Evaluating London Dispersion Interactions in DFT: A Nonlocal Anisotropic Buckingham–Hirshfeld Model

R-8 Dispersion Interaction: Derivation and Application to the Effective Fragment Potential Method

The anisotropic and isotropic R-8 dispersion contributions (disp8) are derived and implemented within the framework of the effective fragment potential (EFP) method formulated with imaginary frequency-dependent Cartesian polarizability tensors distributed at the centroids of the localized molecular orbitals (LMOs). Two forms of damping functions, intermolecular overlap-based and Tang-Toennies, are extended for disp8. To obtain LMO polarizability tensors centered at LMO centroids, an origin-shifting transformation is derived and implemented for the dipole-octopole polarizability tensor and the quadrupole-quadrupole polarizability tensor. The analytic gradient is derived and implemented for the isotropic disp8 contribution. Relative to the previously implemented empirical EFP disp8 energy, the isotropic disp8 component of the interaction energy improves the overall agreement of the EFP dispersion energies with the symmetry-adapted perturbation theory (SAPT) benchmarks, reducing the mean absolute errors (MAEs) and mean absolute percentage errors for most of the databases examined in this work. While the anisotropic disp8 can further enhance the accuracy of the EFP dispersion energy and yield smaller MAEs, significantly overbound dispersion energies are predicted by the anisotropic disp8 when the maximum element in the intermolecular overlap matrix is greater than 0.1, possibly due to the breakdown of the approximations made in the EFP dispersion derivation at a short range. For potential energy scan databases, the newly developed EFP dispersion model with isotropic disp8 yields the overall correct curvature and good agreement with SAPT benchmarks around equilibrium and longer but overestimates the dispersion interactions at a short range. While the overlap-based dispersion-damping functions produce better MAEs than Tang-Toennies damping functions, further improvement is needed to better screen the large attractive dispersion energies at a short range (overlap >0.1).

Enhancement of one- and two-photon absorption and visualization of intramolecular charge transfer of pyrenyl-contained derivatives

To further improve the pyrenyl-contained derivatives two-photon absorption (TPA) and third-order nonlinear optical (NLO) properties, three steps of optimization are employed based on experimental molecule PCVS-B: heteroatomic substitution, exchanging the position of double bonds and adding a branch. The contributions of π electrons to localized orbital locators and Mayer bond orders (LOL-π and I_AB^π) show that the second step can enhance the chemical interaction between pyrenyl and the branched-chain. Two visual methods of charge density difference (CDD) and transition density matrix (TDM) are combined to intuitively analyze the intramolecular charge transfer (ICT) process of one (two) photon absorption; results show that both following two steps can increase the degree of ICT on the conjugated plane of the pyrenyl. The sum over state (SOS) model was used to find out the dominant two-photon transition process. The difference between the dipole moments obtained by the McRae equation is applied to the three-state model, revealing the inherent law of the second static hyperpolarizability.

Effect of Polymerization on the Charge-Transfer Mechanism in the One (Two)-Photon Absorption Process of D-A-Type Triphenylamine Derivatives

To investigate the effect of polymerization (n = 1, 2, 3, and 4) on the charge-transfer (CT) mechanisms in the one (two)-photon absorption (OPA and TPA) process of D-A-type triphenylamine derivatives, charge density difference is used to graphically represent the CT characteristics. A transition density matrix is utilized to reveal the direction of CT on different groups quantitatively. With the n increasing, electrons are mainly transferred between the groups in the middle position of the molecular chain during OPA and TPA processes. Simulated results show that the energy gap and excitation energy have a good linear relationship with the reciprocal of the polymerization degree. Importantly, the polymerization effect can effectively increase the electronic transmission capability, TPA performance, and second hyperpolarizability. Besides, the simplified sum over state model reveals the variation factor of the TPA cross-section and the second static hyperpolarizability. The McRae formula and Bakhshiev formula are used to estimate the difference of dipole moments, which is an important parameter of the second hyperpolarizability. The comprehensive analysis of the nonlinear optical (NLO) parameters of triphenylamine derivatives can provide some significant guidance for molecular design and improve the NLO performance of D-A molecular materials. Also, the thermodynamic parameters can provide some theoretical supports for solving practical problems.

