1
|
Tyrcha B, Brzęk F, Żuchowski PS. Second quantization-based symmetry-adapted perturbation theory: Generalizing exchange beyond single electron pair approximation. J Chem Phys 2024; 160:044118. [PMID: 38295062 DOI: 10.1063/5.0184750] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/26/2023] [Accepted: 01/01/2024] [Indexed: 02/02/2024] Open
Abstract
This paper presents a general second-quantized form of a permutation operator interchanging n pairs of electrons between interacting subsystems in the framework of the symmetry-adapted perturbation theory (SAPT). We detail the procedure for constructing this operator through the consecutive multiplication of single-pair permutation operators. This generalized form of the permutation operator has enabled the derivation of universal formulas for S2n approximations of the exchange energies in the first and second order of the interaction operator. We present expressions for corrections of S4 approximations and assess its efficacy on a selection of systems anticipated to exhibit a slowly converging overlap expansion. Additionally, we outline a method to sum the overlap expansion series to infinity in second-quantization, up to the second order in V. This new approach offers an alternative to the existing formalism based on density-matrix formulations. When combined with a symbolic algebra program for automated derivations, it paves the way for advancements in SAPT theory, particularly for intricate wavefunction theories.
Collapse
Affiliation(s)
- Bartosz Tyrcha
- Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University in Toruń, Grudziądzka 5/7, 87-100 Toruń, Poland
| | - Filip Brzęk
- Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University in Toruń, Grudziądzka 5/7, 87-100 Toruń, Poland
| | - Piotr S Żuchowski
- Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University in Toruń, Grudziądzka 5/7, 87-100 Toruń, Poland
| |
Collapse
|
2
|
Derbali E, Ajili Y, Mehnen B, Żuchowski PS, Kędziera D, Al-Mogren MM, Jaidane NE, Hochlaf M. Towards the generation of potential energy surfaces of weakly bound medium-sized molecular systems: the case of benzonitrile-He complex. Phys Chem Chem Phys 2023; 25:30198-30210. [PMID: 37807943 DOI: 10.1039/d3cp02720a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/10/2023]
Abstract
Currently, the explicitly correlated coupled cluster method is used routinely to generate the multi-dimensional potential energy surfaces (mD-PESs) of van der Waals complexes of small molecular systems relevant for atmospheric, astrophysical and industrial applications. Although very accurate, this method is computationally prohibitive for medium and large molecules containing clusters. For instance, the recent detections of complex organic molecules (COMs) in the interstellar medium, such as benzonitrile, revealed the need to establish an accurate enough electronic structure approach to map the mD-PESs of these species interacting with the surrounding gases. As a benchmark, we have treated the case of the polar molecule benzonitrile interacting with helium, where we use post-Hartree-Fock and symmetry-adapted perturbation theory (SAPT) techniques. Accordingly, we show that MP2 and distinguishable-cluster approximation (DCSD) cannot be used for this purpose, whereas accurate enough PESs may be obtained using the corresponding explicitly correlated versions (MP2-F12 or DCSD-F12) with a reduction in computational costs. Alternatively, computations revealed that SAPT(DFT) is as performant as CCSD(T)-F12/aug-cc-pVTZ, making it the method of choice for mapping the mD-PESs of COMs containing clusters. Therefore, we have used this approach to generate the 3D-PES of the benzonitrile-He complex along the intermonomer Jacobi coordinates. As an application, we have incorporated the analytic form of this PES into quantum dynamical computations to determine the cross sections of the rotational (de-)excitation of benzonitrile colliding with helium at a collision energy of 10 cm-1.
