Topological analysis of electron densities from Kohn-Sham and subsystem density functional theory

In this study, we compare the electron densities for a set of hydrogen-bonded complexes obtained with either conventional Kohn-Sham density functional theory (DFT) calculations or with the frozen-density embedding (FDE) method, which is a subsystem approach to DFT. For a detailed analysis of the differences between these two methods, we compare the topology of the electron densities obtained from Kohn-Sham DFT and FDE in terms of deformation densities, bond critical points, and the negative Laplacian of the electron density. Different kinetic-energy functionals as needed for the frozen-density embedding method are tested and compared to a purely electrostatic embedding. It is shown that FDE is able to reproduce the characteristics of the density in the bonding region even in systems such as the F-H-F(-) molecule, which contains one of the strongest hydrogen bonds. Basis functions on the frozen system are usually required to accurately reproduce the electron densities of supermolecular calculations. However, it is shown here that it is in general sufficient to provide just a few basis functions in the boundary region between the two subsystems so that the use of the full supermolecular basis set can be avoided. It also turns out that electron-density deformations upon bonding predicted by FDE lack directionality with currently available functionals for the nonadditive kinetic-energy contribution.     

Modeling solvent effects on electron-spin-resonance hyperfine couplings by frozen-density embedding

In this study, we investigate the performance of the frozen-density embedding scheme within density-functional theory [J. Phys. Chem. 97, 8050 (1993)] to model the solvent effects on the electron-spin-resonance hyperfine coupling constants (hfcc's) of the H2NO molecule. The hfcc's for this molecule depend critically on the out-of-plane bending angle of the NO bond from the molecular plane. Therefore, solvent effects can have an influence on both the electronic structure for a given configuration of solute and solvent molecules and on the probability for different solute (plus solvent) structures compared to the gas phase. For an accurate modeling of dynamic effects in solution, we employ the Car-Parrinello molecular-dynamics (CPMD) approach. A first-principles-based Monte Carlo scheme is used for the gas-phase simulation, in order to avoid problems in the thermal equilibration for this small molecule. Calculations of small H2NO-water clusters show that microsolvation effects of water molecules due to hydrogen bonding can be reproduced by frozen-density embedding calculations. Even simple sum-of-molecular-densities approaches for the frozen density lead to good results. This allows us to include also bulk solvent effects by performing frozen-density calculations with many explicit water molecules for snapshots from the CPMD simulation. The electronic effect of the solvent at a given structure is reproduced by the frozen-density embedding. Dynamic structural effects in solution are found to be similar to the gas phase. But the small differences in the average structures still induce significant changes in the computed shifts due to the strong dependence of the hyperfine coupling constants on the out-of-plane bending angle.     

Couplings between electronic transitions in a subsystem formulation of time-dependent density functional theory

A subsystem formulation of time-dependent density functional theory (TDDFT) within the frozen-density embedding (FDE) framework and its practical implementation are presented, based on the formal TDDFT generalization of the FDE approach by Casida and Wesolowski [Int. J. Quantum Chem. 96, 577 (2004)]. It is shown how couplings between electronic transitions on different subsystems can be seamlessly incorporated into the formalism to overcome some of the shortcomings of the approximate TDDFT-FDE approach in use so far, which was only applicable for local subsystem excitations. In contrast to that, the approach presented here allows to include couplings between excitations on different subsystems, which become very important in aggregates composed of several similar chromophores, e.g., in biological or biomimetic light-harvesting systems. A connection to Forster- and Dexter-type excitation energy coupling expressions is established. A hybrid approach is presented and tested, in which excitation energy couplings are selectively included between different chromophore fragments, but neglected for inactive parts of the environment. It is furthermore demonstrated that the coupled TDDFT-FDE approach can cure the inability of the uncoupled FDE approach to describe induced circular dichroism in dimeric chromophores, a feature known as a "couplet," which is also related to couplings between (nearly) degenerate electronic transitions.     

