We have contributed to some of the new developments included in the latest release of the OpenMolcas electronic structure package
OpenMolcas is one of the leading electronic structure theory codes for the simulation of excited state processes with multiconfigurational wave functions. We contribute to this international collaboration, and in this release paper[1] we preview one of our latest implementations.
This paper release covers a very wide range of advances made by research groups worldwide contributing to the OpenMolcas software: from the latest implementation of analytic CASPT2 gradients and couplings, to advances in in-built molecular dynamics, novel interfaces to multiple programs enabling new functions, as well as the latest advances in full configuration interaction solvers and pair density functional theory approaches amongst others.
Our small contribution to this release[1] focusses on extending the implementation of the frozen natural orbital (FNO) approximation to the different multireference perturbation theory models available in OpenMolcas. Mostly used for single reference many body perturbation theories,[2] the FNO approach reduces the number of virtual orbitals retained during the perturbation step by removing those least contributing, i.e. in this case those with very small occupation numbers. This method was originally implemented within the context of Cholesky-decomposed (CD)-CASPT2 by Francesco Aquilante et al.,[3] and was further improved by myself, Marco Garavelli and Francesco to account for varying numbers of deleted virtual orbitals along a photochemical reaction pathway while retaining (an almost) constant amount of dynamic electron correlation throughout.[4] This was necessary for the application of FNO to photochemical problems, as swift changes in geometry are concomitant with vast rearrangements of the virtual space, which hampers the use of the standard implementation that removes a fixed number (or percentage) of the top virtual orbitals.[3]
Our work covered in this release paper relates specifically to the extension of the FNO approach to restricted active space self-consistent field (RASSCF) wave functions, leading to the FNO-RASPT2 method. In it we show how by using RASSCF wave functions with small involvement of RAS3 orbitals in the deleted orbital selection criterion, we need to introduce a renormalisation in the selection procedure via a level shift approach,[1] which removes singularities emerging due to intruder state-like behaviour in the denominators. We show how using this level shift does not affect the numerical outcome, and enables a more robust procedure for selecting deleted orbitals, particularly when considering restricted (or generalised) active spaces. The implementation follows our deletion criterion implemented for FNO-CASPT2,[4] and ensure smooth potential energy surfaces across multiple geometries enabling its use for photochemistry applications.
Ongoing work soon to be published will include more details on this novel FNO implementation, which we have also extended to generalised active space self-consistent field (GASSCF) wave functions and their second-order perturbation theory counterparts, facilitating also an implementation of the FNO-GASPT2 method. The FNO-RASPT2 code is readily available in OpenMolcas version 23 onwards, and an example input is provided in the supporting information of this article for those who might be interested in using it!
References
[1] G. Li Manni et al., "The OpenMolcas Web: A Community-Driven Approach to Advancing Computational Chemistry", J. Chem. Theory Comput. 2023, DOI:10.1021/acs.jctc.3c00182.
[2] A. G. Taube and R. J. Bartlett, "Frozen natural orbital coupled-cluster theory: Forces and application to decomposition of nitroethane", J. Chem. Phys. 2008, 128, 164101.
[3] F. Aquilante, T. K. Todorova, L. Gagliardi, T. B. Pedersen and B. O. Roos, "Systematic truncation of the virtual space in multiconfigurational perturbation theory", J. Chem. Phys. 2009, 131, 034113. [4] J. Segarra-Martí, M. Garavelli and F. Aquilante, "Multiconfigurational Second-Order Perturbation Theory with Frozen Natural Orbitals Extended to the Treatment of Photochemical Problems", J. Chem. Theory Comput. 2015, 11, 8, 3772–3784.