Dispersion Energy from Local Polarizability Density

Dispersionless Nonhybrid Density Functional

A dispersion-corrected density functional theory (DFT+D) method has been developed. It includes a nonhybrid dispersionless generalized gradient approximation (GGA) functional paired with a literature-parametrized dispersion function. The functional's 9 adjustable parameters were optimized using a training set of 589 benchmark interaction energies. The resulting method performs better than other GGA-based DFT+D methods, giving a mean unsigned error of 0.33 kcal/mol. It even performs better than some more expensive meta-GGA or hybrid dispersion-corrected functionals. An important advantage of using the new functional is that its dispersion energy given by the D component is very close to the true dispersion energy at all intermolecular separations, whereas in other similarly accurate DFT+D approaches, such a dispersion contribution in the van der Waals minimum region is only a small fraction of the true value.

Multistate Energy Decomposition Analysis of Molecular Excited States

A multistate energy decomposition analysis (MS-EDA) method is described to dissect the energy components in molecular complexes in excited states. In MS-EDA, the total binding energy of an excimer or an exciplex is partitioned into a ground-state term, called local interaction energy, and excited-state contributions that include exciton excitation energy, superexchange stabilization, and orbital and configuration-state delocalization. An important feature of MS-EDA is that key intermediate states associated with different energy terms can be variationally optimized, providing quantitative insights into widely used physical concepts such as exciton delocalization and superexchange charge-transfer effects in excited states. By introducing structure-weighted adiabatic excitation energy as the minimum photoexcitation energy needed to produce an excited-state complex, the binding energy of an exciplex and excimer can be defined. On the basis of the nature of intermolecular forces through MS-EDA analysis, it was found that molecular complexes in the excited states can be classified into three main categories, including (1) encounter excited-state complex, (2) charge-transfer exciplex, and (3) intimate excimer or exciplex. The illustrative examples in this Perspective highlight the interplay of local excitation polarization, exciton resonance, and superexchange effects in molecular excited states. It is hoped that MS-EDA can be a useful tool for understanding photochemical and photobiological processes.

Excimer Energies

A multistate energy decomposition analysis (MS-EDA) method is introduced for excimers using density functional theory. Although EDA has been widely applied to intermolecular interactions in the ground state, few methods are currently available for excited-state complexes. Here, the total energy of an excimer state is separated into exciton excitation energy ΔE_Ex(|Ψ_X·Ψ_Y⟩*), resulting from the state interaction between locally excited monomer states |Ψ_X^*·Ψ_Y⟩ and |Ψ_X·Ψ_Y^*⟩ , a superexchange stabilization energy ΔE_SE, originating from the mutual charge transfer between two monomers |Ψ_X⁺·Ψ_Y⟩ and |Ψ_X^-·Ψ_Y⁺⟩ , and an orbital-and-configuration delocalization term ΔE_OCD due to the expansion of configuration space and block-localized orbitals to the fully delocalized dimer system. Although there is no net charge transfer in symmetric excimer cases, the resonance of charge-transfer states is critical to stabilizing the excimer. The monomer localized excited and charge-transfer states are variationally optimized, forming a minimal active space for nonorthogonal state interaction (NOSI) calculations in multistate density functional theory to yield the intermediate states for energy analysis. The present MS-EDA method focuses on properties unique to excited states, providing insights into exciton coupling, superexchange and delocalization energies. MS-EDA is illustrated on the acetone and pentacene excimer systems; three configurations of the latter case are examined, including the optimized excimer, a stacked configuration of two pentacene molecules and the fishbone orientation. It is found that excited-state energy splitting is strongly dependent on the relative energies of the monomer excited states and the phase-matching of the monomer wave functions.

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.

Fragment Exchange Potential for Realizing Pauli Deformation of Interfragment Interactions

In fragment-based methods, the lack of explicit short-range exchange interactions between monomers can result in unphysical deformation in charge density. In this study, we describe a fragment exchange potential (XFP) to explicitly account for interfragmental Pauli deformation. In our implementation, a Kohn-Sham exchange potential is adopted along with the Yukawa potential. The method has been validated by comparison of the computed exchange energies using the XFP potential with results obtained from antisymmetrized fragmental orbitals on the S66×8 data set containing 528 bimolecular interactions of equilibrium and arbitrary geometries. It was also found that it is only necessary to deploy numerical grids on atoms within their van der Waals contacts, significantly reducing the small, albeit extra, computational cost. We anticipate that the XFP presented here may be applied to molecular dynamics simulations of macromolecules using a fragment-based quantum mechanical potential with improved SCF convergence and computational accuracy.

SAPT codes for calculations of intermolecular interaction energies

Symmetry-adapted perturbation theory (SAPT) is a method for calculations of intermolecular (noncovalent) interaction energies. The set of SAPT codes that is described here, the current version named SAPT2020, includes virtually all variants of SAPT developed so far, among them two-body SAPT based on perturbative, coupled cluster, and density functional theory descriptions of monomers, three-body SAPT, and two-body SAPT for some classes of open-shell monomers. The properties of systems governed by noncovalent interactions can be predicted only if potential energy surfaces (force fields) are available. SAPT is the preferred approach for generating such surfaces since it is seamlessly connected to the asymptotic expansion of interaction energy. SAPT2020 includes codes for automatic development of such surfaces, enabling generation of complete dimer surfaces with a rigid monomer approximation for dimers containing about one hundred atoms. These codes can also be used to obtain surfaces including internal degrees of freedom of monomers.

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.

Nine questions on energy decomposition analysis

The paper collects the answers of the authors to the following questions: Is the lack of precision in the definition of many chemical concepts one of the reasons for the coexistence of many partition schemes? Does the adoption of a given partition scheme imply a set of more precise definitions of the underlying chemical concepts? How can one use the results of a partition scheme to improve the clarity of definitions of concepts? Are partition schemes subject to scientific Darwinism? If so, what is the influence of a community's sociological pressure in the "natural selection" process? To what extent does/can/should investigated systems influence the choice of a particular partition scheme? Do we need more focused chemical validation of Energy Decomposition Analysis (EDA) methodology and descriptors/terms in general? Is there any interest in developing common benchmarks and test sets for cross-validation of methods? Is it possible to contemplate a unified partition scheme (let us call it the "standard model" of partitioning), that is proper for all applications in chemistry, in the foreseeable future or even in principle? In the end, science is about experiments and the real world. Can one, therefore, use any experiment or experimental data be used to favor one partition scheme over another? © 2019 Wiley Periodicals, Inc.