Collapse
Affiliation(s)
- Eya Derbali
- Laboratoire de Spectroscopie Atomique, Moléculaire et Applications LSAMA, Université de Tunis Al Manar, Tunis, Tunisia.
| | - Yosra Ajili
- Laboratoire de Spectroscopie Atomique, Moléculaire et Applications LSAMA, Université de Tunis Al Manar, Tunis, Tunisia.
| | - Bilel Mehnen
- Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University in Toruń, Grudziadz Street 5, 87-100 Toruń, Poland
| | - Piotr S Żuchowski
- Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University in Toruń, Grudziadz Street 5, 87-100 Toruń, Poland
| | - Dariusz Kędziera
- Faculty of Chemistry, Nicolaus Copernicus University in Toruń, ul. Gagarina 7, PL 87-100 Toruń, Poland.
| | - Muneerah Mogren Al-Mogren
- Department of Chemistry, College of Sciences, King Saud University, PO Box 2455, Riyadh 11451, Saudi Arabia
| | - Nejm-Edine Jaidane
- Laboratoire de Spectroscopie Atomique, Moléculaire et Applications LSAMA, Université de Tunis Al Manar, Tunis, Tunisia.
| | - Majdi Hochlaf
- Université Gustave Eiffel, COSYS/IMSE, 5 Bd Descartes 77454, Champs sur Marne, France.
| |
Collapse
|
3
|
Luu D, Patkowski K. Overcoming Artificial Multipoles in Intramolecular Symmetry-Adapted Perturbation Theory. J Phys Chem A 2023; 127:356-377. [PMID: 36563050 DOI: 10.1021/acs.jpca.2c06465] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
Abstract
Intramolecular symmetry-adapted perturbation theory (ISAPT) is a method to compute and decompose the noncovalent interaction energy between two molecular fragments A and B covalently connected via a linker C. However, the existing ISAPT algorithm displays several issues for many fragmentation patterns (that is, specific assignments of atoms to the A/B/C subsystems), including an artificially repulsive electrostatic energy (even when the fragments are hydrogen-bonded) and very large and mutually cancelling induction and exchange-induction terms. We attribute those issues to the presence of artificial dipole moments at the interfragment boundary, as the atoms of A and B directly connected to C are missing electrons on one of their hybrid orbitals. Therefore, we propose several new partitioning algorithms which reassign one electron, on a singly occupied link hybrid orbital, from C to each of A/B. Once the contributions from these link orbitals are added to fragment density matrices, the computation of ISAPT electrostatic, induction, and dispersion energies proceeds exactly as normal, and the exchange energy expressions need only minor modifications. Among the link partitioning algorithms introduced, the so-called ISAPT(SIAO1) approach (in which the link orbital is obtained by a projection onto the intrinsic atomic orbitals (IAOs) of a given fragment followed by orthogonalization to this fragment's occupied space) leads to reasonable values of all ISAPT corrections for all fragmentation patterns, and exhibits a fast and systematic basis set convergence. This improvement is made possible by a significant reduction in magnitude (even though not a complete elimination) of the unphysical dipole moments at the interfragment boundaries. We demonstrate the utility of the improved ISAPT partitioning by examining intramolecular interactions in several pentanediol isomers, examples of linear and branched alkanes, and the open and closed conformations of a family of N-arylimide molecular torsion balances.
Collapse
Affiliation(s)
- Du Luu
- Department of Chemistry and Biochemistry, Auburn University, Auburn, Alabama 36849, United States
| | - Konrad Patkowski
- Department of Chemistry and Biochemistry, Auburn University, Auburn, Alabama 36849, United States
| |
Collapse
|
4
|
Szalewicz K, Jeziorski B. Physical mechanisms of intermolecular interactions from symmetry-adapted perturbation theory. J Mol Model 2022; 28:273. [PMID: 36006512 DOI: 10.1007/s00894-022-05190-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/28/2022] [Accepted: 05/12/2022] [Indexed: 10/15/2022]
Abstract
Symmetry-adapted perturbation theory (SAPT) is a method for computational studies of noncovalent interactions between molecules. This method will be discussed here from the perspective of establishing the paradigm for understanding mechanisms of intermolecular interactions. SAPT interaction energies are obtained as sums of several contributions. Each contribution possesses a clear physical interpretation as it results from some specific physical process. It also exhibits a specific dependence on the intermolecular separation R. The four major contributions are the electrostatic, induction, dispersion, and exchange energies, each due to a different mechanism, valid at any R. In addition, at large R, SAPT interaction energies are seamlessly connected with the corresponding terms in the asymptotic multipole expansion of interaction energy in inverse powers of R. Since such expansion explicitly depends on monomers' multipole moments and polarizabilities, this connection provides additional insights by rigorously relating interaction energies to monomers' properties.
