A comparison of linear and nonlinear correlation factors for basis set limit Møller-Plesset second order binding energies and structures of He2, Be2, and Ne2

Cluster-in-Molecule Approach with Explicitly Correlated Methods for Large Molecules

In this article, we present a series of explicitly correlated local correlation methods developed under the cluster-in-molecule (CIM) framework, including explicitly correlated second-order Møller-Plesset perturbation (MP2), coupled-cluster singles and doubles (CCSD), domain-based local pair natural orbital CCSD (DLPNO-CCSD), and DLPNO-CCSD with perturbative triples (DLPNO-CCSD(T)). In these methods, F12 correction is decomposed into contributions from each occupied local molecular orbital and then evaluated independently in a given cluster, which consists of a subset of localized orbitals. These newly developed methods allow F12 calculations of large molecules (up to 145 atoms for quasi-one-dimensional systems) on a single node. We use these methods to investigate the relative stability between extended and folded alkane C30H62, the relative stability of four secondary structures of a polyglycine Ace(Gly)10NH2, and the binding energies of two host-guest complexes. The results demonstrate that the combination of CIM with F12 methods is a promising way to investigate large molecules with small basis set errors.

Nonunitary projective transcorrelation theory inspired by the F12 ansatz

An alternative nonunitary transcorrelation, inspired by the F12 ansatz, is investigated. In contrast to the Jastrow transcorrelation of Boys-Handy, the effective Hamiltonian of this projective transcorrelation features: 1. a series terminating formally at four-body interactions. 2. no spin-contamination within the non-relativistic framework. 3. simultaneous satisfaction of the singlet and triplet first-order cusp conditions. 4. arbitrary choices of pairs for correlation including frozen-core approximations. We discuss the connection between the projective transcorrelation and F12 theory with applications to small molecules, to show that the cusp conditions play an important role to reduce the uncertainty arising from the nonunitary transformation.

Efficient Density-Fitted Explicitly Correlated Dispersion and Exchange Dispersion Energies

The leading-order dispersion and exchange-dispersion terms in symmetry-adapted perturbation theory (SAPT), E_disp⁽²⁰⁾ and E_exch-disp⁽²⁰⁾, suffer from slow convergence to the complete basis set limit. To alleviate this problem, explicitly correlated variants of these corrections, E_disp⁽²⁰⁾-F12 and E_exch-disp⁽²⁰⁾-F12, have been proposed recently. However, the original formalism (M., Kodrycka , J. Chem. Theory Comput. 2019, 15, 5965-5986), while highly successful in terms of improving convergence, was not competitive to conventional orbital-based SAPT in terms of computational efficiency due to the need to manipulate several kinds of two-electron integrals. In this work, we eliminate this need by decomposing all types of two-electron integrals using robust density fitting. We demonstrate that the error of the density fitting approximation is negligible when standard auxiliary bases such as aug-cc-pVXZ/MP2FIT are employed. The new implementation allowed us to study all complexes in the A24 database in basis sets up to aug-cc-pV5Z, and the E_disp⁽²⁰⁾-F12 and E_exch-disp⁽²⁰⁾-F12 values exhibit vastly improved basis set convergence over their conventional counterparts. The well-converged E_disp⁽²⁰⁾-F12 and E_exch-disp⁽²⁰⁾-F12 numbers can be substituted for conventional E_disp⁽²⁰⁾ and E_exch-disp⁽²⁰⁾ ones in a calculation of the total SAPT interaction energy at any level (SAPT0, SAPT2+3, ...). We show that the addition of F12 terms does not improve the accuracy of low-level SAPT treatments. However, when the theory errors are minimized in high-level SAPT approaches such as SAPT2+3(CCD)δMP2, the reduction of basis set incompleteness errors thanks to the F12 treatment substantially improves the accuracy of small-basis calculations.

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.

