Enabling ab initio Hessian and frequency calculations of large molecules

Abstract

A linear scaling method, termed as cardinality guided molecular tailoring approach, is applied for the estimation of the Hessian matrix and frequency calculations of spatially extended molecules. The method is put to test on a number of molecular systems largely employing the Hartree-Fock and density functional theory for a variety of basis sets. To demonstrate its ability for correlated methods, we have also performed a few test calculations at the Moller-Plesset second order perturbation theory. A comparison of central processing unit and memory requirements for medium-sized systems with those for the corresponding full ab initio computation reveals substantial gains with negligible loss of accuracy. The technique is further employed for a set of larger molecules, Hessian and frequency calculations of which are not possible on commonly available personal-computer-type hardware.

Molecular tailoring approach in conjunction with MP2 and Ri‐MP2 codes: A comparison with fragment molecular orbital method

“…In fact, in this work, Kohn prophesied that the DC-type methods would be applicable, within the following few years, to systems comprising of 10 3 to 10 5 atoms. Since 1994, Gadre and coworkers have independently developed the Molecular Tailoring Approach (MTA), [31][32][33][34][35][36] initially for molecular property evaluation and later for geometry optimization as well as Hessian calculation, along with its parallel implementation. MTA is based on DC-type of algorithm, which is built around a locally modified version of public domain ab initio quantum chemistry package GAMESS.…”

“…Earlier benchmarks have showed that a scheme with minimum R g in range 3-4 Å , scaling factor less than 3 is generally good enough for reliable results for spatially extended molecules with minimal computational efforts. [32][33][34][35][36] Details of MTA, determination of R g value for atoms as well as for the scheme, correlation of R g with accuracy of the scheme, cardinality based equations for patching fragment-energies, etc., are discussed in detail in references. [34][35] After fragmentation, cardinality based expressions 34,35 for energy and gradients are set up.…”

“…2 The details of the algorithm are given elsewhere. [31][32][33][34][35][36] MTA cuts a spatially extended large molecule into a set of small, overlapping fragments. While fragmenting, sensitive structures such as planar rings, multiple bonds are kept intact.…”

Analytic second derivative of the energy for density functional theory based on the three-body fragment molecular orbital method

“…[26][27][28] Some fragment based approaches [29][30][31][32][33][34][35][36][37][38][39][40] feature analytic second derivatives. [41][42][43][44][45][46] The fragment molecular orbital (FMO) method [47][48][49][50][51] is a fragment-based approach. In the FMO method, the system is divided into a set of fragments (also called monomers).…”

The role of the exchange in the embedding electrostatic potential for the fragment molecular orbital method

“…Recently, a large number of fragment-based methods [1][2][3][4][5][6][7][8][9][10] have been suggested in order to facilitate computing large systems with quantum-mechanical methods. The fragment molecular orbital ͑FMO͒ [11][12][13] method is based on dividing the system into pieces ͑fragments͒ and performing ab initio calculations on fragments, their pairs, and, optionally, triples.…”