Alisa Krishtal

A Hirshfeld partitioning of polarizabilities of water clusters

A new Hirshfeld partitioning of cluster polarizability into intrinsic polarizabilities and charge delocalization contributions is presented. For water clusters, density-functional theory calculations demonstrate that the total polarizability of a water molecule in a cluster depends upon the number and type of hydrogen bonds the molecule makes with its neighbors. The intrinsic contribution to the molecular polarizability is transferable between water molecules displaying the same H-bond scheme in clusters of different sizes, and geometries, while the charge delocalization contribution also depends on the cluster size. These results could be used to improve the existing force fields.

An Extension of the Hirshfeld Method to Open Shell Systems Using Fractional Occupations.

In this work, a new partitioning method is presented which allows one to calculate properties of radicals, in particular, atomic spin populations. The method can be seen as an extension of the Hirshfeld-I method [ Bultinck , P. et al. J. Chem. Phys. 2007 , 126 , 144111 ], in which the atomic weight functions, defining the atoms-in-molecules, are constructed by means of an iterative scheme in which the charges of the atoms-in-molecules are altered but the spin remains fixed. The Hirshfeld-I method is therefore not suitable for the calculation of atomic spin populations of open-shell systems. The new fractional occupation Hirshfeld-I (FOHI) uses an iterative scheme in which both the atomic charge and spin are optimized, resulting in a self-consistent method for the calculation of atomic spin populations. The results obtained with the FOHI method are compared with experimental results obtained using polarized neutron diffraction, thus serving as a validation of the FOHI method as well as the Hirshfeld definition of atoms-in-molecules in general.

Accurate interaction energies at density functional theory level by means of an efficient dispersion correction.

This paper presents an approach for obtaining accurate interaction energies at the density functional theory level for systems where dispersion interactions are important. This approach combines Becke and Johnsons [J. Chem. Phys. 127, 154108 (2007)] method for the evaluation of dispersion energy corrections and a Hirshfeld method for partitioning of molecular polarizability tensors into atomic contributions. Due to the availability of atomic polarizability tensors, the method is extended to incorporate anisotropic contributions, which prove to be important for complexes of lower symmetry. The method is validated for a set of 18 complexes, for which interaction energies were obtained with the B3LYP, PBE, and TPSS functionals combined with the aug-cc-pVTZ basis set and compared with the values obtained at the CCSD(T) level extrapolated to a complete basis set limit. It is shown that very good quality interaction energies can be obtained by the proposed method for each of the examined functionals, the overall performance of the TPSS functional being the best, which with a slope of 1.00 in the linear regression equation and a constant term of only 0.1 kcal/mol allows to obtain accurate interaction energies without any need of a damping function for complexes close to their exact equilibrium geometry.

Subsystem density-functional theory as an effective tool for modeling ground and excited states, their dynamics and many-body interactions

Subsystem density-functional theory (DFT) is an emerging technique for calculating the electronic structure of complex molecular and condensed phase systems. In this topical review, we focus on some recent advances in this field related to the computation of condensed phase systems, their excited states, and the evaluation of many-body interactions between the subsystems. As subsystem DFT is in principle an exact theory, any advance in this field can have a dual role. One is the possible applicability of a resulting method in practical calculations. The other is the possibility of shedding light on some quantum-mechanical phenomenon which is more easily treated by subdividing a supersystem into subsystems. An example of the latter is many-body interactions. In the discussion, we present some recent work from our research group as well as some new results, casting them in the current state-of-the-art in this review as comprehensively as possible.

The use of atomic intrinsic polarizabilities in the evaluation of the dispersion energy

The recent approach presented by Becke and Johnson [J. Chem. Phys. 122, 154104 (2005); 123, 024101 (2005); 123, 154101 (2005); 124, 174104 (2006); 124, 014104 (2006)] for the evaluation of dispersion interactions based on the properties of the exchange-hole dipole moment is combined with a Hirshfeld-type partitioning for the molecular polarizabilities into atomic contributions, recently presented by some of the present authors [A. Krishtal et al., J. Chem. Phys. 125, 034312 (2006)]. The results on a series of nine dimers, involving neon, methane, ethene, acetylene, benzene, and CO(2), taken at their equilibrium geometry, indicate that when the C(6), C(8), and C(10) terms are taken into account, the resulting dispersion energies can be obtained deviating 3% or 8% from high level literature data [E. R. Johnson and A. D. Becke, J. Chem. Phys. 124, 174104 (2006)], without the use of a damping function, the only outlier being the parallel face-to-face benzene dimer.

Variation of ion polarizability from vacuum to hydration: insights from Hirshfeld partitioning.

