Explicitly correlated PNO-MP2 and PNO-CCSD and their application to the S66 set and large molecular systems

Abstract

We present our current progress on the combination of explicit electron correlation with the pair natural orbital (PNO) representation. In particular we show cubic scaling PNO-MP2-F12, and PNO-CCSD[F12] implementations. The PNOs are constructed using a hybrid scheme, where the PNOs are generated in a truncated doubles space, spanned by orbital specific virtuals obtained using an iterative eigenvector algorithm. We demonstrate the performance of our implementation through calculations on a series of glycine chains. The accuracy of the local approximations is assessed using the S66 benchmark set, and we report for the first time explicitly correlated CCSD results for the whole set and improved estimates for the CCSD/CBS limits. For several dimers the PNO-CCSD[F12] calculations are more accurate than the current reference values. Additionally, we present pilot applications of our PNO-CCSD[F12] code to host-guest interactions in a cluster model for zeolite H-ZSM-5 and in a calix[4]arene-water complex.

Perspective: Explicitly correlated electronic structure theory for complex systems

“…One major technical challenge is to avoid different many-electron integrals in explicitly correlated theories, as these are expensive, increasing the computational cost compared with their parent methods for electron correlation. Many promising approaches to overcome these problems have already been proposed for large or periodic systems, including Monte Carlo techniques, 115,116 local explicitly correlated methods, 136,145,146 and plane wave basis set techniques. 44,121 These methods exhibit a trade-off between computational cost and accuracy that is strongly dependent on the system size, dimensionality, and possibly the band gap.…”

“…143 Independently, Hättig, Tew, and co-workers developed a hybrid OSV-PNO scheme for F12 using auxiliary PNOs (X-PNOs) and reported PNO-CC-F12 implementations. 144,145 The recent development of the domain-based local PNO MP2-F12 (DLPNO-MP2-F12) for the O(N) scaling exhibits subquadratic scaling for quasi one-dimensional n-alkanes. 146 All of these implementations employ DF in their local representations to reduce the computational cost and memory requirement.…”

Communication: Improved pair approximations in local coupled-cluster methods

“…The errors caused by weak pair approximations were assumed to be small since the pair correlation energies decay as r −6 i j with the distance r i j between the charge centroids of the local orbitals φ i and φ j . However, this situation has changed, since with modern pair natural orbital (PNO) approaches, [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25] the domain error can be systematically controlled and made very small (<1 kJ mol −1 for relative energies), in particular when explicitly correlated terms are included. 5,12,25,26 On the other hand, we demonstrate in the current work that pair approximations based on local second-order Møller-Plesset theory (LMP2) can lead to very large errors (up to ≈ 40 kJ mol −1 in the present examples) for reaction and activation energies of complex chemical reactions.…”

“…In practice, non-orthogonal virtual orbitals [projected atomic orbitals (PAOs), [1][2][3][4] orbital specific virtuals (OSVs), [41][42][43] or PNOs [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25] ] are used, which leads to additional contractions with overlap matrices, but the general arguments are not affected.…”

Experimental and Theoretical Determination of Dissociation Energies of Dispersion-Dominated Aromatic Molecular Complexes

“…Also various explicitly-correlated variants of (PNO-based) local correlation methods have been implemented. 101,[104][105][106][107][108] In view of the progress made in recent years, one is tempted to conclude that basically from today on, explicitlycorrelated -that is, near complete-basis-set limit -CCSD(T) calculations can be performed with computational effort (computation time and other computer resources) that scales linearly with the size of the molecular system. This would render more approximate and much less accurate approaches redundant, except perhaps for optimizing the required equilibrium structures as long as analytical nuclear gradients have not yet been implemented for the (explicitly-correlated) PNO-based LCC methods.…”