DMRG-CASPT2 study of the longitudinal static second hyperpolarizability of all-trans polyenes

TL;DR

This study implements DMRG-CASPT2 to accurately compute the second hyperpolarizability of all-trans polyenes, revealing lower values and different scaling behavior than traditional methods, thus advancing computational techniques for nonlinear optical properties.

Contribution

The paper introduces an implementation of DMRG-CASPT2 using spin-adapted matrix product states to compute high-order response properties of conjugated molecules.

Findings

DMRG-CASPT2 yields lower hyperpolarizability values than RHF and MP2.

The method shows different size-scaling behavior compared to traditional approaches.

Application to polyenes demonstrates improved accuracy for nonlinear optical property calculations.

Abstract

We have implemented internally contracted complete active space second order perturbation theory (CASPT2) with the density matrix renormalization group (DMRG) as active space solver [Y. Kurashige and T. Yanai, J. Chem. Phys. 135, 094104 (2011)]. Internally contracted CASPT2 requires to contract the generalized Fock matrix with the 4-particle reduced density matrix (4-RDM) of the reference wavefunction. The required 4-RDM elements can be obtained from 3-particle reduced density matrices (3-RDM) of different wavefunctions, formed by symmetry-conserving single-particle excitations op top of the reference wavefunction. In our spin-adapted DMRG code chemps2 [https://github.com/sebwouters/chemps2], we decompose these excited wavefunctions as spin-adapted matrix product states, and calculate their 3-RDM in order to obtain the required contraction of the generalized Fock matrix with the 4-RDM of the reference wavefunction. In this work, we study the longitudinal static second hyperpolarizability of all-trans polyenes C$_{2n}$H$_{2n+2}$ [n = 4 - 12] in the cc-pVDZ basis set. DMRG-SCF and DMRG-CASPT2 yield substantially lower values and scaling with system size compared to RHF and MP2, respectively.