Marcin Dulak

Equilibrium Geometries of Noncovalently Bound Intermolecular Complexes Derived from Subsystem Formulation of Density Functional Theory

The subsystem formulation of density functional theory is used to obtain equilibrium geometries and interaction energies for a representative set of noncovalently bound intermolecular complexes. The results are compared with literature benchmark data. The range of applicability of two considered approximations to the exchange-correlation- and nonadditive kinetic energy components of the total energy is determined. Local density approximation, which does not involve any empirical parameters, leads to excellent intermolecular equilibrium distances for hydrogen-bonded complexes (maximal error 0.13 Å for NH3-NH3). It is a method of choice for a wide class of weak intermolecular complexes including also dipole-bound and the ones formed by rare gas atoms or saturated hydrocarbons. The range of applicability of the chosen generalized gradient approximation, which was shown in our previous works to lead to good interaction energies in such complexes, where π-electrons are involved in the interaction, remains limited to this group because it improves neither binding energies nor equilibrium geometries in the wide class of complexes for which local density approximation is adequate. An efficient energy minimization procedure, in which optimization of the geometry and the electron density of each subsystem is made simultaneously, is proposed and tested.

Interaction energies in hydrogen-bonded systems: A testing ground for subsystem formulation of density-functional theory

The formalism based on the total energy bifunctional (E[rhoI,rhoII]) is used to derive interaction energies for several hydrogen-bonded complexes (water dimer, HCN-HF, H2CO-H2O, and MeOH-H2O). Benchmark ab initio data taken from the literature were used as a reference in the assessment of the performance of gradient-free [local density approximation (LDA)] and gradient-dependent [generalized gradient approximation (GGA)] approximations to the exchange-correlation and nonadditive kinetic-energy components of E[rhoI,rhoII]. On average, LDA performs better than GGA. The average absolute error of calculated LDA interaction energies amounts to 1.0 kJ/mol. For H2CO-H2O and H2O-H2O complexes, the potential-energy curves corresponding to the stretching of the intermolecular distance are also calculated. The positions of the minima are in a good agreement (less than 0.2 A) with the reference ab initio data. Both variational and nonvariational calculations are performed to assess the energetic effects associated with complexation-induced deformations of molecular electron densities.

The energy-differences based exact criterion for testing approximations to the functional for the kinetic energy of non-interacting electrons

Gradient-dependent approximations to the functional of the kinetic energy of non-interacting electrons (Ts[ρ]), which reflect various properties of the exact functional, are considered. For specially constructed pairs of electron densities, for which the analytic expression for the differences of Ts[ρ] is known, it is shown that the accuracy of the quantities derivable from a given approximation to Ts[ρ]: energy differences and their functional derivatives, does not reflect that of Ts[ρ] itself. The comparisons between the exact values of the kinetic energy in such cases are proposed as an independent condition/criterion for appraisal of approximations to Ts[ρ].

On the electron leak problem in orbital-free embedding calculations

Computer simulation methods using orbital level of description only for a selected part of the larger systems are prone to the artificial charge leak to the parts which are described without orbitals. The absence of orbitals in one of the subsystems makes it impossible to impose explicitly the orthogonality condition. Using the subsystem formulation of density functional theory, it is shown that the absence of explicit condition of orthogonality between orbitals belonging to different subsystems, does not cause any breakdown of this type of description for the chosen intermolecular complexes (F(-)H(2)O and Li(+)H(2)O), for which a significant charge-leak problem could be a priori expected.

Nonlinearity of the Bifunctional of the Nonadditive Kinetic Energy: Numerical Consequences in Orbital-Free Embedding Calculations.

The bifunctional of the nonadditive kinetic energy in the reference system of noninteracting electrons ([Formula: see text] [ρA, ρB] = Ts[ρA + ρB] - Ts[ρA] - Ts[ρB]) is the key quantity in orbital-free embedding calculations because they hinge on approximations to[Formula: see text] [ρA,ρB]. Since[Formula: see text] [ρA,ρB] is not linear in ρA, the associated potential (functional derivative)[Formula: see text] [ρ,ρB]/δρ|ρ=ρA(r⃗) changes if ρA varies. In this work, for two approximations to[Formula: see text] [ρA,ρB], which are nonlinear in ρA (gradient-free and gradient-dependent), their linearized versions are constructed, and the resulting changes (linearization errors) in various properties of embedded systems (orbital energies, dipole moments, interaction energies, and electron densities) are analyzed. The considered model embedded systems represent typical nonbonding interactions:  van der Waals contacts, hydrogen bonds, complexes involving charged species, and intermolecular complexes of the charge-transfer character. For van der Waals and hydrogen bonded complexes, the linearization of[Formula: see text] [ρA,ρB] affects negligibly the calculated properties. Even for complexes, for which large complexation induced changes of the electron density can be expected, such as the water molecule in the field of a cation, the linearization errors are about 2 orders of magnitude smaller than the interaction induced shifts of the corresponding properties. Linearization of[Formula: see text] [ρA,ρB] is shown to be inadequate for the complexes of a strong charge-transfer character. Compared to gradient-free approximation to[Formula: see text] [ρA,ρB], introduction of gradients increases the linearization error.

One-Electron Equations for Embedded Electron Density and Their Applications to Study Electronic Structure of Atoms and Molecules in Condensed Phase

Recent applications of one-electron equations for embedded electron density introduced originally for multi-level modeling of solvated molecules (T.A. Wesolowski, A. Warshel, J. Phys. Chem. 1993, 97, 8050) are reviewed. The considered applications concern properties directly related to the electronic structure of molecules (or an atom) in condensed phase such as: i) localized electronic excitations in a chromophore involved in a hydrogen-bonded intermolecular complex; ii) UV/Vis spectra of acetone in water; and iii) energy levels of f-orbitals for lanthanide cations in a crystalline environment. For each case studied, the embedding potential is represented graphically and its qualitative features are discussed.