Related Experiment Video
Updated: Mar 29, 2026

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry
Published on: April 8, 2020
Quartic-Scaling Analytical Energy Gradient of Scaled Opposite-Spin Second-Order Møller-Plesset Perturbation Theory
Rohini C Lochan1, Yihan Shao1, Martin Head-Gordon1
1Department of Chemistry, University of California, Berkeley, California 94720, Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720 and Q-Chem, Inc., Pittsburgh, Pennsylvania 15213.
Abstract:
The analytical gradient of the "scaled opposite spin" (SOS-) and "modified opposite spin" (MOS-) second-order Møller-Plesset perturbation theory (MP2) methods is derived and implemented. Both energy and the first derivative can be evaluated efficiently with a fourth-order scaling algorithm by using a combination of auxiliary basis expansions and Laplace transformation techniques as opposed to the traditional fifth-order approach of MP2. A statistical analysis of 178 small molecules suggests that the new gradient scheme provides geometries of MP2 quality, indicating the reliability of the method in general chemical applications. A more specific study of the group VI transition metal carbonyl complexes indicates that the new scheme improves the MP2 description relative to available experimental data and higher-order theories. The proposed gradient scheme thus endeavors to obtain improved structural features at reduced computational cost.
Related Concept Videos
¹H NMR: Interpreting Distorted and Overlapping Signals
As Δν decreases and the signals move closer, the doublets appear increasingly distorted. The intensities of the inner lines increase at the cost of those of the outer lines as the signals are...
Scaling
The Pauli Exclusion Principle
Atomic Nuclei: Nuclear Spin State Overview
Molecular Orbital Theory II
Castigliano's Theorem

