Combining explicitly correlated R12 and Gaussian geminal electronic structure theories

Gaussians for Electronic and Rovibrational Quantum Dynamics

The assumptions underpinning the adiabatic Born-Oppenheimer (BO) approximation are broken for molecules interacting with attosecond laser pulses, which generate complicated coupled electronic-nuclear wave packets that generally will have components of electronic and dissociation continua as well as bound-state contributions. The conceptually most straightforward way to overcome this challenge is to treat the electronic and nuclear degrees of freedom on equal quantum-mechanical footing by not invoking the BO approximation at all. Explicitly correlated Gaussian (ECG) basis functions have proved successful for non-BO calculations of stationary molecular states and energies, reproducing rovibrational absorption spectra with very high accuracy. In this Article, we present a proof-of-principle study of the ability of fully flexible ECGs (FFECGs) to capture the intricate electronic and rovibrational dynamics generated by short, high-intensity laser pulses. By fitting linear combinations of FFECGs to accurate wave function histories obtained on a large real-space grid for a regularized 2D model of the hydrogen atom and for the 2D Morse potential, we demonstrate that FFECGs provide a very compact description of laser-driven electronic and rovibrational dynamics.

Explicitly Correlated Dispersion and Exchange Dispersion Energies in Symmetry-Adapted Perturbation Theory

The individual interaction energy terms in symmetry-adapted perturbation theory (SAPT) not only have different physical interpretations but also converge to their complete basis set (CBS) limit values at quite different rates. Dispersion energy is notoriously the slowest converging interaction energy contribution, and exchange dispersion energy, while smaller in absolute value, converges just as poorly in relative terms. To speed up the basis set convergence of the lowest-order SAPT dispersion and exchange dispersion energies, we borrow the techniques from explicitly correlated (F12) electronic structure theory and develop practical expressions for the closed-shell E_disp⁽²⁰⁾-F12 and E_exch-disp⁽²⁰⁾-F12 contributions. While the latter term has been derived and implemented for the first time, the former correction was recently proposed by Przybytek [ J. Chem. Theory Comput. 2018 , 14 , 5105 - 5117 ] using an Ansatz with a full optimization of the explicitly correlated amplitudes. In addition to reimplementing the fully optimized variant of E_disp⁽²⁰⁾-F12, we propose three approximate Ansätze that substantially improve the scaling of the method and at the same time avoid the numerical instabilities of the unrestricted optimization. The performance of all four resulting flavors of E_disp⁽²⁰⁾-F12 and E_exch-disp⁽²⁰⁾-F12 is first tested on helium, neon, argon, water, and methane dimers, with orbital and auxiliary basis sets up to aug-cc-pV5Z and aug-cc-pV5Z-RI, respectively. The double- and triple-ζ basis set calculations are then extended to the entire A24 database of noncovalent interaction energies and compared with CBS estimates for E_disp⁽²⁰⁾ and E_exch-disp⁽²⁰⁾ computed using conventional SAPT with basis sets up to aug-cc-pV6Z with midbond functions. It is shown that the F12 treatment is highly successful in improving the basis set convergence of the SAPT terms, with the F12 calculations in an X-tuple ζ basis about as accurate as conventional calculations in bases with cardinal numbers (X + 2) for E_disp⁽²⁰⁾ and either (X + 1) or (X + 2) for E_exch-disp⁽²⁰⁾. While the full amplitude optimization affords the highest accuracy for both corrections, the much simpler and numerically stable optimized diagonal Ansatz is a very close second. We have also tested the performance of the simple F12 correction based on the second-order Møller-Plesset perturbation theory, SAPT-F12(MP2) [ Frey , J. A. ; Chem. Rev. 2016 , 116 , 5614 - 5641 ] and observed that it is also quite successful in speeding up the basis set convergence of conventional E_disp⁽²⁰⁾ + E_exch-disp⁽²⁰⁾, albeit with some outliers.