The results of iterative Hirshfeld partitioning on the polarizability of monovalent anions (F(-), Cl(-), and Br(-)) and Na(+) in water clusters ranging from n = 0 to n = 25 are presented. In each case, the ions reach a limiting intrinsic polarizability in the fully hydrated state. For F(-), Cl(-), and Br(-) using B3LYP/aug-cc-pVDZ, the intrinsic polarizabilities in the condensed-phase limit are 47.2 +/- 0.7%, 47.2 +/- 0.3%, and 54.2 +/- 0.4% of their gas-phase value at the corresponding level of theory. The extent of this scaling depends on the basis set (we also consider B3LYP/aug-cc-pVTZ), but intrinsic polarizabilities are generally within 35-55% of the gas-phase value. The sodium cation is the least polarizable in the condensed-phase limit. The average intrinsic polarizability of water in these clusters decreases with the size of the cluster, which is consistent with earlier Hirshfeld analysis of intrinsic polarizabilities of pure water (Krishtal, A.; Senet, P.; Yang, M.; van Alsenoy, C. J. Chem. Phys. 2006, 125, 034312). Further analysis demonstrates that water molecules near ions in sufficiently large clusters (n = 25) have intrinsic polarizabilities similar to those of water molecules fully coordinated in a pure aqueous cluster. The observed binodal distribution of the water intrinsic polarizability within the cluster is attributed to polarizability differences between interior and exterior water molecules. This observation is in qualitative agreement with arguments based on Paulis exclusion principle that suggest a reduced polarizability for condensed-phase water relative to the vacuum value.

Effect of Structural Parameters on the Polarizabilities of Methanol Clusters: A Hirshfeld Study

The polarizabilities of fifty methanol clusters (CH3OH)n, n = 1 to 12, were calculated at the B3LYP/6-311++G** level of theory and partitioned into molecular contributions using the Hirshfeld-I method. The resulting molecular polarizabilities were found to be determined by the polarizabilities of the two parts of the molecule, the hydrophilic hydroxyl group and the hydrophobic methyl group, each exhibiting a different dependency upon the local environment. The polarizability of the hydroxyl group was found to be dependent on the number, type, and strength of the hydrogen bonds a methanol molecule makes, whereas the polarizability of the methyl groups is mostly influenced by sterical hindrance. The findings were compared with the results obtained in a previous study on water clusters. The influence of the BSSE correction was investigated and found to increase polarizability values by up to 8.5%.

Influence of structure on the polarizability of hydrated methane sulfonic acid clusters

The relationship between polarizability and structure is investigated in methane sulfonic acid (MSA) and in 36 hydrated MSA clusters. The polarizabilities are calculated at B3LYP and MP2 level and further partitioned into molecular contributions using classic and iterative Hirshfeld methods. The differences in the two approaches for partitioning of polarizabilities are thoroughly analyzed. The polarizabilities of the molecules are found to be influenced in a systematic way by the hydrogen bond network in the clusters, proton transfer between MSA and water molecules, and weak interactions between water molecules and the methyl group of MSA.

Origin of the size-dependence of the polarizability per atom in heterogeneous clusters: The case of AlP clusters

An analysis of the atomic polarizabilities α in stoichiometric aluminum phosphide clusters, computed at the MP2 and density functional theory (DFT) levels, the latter using the B3LYP functional, and partitioned using the classic and iterative versions of the Hirshfeld method, is presented. Two sets of clusters are examined: the ground-state Al(n)P(n) clusters (n=2-9) and the prolate clusters (Al(2)P(2))(N) and (Al(3)P(3))(N) (N≤6). In the ground-state clusters, the mean polarizability per atom, i.e., α/2n, decreases with the cluster size but shows peaks at n=5 and at n=7. We demonstrate that these peaks can be explained by a large polarizability of the Al atoms and by a low polarizability of the P atoms in Al(5)P(5) and Al(7)P(7) due to the presence of homopolar bonds in these clusters. We show indeed that the polarizability of an atom within an Al(n)P(n) cluster depends on the cluster size and the heteropolarity of the bonds it forms within the cluster, i.e., on the charges of the atoms. The polarizabilities of the fragments Al(2)P(2) and Al(3)P(3) in the prolate clusters were found to depend mainly on their location within the cluster. Finally, we show that the iterative Hirshfeld method is more suitable than the classic Hirshfeld method for describing the atomic polarizabilities and the atomic charges in clusters with heteropolar bonds, although both versions of the Hirshfeld method lead to similar conclusions.

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

In this work, we present a novel model, referred to as BH-DFT-D, for the evaluation of London dispersion, with the purpose to correct the performance of local DFT exchange-correlation functionals for the description of van der Waals interactions. The new BH-DFT-D model combines the equations originally derived by Buckingham [Buckingham, A. D. Adv. Chem. Phys1967, 12, 107] with the definition of distributed multipole polarizability tensors within the Hirshfeld method [Hirshfeld, F.L. Theor. Chim. Acta1977, 44, 129], resulting in nonlocal, fully anisotropic expressions. Since no damping function has been introduced yet into the model, it is suitable in its present form for the evaluation of dispersion interactions in van der Waals dimers with no or negligible overlap. The new method is tested for an extended collection of van der Waals dimers against high-level data, where it is found to reproduce interaction energies at the BH-B3LYP-D/aug-cc-pVTZ level with a mean average error (MAE) of 0.20 kcal/mol. Next, development steps of the model will consist of adding a damping function, analytical gradients, and generalization to a supramolecular system.