The electronic spectrum of CUONg(4) (Ng = Ne, Ar, Kr, Xe): New insights in the interaction of the CUO molecule with noble gas matrices

The electronic spectrum of the CUO molecule was investigated with the IHFSCC-SD (intermediate Hamiltonian Fock-space coupled cluster with singles and doubles) method and with TD-DFT (time-dependent density functional theory) employing the PBE and PBE0 exchange-correlation functionals. The importance of both spin-orbit coupling and correlation effects on the low-lying excited-states of this molecule are analyzed and discussed. Noble gas matrix effects on the energy ordering and vibrational frequencies of the lowest electronic states of the CUO molecule were investigated with density functional theory (DFT) and TD-DFT in a supermolecular as well as a frozen density embedding (FDE) subsystem approach. This data is used to test the suitability of the FDE approach to model the influence of different matrices on the vertical electronic transitions of this molecule. The most suitable potential was chosen to perform relativistic wave function theory in density functional theory calculations to study the vertical electronic spectra of the CUO and CUONg(4) with the IHFSCC-SD method.     

Calculation of nuclear magnetic resonance shieldings using frozen-density embedding

We have extended the frozen-density embedding (FDE) scheme within density-functional theory [T. A. Wesolowski and A. Warshel, J. Phys. Chem. 97, 8050 (1993)] to include external magnetic fields and applied this extension to the nonrelativistic calculation of nuclear magnetic resonance (NMR) shieldings. This leads to a formulation in which the electron density and the induced current are calculated separately for the individual subsystems. If the current dependence of the exchange-correlation functional and of the nonadditive kinetic-energy functional are neglected, the induced currents in the subsystems are not coupled and each of them can be determined without knowledge of the induced current in the other subsystem. This allows the calculation of the NMR shielding as a sum of contributions of the individual subsystems. As a test application, we have calculated the solvent shifts of the nitrogen shielding of acetonitrile for different solvents using small geometry-optimized clusters consisting of acetonitrile and one solvent molecule. By comparing to the solvent shifts obtained from supermolecular calculations we assess the accuracy of the solvent shifts obtained from FDE calculations. We find a good agreement between supermolecular and FDE calculations for different solvents. In most cases it is possible to neglect the contribution of the induced current in the solvent subsystem to the NMR shielding, but it has to be considered for aromatic solvents. We demonstrate that FDE can describe the effect of induced currents in the environment accurately.     

Chiral-achiral molecular coupling: The effect on the chiral partner

Pair coupling between a chiral molecule and an achiral molecule can induce weak circular dichroism in the achiral partner, as is well known in induced circular dichroism. Here the effect of the same coupling on the chiral partner is analyzed. The effect is an increase or decrease in the rotatory strength that may be detectable under conditions where the effect is enhanced by a near-resonance.     

Simulation of Electronic Circular Dichroism of Nucleic Acids: From the Structure to the Spectrum

We present a quantum mechanical (QM) simulation of the electronic circular dichroism (ECD) of nucleic acids (NAs). The simulation combines classical molecular dynamics, to obtain the structure and its temperature‐dependent fluctuations, with a QM excitonic model to determine the ECD. The excitonic model takes into account environmental effects through a polarizable embedding and uses a refined approach to calculate the electronic couplings in terms of full transition densities. Three NAs with either similar conformations but different base sequences or similar base sequences but different conformations have been investigated and the results were compared with experimental observations; a good agreement was seen in all cases. A detailed analysis of the nature of the ECD bands in terms of their excitonic composition was also carried out. Finally, a comparison between the QM and the DeVoe models clearly revealed the importance of including fluctuations of the excitonic parameters and of accurately determining the electronic couplings. This study demonstrates the feasibility of the ab initio simulation of the ECD spectra of NAs, that is, without the need of experimental structural or electronic data.     

