Frozen natural orbital coupled-cluster theory: Forces and application to decomposition of nitroethane

Abstract

The frozen natural orbital ͑FNO͒ coupled-cluster method increases the speed of coupled-cluster ͑CC͒ calculations by an order of magnitude with no consequential error along a potential energy surface. This method allows the virtual space of a correlated calculation to be reduced by about half, significantly reducing the time spent performing the coupled-cluster ͑CC͒ calculation. This paper reports the derivation and implementation of analytical gradients for FNO-CC, including all orbital relaxation for both noncanonical and semicanonical perturbed orbitals. These derivatives introduce several new orbital relaxation contributions to the CC density matrices. FNO-CCSD͑T͒ and FNO-⌳CCSD͑T͒ are applied to a test set of equilibrium structures, verifying that these methods are capable of reproducing geometries and vibrational frequencies accurately, as well as energies. Several decomposition pathways of nitroethane are investigated using CCSD͑T͒ and ⌳CCSD͑T͒ with 60% of the FNO virtual orbitals in a cc-pVTZ basis, and find differences on the order of 5 kcal/ mol with reordering of the transition state energies when compared to B3LYP 6-311 +G͑3df ,2p͒.

At What Chain Length Do Unbranched Alkanes Prefer Folded Conformations?

“…Therefore we opted for an approximate treatment using the CCSD FNO(T) virtual space truncation scheme. 19,20 Numerical tests show that an occupation number threshold of 1×10 −4 is sufficient to drop approximately 40% of the virtual space while retaining ∼ 0.1 kcal/mol accuracy compared to the full virtual space result, as illustrated in Table II. Because of the size extensivity of these many-body methods this error grows very slowly with the number of electrons, reaching 0.15 kcal/mol at chain lengths of n = 14.…”

“…In order to alleviate the cost of including triples it is possible to truncate the virtual space by some amount p, providing a p 4 prefactor which can enable larger calculations to be done. To do so systematically and unambiguously we use the frozen natural orbital (FNO) method 19,20 which uses the MP2 density matrix to make new virtual orbitals. The Hartree-Fock virtual orbitals can then be replaced with the appropriately transformed MP2 virtual natural orbitals, resulting in a set of virtual orbitals sorted by their contribution to the correlation energy.…”

Communication: Resolving the three-body contribution to the lattice energy of crystalline benzene: Benchmark results from coupled-cluster theory

“…The aug-ccpVDZ-JKFIT 35 was used for the DF-SCF procedure, and the aug-cc-pVDZ-MP2FIT 42 basis was used for the DF-MP2 computations. CCSD(T) computations utilized CD [43][44][45][46][47] with a tolerance of 10 −4 , and they were also accelerated with Frozen Natural Orbitals [48][49][50][51][52][53] (FNOs), truncating at a very conservative 53 natural orbital occupation of 10 −7 . With this cutoff, the FNO approximation led to errors on the order of 10 −4 kcal mol −1 for the trimers with the largest three-body contributions.…”

The orbital-specific-virtual local coupled cluster singles and doubles method

“…The canonical amplitudes can then be approximated as in Eqs. (22) and (23). The OSVs for a given LMO are orthonormal, but OSVs for different LMOs are non-orthogonal.…”

“…Matrix factorizations, such as the Cholesky decomposition, and density fitting (DF) [some-times also called resolution of the identity] (Refs. [3][4][5][6][7][8][9][10][11][12][13][14][15] are obvious examples, but methods which define new occupied and virtual orbital sets, such as the projected atomic orbital (PAO), [16][17][18][19][20] frozen natural orbital, [21][22][23][24][25] and pair natural orbital (PNO) (Refs. [26][27][28][29][30][31][32][33] methods, can also be understood in this mathematical language.…”