Role of Spin Polarization and Dynamic Correlation in Singlet-Triplet Gap Inversion of Heptazine Derivatives

The new generation of proposed light-emitting molecules for organic light-emitting diodes (OLEDs) has raised considerable research interest due to its exceptional feature─a negative singlet-triplet (ST) gap violating Hund's multiplicity rule in the excited S1 and T1 states. We investigate the role of spin polarization in the mechanism of ST gap inversion. Spin polarization is associated with doubly excited determinants of certain types, whose presence in the wave function expansion favors the energy of the singlet state more than that of the triplet. Using a perturbation theory-based model for spin polarization, we propose a simple descriptor for prescreening of candidate molecules with negative ST gaps and prove its usefulness for heptazine-type molecules. Numerical results show that the quantitative effect of spin polarization decreases linearly with the increasing highest occupied molecular orbital-lowest unoccupied molecular orbital (HOMO-LUMO) exchange integral. Comparison of single- and multireference coupled-cluster predictions of ST gaps shows that the former methods provide good accuracy by correctly balancing the effects of doubly excited determinants and dynamic correlation. We also show that accurate ST gaps may be obtained using a complete active space model supplemented with dynamic correlation from multireference adiabatic connection theory.

Efficient Calculation of the Dispersion Energy for Multireference Systems with Cholesky Decomposition: Application to Excited-State Interactions

Accurate and efficient prediction of dispersion interactions in excited-state complexes poses a challenge due to the complex nature of electron correlation effects that need to be simultaneously considered. We propose an algorithm for computing the dispersion energy in nondegenerate ground- or excited-state complexes with arbitrary spin. The algorithm scales with the fifth power of the system size due to employing Cholesky decomposition of Coulomb integrals and a recently developed recursive formula for density response functions of the monomers. As a numerical illustration, we apply the new algorithm in the framework of multiconfigurational symmetry adapted perturbation theory, SAPT(MC), to study interactions in dimers with localized excitons. The SAPT(MC) analysis reveals that the dispersion energy may be the main force stabilizing excited-state dimers.

TREXIO: A file format and library for quantum chemistry

TREXIO is an open-source file format and library developed for the storage and manipulation of data produced by quantum chemistry calculations. It is designed with the goal of providing a reliable and efficient method of storing and exchanging wave function parameters and matrix elements, making it an important tool for researchers in the field of quantum chemistry. In this work, we present an overview of the TREXIO file format and library. The library consists of a front-end implemented in the C programming language and two different back-ends: a text back-end and a binary back-end utilizing the hierarchical data format version 5 library, which enables fast read and write operations. It is compatible with a variety of platforms and has interfaces for Fortran, Python, and OCaml programming languages. In addition, a suite of tools have been developed to facilitate the use of the TREXIO format and library, including converters for popular quantum chemistry codes and utilities for validating and manipulating data stored in TREXIO files. The simplicity, versatility, and ease of use of TREXIO make it a valuable resource for researchers working with quantum chemistry data.

Toward more accurate adiabatic connection approach for multireference wavefunctions

A multiconfigurational adiabatic connection (AC) formalism is an attractive approach to compute the dynamic correlation within the complete active space self-consistent field and density matrix renormalization group (DMRG) models. Practical realizations of AC have been based on two approximations: (i) fixing one- and two-electron reduced density matrices (1- and 2-RDMs) at the zero-coupling constant limit and (ii) extended random phase approximation (ERPA). This work investigates the effect of removing the "fixed-RDM" approximation in AC. The analysis is carried out for two electronic Hamiltonian partitionings: the group product function- and the Dyall Hamiltonians. Exact reference AC integrands are generated from the DMRG full configuration interaction solver. Two AC models are investigated, employing either exact 1- and 2-RDMs or their second-order expansions in the coupling constant in the ERPA equations. Calculations for model molecules indicate that lifting the fixed-RDM approximation is a viable way toward improving the accuracy of existing AC approximations.

Efficient Adiabatic Connection Approach for Strongly Correlated Systems: Application to Singlet-Triplet Gaps of Biradicals

Strong electron correlation can be captured with multireference wave function methods, but an accurate description of the electronic structure requires accounting for the dynamic correlation, which they miss. In this work, a new approach for the correlation energy based on the adiabatic connection (AC) is proposed. The AC_n method accounts for terms up to order n in the coupling constant, and it is size-consistent and free from instabilities. It employs the multireference random phase approximation and the Cholesky decomposition technique, leading to a computational cost growing with the fifth power of the system size. Because of the dependence on only one- and two-electron reduced density matrices, AC_n is more efficient than existing ab initio multireference dynamic correlation methods. AC_n affords excellent results for singlet-triplet gaps of challenging organic biradicals. The development presented in this work opens new perspectives for accurate calculations of systems with dozens of strongly correlated electrons.