Ab initio instanton rate theory made efficient using Gaussian process regression

Ab initio instanton rate theory is a computational method for rigorously including tunnelling effects into the calculations of chemical reaction rates based on a potential-energy surface computed on the fly from electronic-structure theory. This approach is necessary to extend conventional transition-state theory into the deep-tunnelling regime, but it is also more computationally expensive as it requires many more ab initio calculations. We propose an approach which uses Gaussian process regression to fit the potential-energy surface locally around the dominant tunnelling pathway. The method can be converged to give the same result as from an on-the-fly ab initio instanton calculation but it requires far fewer electronic-structure calculations. This makes it a practical approach for obtaining accurate rate constants based on high-level electronic-structure methods. We show fast convergence to reproduce benchmark H + CH4 results and evaluate new low-temperature rates of H + C2H6 in full dimensionality at a UCCSD(T)-F12b/cc-pVTZ-F12 level.

Explicitly Correlated Orbital Optimized Contracted Pair Correlation Methods: A Short Overview

Designing efficient algorithms to apply highly accurate pair correlation methods to large molecules of scientific interest has remained an important field of research for a long period of time. We present a new approach toward fast algorithms, which represents an interesting alternative and extension to currently existing methods. The presented new contraction scheme saves a significant amount of memory and can be easily combined with efficient linear scaling algorithms. Additionally, the extension to orbital optimization and explicitly correlated f₁₂-theory is demonstrated to further improve accuracy and applicablility.

Explicitly correlated second-order Møller-Plesset perturbation theory employing pseudospectral numerical quadratures

We implemented explicitly correlated second-order Møller-Plesset perturbation theory with numerical quadratures using pseudospectral construction of grids. Introduction of pseudospectral approach for the calculation of many-electron integrals gives a possibility to use coarse grids without significant loss of precision in correlation energies, while the number of points in the grid is reduced about nine times. The use of complementary auxiliary basis sets as the sets of dealiasing functions is justified at both theoretical and computational levels. Benchmark calculations for a set of 16 molecules have shown the possibility to keep an error of second-order correlation energies within 1 milihartree (mH) with respect to MP2-F12 method with dense grids. Numerical tests for a set of 13 isogyric reactions are also performed.

The MP2-F12 method in the Turbomole program package

A detailed description of the explicitly correlated second-order Møller-Plesset perturbation theory (MP2-F12) method, as implemented in the TURBOMOLE program package, is presented. The TURBOMOLE implementation makes use of density fitting, which greatly reduces the prefactor for integral evaluation. Methods are available for the treatment of ground states of open- and closed-shell species, using unrestricted as well as restricted (open-shell) Hartree-Fock reference determinants. Various methodological choices and approximations are discussed. The performance of the TURBOMOLE implementation is illustrated by example calculations of the molecules leflunomide, prednisone, methotrexate, ethylenedioxytetrafulvalene, and a cluster model for the adsorption of methanol on the zeolite H-ZSM-5. Various basis sets are used, including the correlation-consistent basis sets specially optimized for explicitly correlated calculations (cc-pVXZ-F12).

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.

Simplified CCSD(T)-F12 methods: theory and benchmarks

The simple and efficient CCSD(T)-F12x approximations (x = a,b) we proposed in a recent communication [T. B. Adler, G. Knizia, and H.-J. Werner, J. Chem. Phys. 127, 221106 (2007)] are explained in more detail and extended to open-shell systems. Extensive benchmark calculations are presented, which demonstrate great improvements in basis set convergence for a wide variety of applications. These include reaction energies of both open- and closed-shell reactions, atomization energies, electron affinities, ionization potentials, equilibrium geometries, and harmonic vibrational frequencies. For all these quantities, results better than the AV5Z quality are obtained already with AVTZ basis sets, and usually AVDZ treatments reach at least the conventional AVQZ quality. For larger molecules, the additional cost for these improvements is only a few percent of the time for a standard CCSD(T) calculation. For the first time ever, total reaction energies with chemical accuracy are obtained using valence-double-zeta basis sets.