Non-pairwise additivity of the leading-order dispersion energy

The leading-order (i.e., dipole-dipole) dispersion energy is calculated for one-dimensional (1D) and two-dimensional (2D) infinite lattices, and an infinite 1D array of infinitely long lines, of doubly occupied locally harmonic wells. The dispersion energy is decomposed into pairwise and non-pairwise additive components. By varying the force constant and separation of the wells, the non-pairwise additive contribution to the dispersion energy is shown to depend on the overlap of density between neighboring wells. As well separation is increased, the non-pairwise additivity of the dispersion energy decays. The different rates of decay for 1D and 2D lattices of wells is explained in terms of a Jacobian effect that influences the number of nearest neighbors. For an array of infinitely long lines of wells spaced 5 bohrs apart, and an inter-well spacing of 3 bohrs within a line, the non-pairwise additive component of the leading-order dispersion energy is -0.11 kJ mol(-1) well(-1), which is 7% of the total. The polarizability of the wells and the density overlap between them are small in comparison to that of the atomic densities that arise from the molecular density partitioning used in post-density-functional theory (DFT) damped dispersion corrections, or DFT-D methods. Therefore, the nonadditivity of the leading-order dispersion observed here is a conservative estimate of that in molecular clusters.

Structure-dependent interatomic dispersion coefficients in oxides with maximally localized Wannier functions

The interatomic C(6) dispersion coefficients in crystalline and amorphous SiO(2) and ZrO(2) structures were obtained with the approach proposed by Silvestrelli (2008 Phys. Rev. Lett. 100 053002) and based on the use of maximally localized Wannier functions (MLWFs) for partitioning the electron density. Localization of Wannier functions close to the nuclei in oxide systems makes it possible to assign the MLWFs to the atoms in an unambiguous way and then to compute the C(6) coefficients in an atom pairwise manner. A modification of the method is suggested in which the MLWFs are condensed to effective orbitals centred on the atoms and parameters of these effective orbitals are used for computing the interatomic dispersion coefficients. The obtained values of the dispersion coefficients were found to vary not only from one oxide to another, but also between different modifications of the same compound. The oxygen-oxygen coefficient C6(OO) reveals the largest variation and its value in ZrO(2) structures is twice as large as that in SiO(2) ones. Atomic characteristics obtained in the frame of the effective orbital method, such as the self-atom dispersion coefficient, and the oxide ion polarizability were found to correlate with the metal-oxygen bond length and the oxygen coordination number in the systems. This behaviour is attributed to the confinement of electrons by the electrostatic potential. The values of the coefficient and of the polarizability were related to charges of the oxygen atoms. In all studied systems the oxygen atoms having larger absolute values of charge were found to be less polarizable because of a stronger confinement effect. The obtained results can be used in the development of polarizable force fields for the atomistic modelling of oxide materials.

Supramolecular binding thermodynamics by dispersion-corrected density functional theory

The equilibrium association free enthalpies ΔG(a) for typical supramolecular complexes in solution are calculated by ab initio quantum chemical methods. Ten neutral and three positively charged complexes with experimental ΔG(a) values in the range 0 to -21 kcal mol(-1) (on average -6 kcal mol(-1)) are investigated. The theoretical approach employs a (nondynamic) single-structure model, but computes the various energy terms accurately without any special empirical adjustments. Dispersion corrected density functional theory (DFT-D3) with extended basis sets (triple-ζ and quadruple-ζ quality) is used to determine structures and gas-phase interaction energies (ΔE), the COSMO-RS continuum solvation model (based on DFT data) provides solvation free enthalpies and the remaining ro-vibrational enthalpic/entropic contributions are obtained from harmonic frequency calculations. Low-lying vibrational modes are treated by a free-rotor approximation. The accurate account of London dispersion interactions is mandatory with contributions in the range -5 to -60 kcal mol(-1) (up to 200% of ΔE). Inclusion of three-body dispersion effects improves the results considerably. A semilocal (TPSS) and a hybrid density functional (PW6B95) have been tested. Although the ΔG(a) values result as a sum of individually large terms with opposite sign (ΔE vs. solvation and entropy change), the approach provides unprecedented accuracy for ΔG(a) values with errors of only 2 kcal mol(-1) on average. Relative affinities for different guests inside the same host are always obtained correctly. The procedure is suggested as a predictive tool in supramolecular chemistry and can be applied routinely to semirigid systems with 300-400 atoms. The various contributions to binding and enthalpy-entropy compensations are discussed.