Dispersion Interactions in Exciton-Localized States. Theory and Applications to π-π* and n-π* Excited States

We address the problem of intermolecular interaction energy calculations in molecular complexes with localized excitons. Our focus is on the correct representation of the dispersion energy. We derive an extended Casimir-Polder formula for direct computation of this contribution through second order in the intermolecular interaction operator V̂. An alternative formula, accurate to infinite order in V̂, is derived within the framework of the adiabatic connection (AC) theory. We also propose a new parametrization of the VV10 nonlocal correlation density functional, so that it corrects the CASSCF energy for the dispersion contribution and can be applied to excited-state complexes. A numerical investigation is carried out for benzene, pyridine, and peptide complexes with the local exciton corresponding to the lowest π–π* or n– π* states. The extended Casimir-Polder formula is implemented in the framework of multiconfigurational symmetry-adapted perturbation theory, SAPT(MC). A SAPT(MC) analysis shows that the creation of a localized exciton affects mostly the electrostatic component of the interaction energy of investigated complexes. Nevertheless, the changes in Pauli repulsion and dispersion energies cannot be neglected. We verify the performance of several perturbation- and AC-based methods. Best results are obtained with a range-separated variant of an approximate AC approach employing extended random phase approximation and CASSCF wave functions.

Density Matrix Renormalization Group with Dynamical Correlation via Adiabatic Connection

The quantum chemical version of the density matrix renormalization group (DMRG) method has established itself as one of the methods of choice for calculations of strongly correlated molecular systems. Despite its great ability to capture strong electronic correlation in large active spaces, it is not suitable for computations of dynamical electron correlation. In this work, we present a new approach to the electronic structure problem of strongly correlated molecules, in which DMRG is responsible for a proper description of the strong correlation, whereas dynamical correlation is computed via the recently developed adiabatic connection (AC) technique which requires only up to two-body active space reduced density matrices. We report the encouraging results of this approach on typical candidates for DMRG computations, namely, n-acenes (n = 2 → 7), Fe(II)-porphyrin, and the Fe₃S₄ cluster.

Symmetry-Adapted Perturbation Theory Based on Multiconfigurational Wave Function Description of Monomers

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.

Dataset of noncovalent intermolecular interaction energy curves for 24 small high-spin open-shell dimers

We introduce a dataset of 24 interaction energy curves of open-shell noncovalent dimers, referred to as the O24 × 5 dataset. The dataset consists of high-spin dimers up to 11 atoms selected to assure diversity with respect to interaction types: dispersion, electrostatics, and induction. The benchmark interaction energies are obtained at the restricted open-shell CCSD(T) level of theory with complete basis set extrapolation (from aug-cc-pVQZ to aug-cc-pV5Z). We have analyzed the performance of selected wave function methods MP2, CCSD, and CCSD(T) as well as the F12a and F12b variants of coupled-cluster theory. In addition, we have tested dispersion-corrected density functional theory methods based on the PBE exchange-correlation model. The O24 × 5 dataset is a challenge to approximate methods due to the wide range of interaction energy strengths it spans. For the dispersion-dominated and mixed-type subsets, any tested method that does not include the triples contribution yields errors on the order of tens of percent. The electrostatic subset is less demanding with errors that are typically an order of magnitude smaller than the mixed and dispersion-dominated subsets.

How Much Dispersion Energy Is Included in the Multiconfigurational Interaction Energy?

We demonstrate how to quantify the amount of dispersion interaction recovered by supermolecular calculations with the multiconfigurational self-consistent field (MCSCF) wave functions. For this purpose, we present a rigorous derivation which connects the portion of dispersion interaction captured by the assumed wave function model-the residual dispersion interaction-with the size of the active space. Based on the obtained expression for the residual dispersion contribution, we propose a dispersion correction for the MCSCF that avoids correlation double counting. Numerical demonstration for model four-electron dimers in both ground and excited states described with the complete active space self-consistent field (CASSCF) reference serves as a proof-of-concept for the method. Accurate results, largely independent of the size of the active space, are obtained. For many-electron systems, routine CASSCF interaction energy calculations recover a tiny fraction of the full second-order dispersion energy. We found that the residual dispersion is non-negligible only for purely dispersion-bound complexes.

