Revealing electronic open quantum systems with subsystem TDDFT.

Open quantum systems (OQSs) are perhaps the most realistic systems one can approach through simulations. In recent years, describing OQSs with Density Functional Theory (DFT) has been a prominent avenue of research with most approaches based on a density matrix partitioning in conjunction with an ad-hoc description of system-bath interactions. We propose a different theoretical approach to OQSs based on partitioning of the electron density. Employing the machinery of subsystem DFT (and its time-dependent extension), we provide a novel way of isolating and analyzing the various terms contributing to the coupling between the system and the surrounding bath. To illustrate the theory, we provide numerical simulations on a toy system (a molecular dimer) and on a condensed phase system (solvated excimer). The simulations show that non-Markovian dynamics in the electronic system-bath interactions are important in chemical applications. For instance, we show that the superexchange mechanism of transport in donor-bridge-acceptor systems is a non-Markovian interaction between the donor-acceptor (OQS) with the bridge (bath) which is fully characterized by real-time subsystem time-dependent DFT.

Subsystem real-time time dependent density functional theory.

We present the extension of Frozen Density Embedding (FDE) formulation of subsystem Density Functional Theory (DFT) to real-time Time Dependent Density Functional Theory (rt-TDDFT). FDE is a DFT-in-DFT embedding method that allows to partition a larger Kohn-Sham system into a set of smaller, coupled Kohn-Sham systems. Additional to the computational advantage, FDE provides physical insight into the properties of embedded systems and the coupling interactions between them. The extension to rt-TDDFT is done straightforwardly by evolving the Kohn-Sham subsystems in time simultaneously, while updating the embedding potential between the systems at every time step. Two main applications are presented: the explicit excitation energy transfer in real time between subsystems is demonstrated for the case of the Na4 cluster and the effect of the embedding on optical spectra of coupled chromophores. In particular, the importance of including the full dynamic response in the embedding potential is demonstrated.

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.

A Hirshfeld Partitioning of the MP2 Correlation Energy: Method and Its Application to the Benzene Dimers.

In this work a method is presented for the partitioning of MP2 correlation energies through a grid-space partitioning using the iterative Hirshfeld weight function. The correlation energies are partitioned into mono- and diatomic contributions using two alternative schemes, which allow different levels of parallelization. The method is tested on a set of 24 molecules containing various atoms, leading to the conclusion that, while the numerical results of the two schemes slightly differ, the chemical information contained in them is similar. The method is subsequently applied to the analysis of the interaction energy of three benzene dimers.

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.

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 Pauli's exclusion principle that suggest a reduced polarizability for condensed-phase water relative to the vacuum value.

Effect of hydrogen bonds on polarizability of a water molecule in (H2O)(N) (N = 6, 10, 20) isomers.

Polarizabilities of the low-lying isomers of (H(2)O)(N) (N = 6, 10, 20) clusters were computed by using Density Functional Theory. The global polarizabilities of the water isomers were found to depend mainly on the total number of water molecules rather than their cluster structures. We show that this result hides in fact a strong heterogeneity of the molecular polarizability within the different isomers. The global polarizability of a cluster was divided into a sum of molecular contributions by using the Hirshfeld partitioning scheme. We reveal that the value of the local polarizability of a molecule in the cluster is correlated with the number and type of the hydrogen bonds (HB) the molecule forms. Consequently, the molecules located in the interior of the cluster, which usually form more HBs, have smaller molecular polarizabilities than the molecules at the surface, which form less HBs. The contribution of intermolecular interaction to the global polarizability was analyzed by decomposing the cluster polarizability into intra- and inter-molecular contributions. The former measures the polarization within the molecular basin against the external electric field, while the latter is described as the sum of polarizability caused by charge flow through the HBs. These two contributions vary with the cluster size: the intermolecular contribution decreases with the cluster size on the contrary of the intramolecular contribution which increases.

Local softness, softness dipole, and polarizabilities of functional groups: application to the side chains of the 20 amino acids.

The values of molecular polarizabilities and softnesses of the 20 amino acids were computed ab initio (MP2). By using the iterative Hirshfeld scheme to partition the molecular electronic properties, we demonstrate that the values of the softness of the side chain of the 20 amino acids are clustered in groups reflecting their biochemical classification, namely: aliphatic, basic, acidic, sulfur containing, and aromatic amino acids. The present findings are in agreement with previous results using different approximations and partitioning schemes [P. Senet and F. Aparicio, J. Chem. Phys. 126, 145105 (2007)]. In addition, we show that the polarizability of the side chain of an amino acid depends mainly on its number of electrons (reflecting its size) and consequently cannot be used to cluster the amino acids in different biochemical groups, in contrast to the local softness. Our results also demonstrate that the global softness is not simply proportional to the global polarizability in disagreement with the intuition that "a softer moiety is also more polarizable." Amino acids with the same softness may have a polarizability differing by a factor as large as 1.7. This discrepancy can be understood from first principles as we show that the molecular polarizability depends on a "softness dipole vector" and not simply on the global softness.

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 Johnson's [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.

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.

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%.

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.

Dipeptidyl alpha-fluorovinyl Michael acceptors: synthesis and activity against cysteine proteases.

The synthesis of novel dipeptidyl alpha-fluorovinyl sulfones using a Horner-Wadsworth-Emmons approach on N-Boc-l-phenylalaninal is described. Inhibitory assays against a Leishmania mexicana cysteine protease (CPB2.8DeltaCTE) revealed low biological activity. Relative rates of Michael additions of 2'-(phenethyl)thiol with vinyl sulfone and alpha-fluorovinyl sulfone were determined, and ab initio calculations on several Michael acceptor model structures were performed; both were in agreement with the biological testing results.

Bonding study in all-metal clusters containing Al4 units.

The nature of the bonding of a series of gas-phase all-metal clusters containing the Al4 unit attached to an alkaline, alkaline earth, or transition metal is investigated at the DFT level using Mulliken, quantum theory of atoms in molecules (QTAIM), and Hirshfeld iterative (Hirshfeld-I) atomic partitionings. The characterization of ionic, covalent, and metallic bonds is done by means of charge polarization and multicenter electron delocalization. This Article uses for the first time Hirshfeld-I multicenter indices as well as Hirshfeld-I based atomic energy calculations. The QTAIM charges are in line with the electronegativity scale, whereas Hirshfeld-I calculations display deviations for transition metal clusters. The Mulliken charges fail to represent the charge polarization in alkaline metal clusters. The large ionic character of Li-Al and Na-Al bonds results in weak covalent bonds. On the contrary, scarcely ionic bonds (Be-Al, Cu-Al and Zn-Al) display stronger covalent bonds. These findings are in line with the topology of the electron density. The metallic character of these clusters is reflected in large 3-, 4- and 5-center electron delocalization, which is found for all the molecular fragments using the three atomic definitions. The previously reported magnetic inactivity (based on means of magnetic ring currents) of the pi system in the Al42- cluster contrasts with its large pi electron delocalization. However, it is shown that the different results not necessary contradict each other.