Explicitly correlated orbital optimized contracted pair correlation methods: Foundations and applications

Pair correlation methods are able to achieve highly accurate solutions for chemical problems. Unfortunately, their applicability is generally restricted to medium-sized molecules due to storage requirements and computational costs. These restrictions can be partly overcome by local correlation methods. These methods use physical and mathematical criteria to decide which interactions are of such a long range that they do not have to be computed and saved. In our new ansatz, we define an alternative way towards local correlation. The range of interactions is strictly bound to the decay of integrals over Gaussian type geminals in the atomic orbital basis. The number of variables is reduced by orders of magnitude applying an efficient contraction scheme, leading to a naturally local representation of correlation effects. This scheme is extended by orbital optimization to describe multi-reference problems and explicit correlation to improve the basis set convergence.

Calculation of electron-hole recombination probability using explicitly correlated Hartree-Fock method

The electron-hole explicitly correlated Hartree-Fock method (eh-XCHF) is presented as a general strategy for investigation of electron-hole correlation and computation of electron-hole recombination probability. The eh-XCHF method is a variational method which uses explicitly correlated wavefunction that depends on the electron-hole inter-particle distances. It is shown that the explicitly correlated ansatz provides a systematic route to variationally minimize the total energy. The parabolic quantum dot is used as the benchmark system and the eh-XCHF method is used for computation of the ground state energy and electron-hole recombination probability. The results are compared to Hartree-Fock and explicitly correlated full configuration interaction (R12-FCI) calculations. The results indicate that an accurate description of the electron-hole wavefunction at short electron-hole inter-particle distances is crucial for qualitative description of the electron-hole recombination probability. The eh-XCHF method successfully addresses this issue and comparison of eh-XCHF calculations with R12-FCI shows good agreement. The quality of the mean field approximation for electron-hole system is also investigated by comparing HF and R12-FCI energies for electron-electron and electron-hole systems. It was found that performance of the mean field approximation is worse for the electron-hole system as compared to the corresponding electron-electron system.

Benchmark Studies for Explicitly Correlated Perturbation- and Coupled Cluster Theories. javascript:filterformular(´3´)

The recently developed explicitly correlated MP2-F12 and CCSD(T)-F12x (x = a,b) methods are reviewed. The explicit correlation treatment leads to a dramatic improvement of the basis set convergence. Extensive benchmarks for reaction energies, atomization energies, electron affinities, ionization potentials, equilibrium structures, vibrational frequencies, and intermolecular interaction energies are presented which show that for many molecular properties the intrinsic accuracy of the CCSD(T) method is already reached with double-zeta (VDZ-F12) basis sets, while triple-zeta (VTZ-F12) basis sets yield results that are very close to the complete basis set limit. The steep scaling of the MP2-F12 method with molecular size can be reduced by local approximations. This has made it possible to carry out MP2-F12 calculations for molecules with up to 100 atoms. The errors caused bjavascript:filterformular(´3´)y the local domain approximation are largely removed by the explicitly correlated terms, which account for the neglected configurations in an approximate way. Extensions to LCCSD(T)-F12 are discussed and preliminary results for LCCSD-F12 are presented.

Accurate calculations of intermolecular interaction energies using explicitly correlated wave functions

Explicitly correlated second-order Møller-Plesset (MP2-F12) calculations of intermolecular interaction energies for the S22 benchmark set of Jurecka, Sponer, Cerný, and Hobza (Chem. Phys. Phys. Chem. 2006, 8, 1985) are presented and compared with standard MP2 results. The MP2 complete basis set limits are estimated using basis set extrapolation and augmented quadruple-zeta and quintuple-zeta basis sets. Already with augmented double-zeta basis sets the MP2-F12 interaction energies are found to be closer to the complete basis set limits than standard MP2 calculations with augmented quintuple-zeta basis sets. Various possible approximations in the MP2-F12 method are systematically tested. Best results are obtained with localized orbitals and the diagonal MP2-F12/C(D) ansatz. Hybrid approximations, in which some contributions of the auxiliary basis set are neglected and which considerably reduce the computational cost, have a negligible effect on the interaction energies. Also the orbital-invariant fixed-amplitude approximation of Ten-no leads to only slightly less accurate results. Preliminary results for the neon and benzene dimers, obtained with the recently proposed CCSD(T)-F12a approximation, indicate that the CCSD(T) basis set limits can also be very closely approached using augmented triple-zeta basis sets.