Local Enhancement of Dynamic Correlation in Excited States: Fresh Perspective on Ionicity and Development of Correlation Density Functional Approximation Based on the On-Top Pair Density

We discuss the interplay between the nondynamic and dynamic electron correlation in excited states from the perspective of the suppression of dynamic correlation (SDC) and enhancement of dynamic correlation (EDC) effects. We reveal that there exists a connection between the ionic character of a wave function and EDC. Following this finding we introduce a quantitative measure of ionicity based solely on local functions without referring to valence bond models. The ability to recognize both the SDC and EDC regions underlies the presented method, named CASΠDFT, combining complete active space (CAS) wave function and density functional theory (DFT) via the on-top pair density (Π) function. We extend this approach to excited states by devising an improved representation of the EDC effect in the correlation functional. The generalized CASΠDFT uses different DFT functionals for ground and excited states. Numerical demonstration for singlet π → π* excitations shows that CASΠDFT offers satisfactory accuracy at a fraction of the cost of the ab initio approaches.

Reduced Density Matrix-Driven Complete Active Apace Self-Consistent Field Corrected for Dynamic Correlation from the Adiabatic Connection

The recently proposed multireference adiabatic connection (AC) formalism [Pernal, Phys. Rev. Lett. 120, 013001 (2018)] is applied to recover dynamic electron correlation effects lacking in variational two-electron reduced density matrix (v2RDM)-driven complete active space self-consistent field theory (CASSCF). The AC approach is validated by computing potential energy curves for the dissociation of molecular nitrogen and the symmetric double dissociation of H₂O while enforcing two sets of approximate N-representability conditions in the underlying v2RDM-driven CASSCF calculations (either two-particle or two-particle plus partial three-particle conditions). The AC yields smaller absolute errors than second-order N-electron perturbation theory (NEVPT2) at all molecular geometries for both sets of the N-representability conditions considered. The efficacy of the approach for thermochemistry is also assessed for a set of 31 small-molecule reactions. When imposing partial three-particle N-representability conditions, mean and maximum unsigned errors in reaction energies from the AC are superior to those from NEVPT2.

The effect of weak intermolecular interactions on the nuclear magnetic resonance shielding constant in N2

Ab initio calculations are applied to examine the influence of the intermolecular interactions on the shielding constant in gaseous nitrogen. An accurate literature potential energy surface and the nuclear magnetic resonance shielding surface of the N₂ -N₂ complex calculated in this work provide results in satisfactory agreement with the available experimental estimates of the effect.

Second-Order Exchange-Dispersion Energy Based on a Multireference Description of Monomers

We present a method for calculation of the second-order exchange-dispersion energy in the framework of the symmetry-adapted perturbation theory (SAPT) for weakly interacting monomers described with multiconfigurational wave functions. The proposed formalism is based on response properties obtained from extended random phase approximation (ERPA) equations and assumes the single-exchange (S²) approximation. The approach is applicable to closed shell systems where static correlation cannot be neglected or to systems in nondegenerate excited states. We examine the new method in combination with either generalized valence bond perfect pairing (GVB) or complete active space self-consistent field (CASSCF) description of the interacting monomers. For model multireference dimers in ground states (H₂···H₂, Be···Be, He···H₂), exchange-dispersion energies are reproduced accurately. For the interaction between the excited hydrogen molecule and the helium atom we found unacceptably large errors which is attributed to the neglect of diagonal double excitations in the employed approximation to the linear response function.

Capturing the Dynamic Correlation for Arbitrary Spin-Symmetry CASSCF Reference with Adiabatic Connection Approaches: Insights into the Electronic Structure of the Tetramethyleneethane Diradical

The recently proposed approach to multireference dynamic correlation energy based on the adiabatic connection (AC) is extended to an arbitrary spin symmetry of the reference state. We show that both the spin-free AC approach and its computationally inexpensive approximation, AC0, when combined with a complete active space wave function, constitute viable alternatives to the perturbation-based and density-functional-based multiconfiguration methods. In particular, the AC0 approach, thanks to its favorable scaling with the system size and the size of the active space, allows for treating larger systems than its perturbation-based counterparts while maintaining comparable accuracy. We show the method's robustness on illustrative chemical systems, including the elusive tetramethyleneethane (TME) diradical, potential energy surfaces of which present a challenge to most computational approaches. For the latter system, AC0 outperforms other methods, staying in close agreement with the full configuration interaction quantum Monte Carlo benchmark. A careful analysis of the contributions to the correlation energy of TME's lowest singlet and triplet states reveals the subtle interplay of the dynamic and static correlation as the key to understanding the shape of the diradical's potential energy surfaces.

Second-Order Dispersion Energy Based on Multireference Description of Monomers

We propose a method for calculating a second-order dispersion energy for weakly interacting multireference systems in arbitrary electronic states. It is based on response properties obtained from extended random phase approximation equations. The introduced formalism is general and requires only one- and two-particle reduced density matrices of monomers. We combine the new method with either generalized valence bond perfect pairing (GVB) or complete active space (CAS) self-consistent field description of the interacting systems. In addition to a general scheme, three approximations, leading to significant reduction of the computational cost, are developed by exploiting Dyall partitioning of the monomer Hamiltonians. For model multireference systems (H₂···H₂ and Be···Be) the method is accurate, unlike its single-reference-based counterpart. Neither GVB nor CAS description of single-reference monomers improves the dispersion energy with respect to the Hartree-Fock-based results.

