fixe

A Second-Order CASSCF Algorithm with the Cholesky Decomposition of the Two-Electron Integrals

In this contribution, we present the implementation of a second-order CASSCF algorithm in conjunction with the Cholesky decomposition of the two-electron repulsion integrals. The algorithm, called Norm-Extended Optimization, guarantees convergence of the optimization, but it involves the full Hessian of the wavefunction and is therefore computationally expensive. Coupling the second-order procedure with the Cholesky decomposition leads to a significant reduction in the computational cost, reduced memory requirements, and an improved parallel performance. As a result, CASSCF calculations of larger molecular systems become possible as a routine task. The performance of the new implementation is illustrated by means of benchmark calculations on molecules of increasing size, with up to about 3000 basis functions and 14 active orbitals

Analytic evaluation of the dipole Hessian matrix in coupled-cluster theory

The general theory required for the calculation of analytic third energy derivatives at the coupled-cluster level of theory is presented and connected to preceding special formulations for hyperpolarizabilities and polarizability gradients. Based on our theory, we have implemented a scheme for calculating the dipole Hessian matrix in a fully analytical manner within the coupled-cluster singles and doubles approximation. The dipole Hessian matrix is the second geometrical derivative of the dipole moment and thus a third derivative of the energy. It plays a crucial role in IR spectroscopy when taking into account anharmonic effects and is also essential for computing vibrational corrections to dipole moments. The superior accuracy of the analytic evaluation of third energy derivatives as compared to numerical differentiation schemes is demonstrated in some pilot calculations