Collapse
Affiliation(s)
- Krzysztof Szalewicz
- Department of Physics and Astronomy, University of Delaware, Newark, DE, 19716, USA.
| | - Bogumił Jeziorski
- Faculty of Chemistry, University of Warsaw, Pasteura 1, 02093, Warsaw, Poland
| |
Collapse
|
5
|
Hapka M, Przybytek M, Pernal K. Symmetry-Adapted Perturbation Theory Based on Multiconfigurational Wave Function Description of Monomers. J Chem Theory Comput 2021; 17:5538-5555. [PMID: 34517707 PMCID: PMC8444344 DOI: 10.1021/acs.jctc.1c00344] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
![]()
We present a formulation
of the multiconfigurational (MC) wave
function symmetry-adapted perturbation theory (SAPT). The method is
applicable to noncovalent interactions between monomers which require
a multiconfigurational description, in particular when the interacting
system is strongly correlated or in an electronically excited state.
SAPT(MC) is based on one- and two-particle reduced density matrices
of the monomers and assumes the single-exchange approximation for
the exchange energy contributions. Second-order terms are expressed
through response properties from extended random phase approximation
(ERPA). The dispersion components of SAPT(MC) have been introduced
in our previous works [HapkaM.J. Chem. Theory Comput.2019, 15, 1016−102730525591; HapkaM.J. Chem. Theory Comput.2019, 15, 6712–672331670950]. SAPT(MC) is applied either with generalized valence
bond perfect pairing (GVB) or with complete active space self-consistent
field (CASSCF) treatment of the monomers. We discuss two model multireference
systems: the H2 ··· H2 dimer
in out-of-equilibrium geometries and interaction between the argon
atom and excited state of ethylene. Using the C2H4* ··· Ar complex as an example, we examine second-order
terms arising from negative transitions in the linear response function
of an excited monomer. We demonstrate that the negative-transition
terms must be accounted for to ensure qualitative prediction of induction
and dispersion energies and develop a procedure allowing for their
computation. Factors limiting the accuracy of SAPT(MC) are discussed
in comparison with other second-order SAPT schemes on a data set of
small single-reference dimers.
Collapse
Affiliation(s)
- Michał Hapka
- Institute of Physics, Lodz University of Technology, ul. Wolczanska 219, 90-924 Lodz, Poland.,Faculty of Chemistry, University of Warsaw, ul. L. Pasteura 1, 02-093 Warsaw, Poland
| | - Michał Przybytek
- Faculty of Chemistry, University of Warsaw, ul. L. Pasteura 1, 02-093 Warsaw, Poland
| | - Katarzyna Pernal
- Institute of Physics, Lodz University of Technology, ul. Wolczanska 219, 90-924 Lodz, Poland
| |
Collapse
|
6
|
Naseem-Khan S, Gresh N, Misquitta AJ, Piquemal JP. Assessment of SAPT and Supermolecular EDA Approaches for the Development of Separable and Polarizable Force Fields. J Chem Theory Comput 2021; 17:2759-2774. [DOI: 10.1021/acs.jctc.0c01337] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Sehr Naseem-Khan
- Laboratoire de Chimie Théorique, Sorbonne Université, UMR 7616 CNRS, 75005 Paris, France
| | - Nohad Gresh
- Laboratoire de Chimie Théorique, Sorbonne Université, UMR 7616 CNRS, 75005 Paris, France
| | - Alston J. Misquitta
- School of Physics and Astronomy and the Thomas Young Centre for Theory and Simulation of Materials at Queen Mary University of London, London E1 4NS, U.K
| | - Jean-Philip Piquemal
- Laboratoire de Chimie Théorique, Sorbonne Université, UMR 7616 CNRS, 75005 Paris, France
- Institut Universitaire de France, 75005 Paris, France
- Department of Biomedical Engineering, The University of Texas at Austin, Austin, Texas 78712, United States
| |
Collapse
|