How and Why Does Helium Permeate Nonporous Arsenolite Under High Pressure?

Investigations into the helium permeation of arsenolite, the cubic, molecular arsenic(III) oxide polymorph As₄ O₆ , were carried out to understand how and why arsenolite helium clathrate As₄ O₆ ⋅2 He is formed. High-pressure synchrotron X-ray diffraction experiments on arsenolite single crystals revealed that the permeation of helium into nonporous arsenolite depends on the time for which the crystal is subjected to high pressure and on the crystal history. The single crystal was totally transformed into As₄ O₆ ⋅2 He within 45 h under 5 GPa. After release of the pressure, arsenolite was recovered and a repeated increase in pressure up to 3 GPa led to practically instant As₄ O₆ ⋅2 He formation. However, when a pristine arsenolite single crystal was quickly subjected to a pressure of 13 GPa, no helium permeation was observed at all. No neon permeation was observed in analogous experiments. Quantum mechanical computations indicate that there are no specific attractive interactions between He atoms and As₄ O₆ molecules at the distances observed in the As₄ O₆ ⋅2 He crystal structure. Detailed analysis of As₄ O₆ molecular structure changes has shown that the introduction of He into the arsenolite crystal lattice significantly reduces molecular deformations by decreasing the anisotropy of stress exerted on the As₄ O₆ molecules. This effect and the pΔV term, rather than any specific As⋅⋅⋅He binding, are the driving forces for the formation As₄ O₆ ⋅2 He.

The nature of three-body interactions in DFT: Exchange and polarization effects

We propose a physically motivated decomposition of density functional theory (DFT) 3-body nonadditive interaction energies into the exchange and density-deformation (polarization) components. The exchange component represents the effect of the Pauli exclusion in the wave function of the trimer and is found to be challenging for density functional approximations (DFAs). The remaining density-deformation nonadditivity is less dependent upon the DFAs. Numerical demonstration is carried out for rare gas atom trimers, Ar₂-HX (X = F, Cl) complexes, and small hydrogen-bonded and van der Waals molecular systems. None of the tested semilocal, hybrid, and range-separated DFAs properly accounts for the nonadditive exchange in dispersion-bonded trimers. By contrast, for hydrogen-bonded systems, range-separated DFAs achieve a qualitative agreement to within 20% of the reference exchange energy. A reliable performance for all systems is obtained only when the monomers interact through the Hartree-Fock potential in the dispersion-free Pauli blockade scheme. Additionally, we identify the nonadditive second-order exchange-dispersion energy as an important but overlooked contribution in force-field-like dispersion corrections. Our results suggest that range-separated functionals do not include this component, although semilocal and global hybrid DFAs appear to imitate it in the short range.

Noncovalent interactions determine the conformation of aurophilic complexes with 2-mercapto-4-methyl-5-thiazoleacetic acid ligands

The synthesis of three new gold(i) salts is reported. The intermolecular interactions stabilizing the aurophilic dimers are examined by several first principles interpretative techniques.

Symmetry-adapted perturbation theory based on unrestricted Kohn-Sham orbitals for high-spin open-shell van der Waals complexes

Two open-shell formulations of the symmetry-adapted perturbation theory are presented. They are based on the spin-unrestricted Kohn-Sham (SAPT(UKS)) and unrestricted Hartree-Fock (SAPT(UHF)) descriptions of the monomers, respectively. The key reason behind development of SAPT(UKS) is that it is more compatible with density functional theory (DFT) compared to the previous formulation of open-shell SAPT based on spin-restricted Kohn-Sham method of Żuchowski et al. [J. Chem. Phys. 129, 084101 (2008)]. The performance of SAPT(UKS) and SAPT(UHF) is tested for the following open-shell van der Waals complexes: He···NH, H(2)O···HO(2), He···OH, Ar···OH, Ar···NO. The results show an excellent agreement between SAPT(UKS) and SAPT(ROKS). Furthermore, for the first time SAPT based on DFT is shown to be suitable for the treatment of interactions involving Π-state radicals (He···OH, Ar···OH, Ar···NO). In the interactions of transition metal dimers ((3)Σ(u)(+))Au(2) and ((13)Σ(g)(+))Cr(2) we show that SAPT is incompatible with the use of effective core potentials. The interaction energies of both systems expressed instead as supermolecular UHF interaction plus dispersion from SAPT(UKS) result in reasonably accurate potential curves.