Modelling charge transfer reactions with the frozen density embedding formalism

The frozen density embedding (FDE) subsystem formulation of density-functional theory is a useful tool for studying charge transfer reactions. In this work charge-localized, diabatic states are generated directly with FDE and used to calculate electronic couplings of hole transfer reactions in two π-stacked nucleobase dimers of B-DNA: 5'-GG-3' and 5'-GT-3'. The calculations rely on two assumptions: the two-state model, and a small differential overlap between donor and acceptor subsystem densities. The resulting electronic couplings agree well with benchmark values for those exchange-correlation functionals that contain a high percentage of exact exchange. Instead, when semilocal GGA functionals are used the electronic couplings are grossly overestimated.     

An explicit quantum chemical method for modeling large solvation shells applied to aminocoumarin C151

The absorption spectra of aminocoumarin C151 in water and n-hexane solution are investigated by an explicit quantum chemical solvent model. We improved the efficiency of the frozen-density embedding scheme, as used in a former study on solvatochromism (J. Chem. Phys. 2005, 122, 094115) to describe very large solvent shells. The computer time used in this new implementation scales approximately linearly (with a low prefactor) with the number of solvent molecules. We test the ability of the frozen-density embedding to describe specific solvent effects due to hydrogen bonding for a small example system, as well as the convergence of the excitation energy with the number of solvent molecules considered in the solvation shell. Calculations with up to 500 water molecules (1500 atoms) in the solvent system are carried out. The absorption spectra are studied for C151 in aqueous or n-hexane solution for direct comparison with experimental data. To obtain snapshots of the dye molecule in solution, for which subsequent excitation energies are calculated, we use a classical molecular dynamics (MD) simulation with a force field adapted to first-principles calculations. In the calculation of solvatochromic shifts between solvents of different polarity, the vertical excitation energy obtained at the equilibrium structure of the isolated chromophore is sometimes taken as a guess for the excitation energy in a nonpolar solvent. Our results show that this is, in general, not an appropriate assumption. This is mainly due to the fact that the solute dynamics is neglected. The experimental shift between n-hexane and water as solvents is qualitatively reproduced, even by the simplest embedding approximation, and the results can be improved by a partial polarization of the frozen density. It is shown that the shift is mainly due to the electronic effect of the water molecules, and the structural effects are similar in n-hexane and water. By including water molecules, which might be directly involved in the excitation, in the embedded region, an agreement with experimental values within 0.05 eV is achieved.     

Orbital-free embedding applied to the calculation of induced dipole moments in CO2...X (X = He, Ne, Ar, Kr, Xe, Hg) van der Waals complexes

The orbital-free frozen-density embedding scheme within density-functional theory [T. A. Wesolowski and A. Warshel, J. Phys. Chem. 97, 8050 (1993)] is applied to the calculation of induced dipole moments of the van der Waals complexes CO2...X (X = He, Ne, Ar, Kr, Xe, Hg). The accuracy of the embedding scheme is investigated by comparing to the results of supermolecule Kohn-Sham density-functional theory calculations. The influence of the basis set and the consequences of using orbital-dependent approximations to the exchange-correlation potential in embedding calculations are examined. It is found that in supermolecular Kohn-Sham density-functional calculations, different common approximations to the exchange-correlation potential are not able to describe the induced dipole moments correctly and the reasons for this failure are analyzed. It is shown that the orbital-free embedding scheme is a useful tool for applying different approximations to the exchange-correlation potential in different subsystems and that a physically guided choice of approximations for the different subsystems improves the calculated dipole moments significantly.     

The merits of the frozen-density embedding scheme to model solvatochromic shifts

We investigate the usefulness of a frozen-density embedding scheme within density-functional theory [J. Phys. Chem. 97, 8050 (1993)] for the calculation of solvatochromic shifts. The frozen-density calculations, particularly of excitation energies have two clear advantages over the standard supermolecule calculations: (i) calculations for much larger systems are feasible, since the time-consuming time-dependent density functional theory (TDDFT) part is carried out in a limited molecular orbital space, while the effect of the surroundings is still included at a quantum mechanical level. This allows a large number of solvent molecules to be included and thus affords both specific and nonspecific solvent effects to be modeled. (ii) Only excitations of the system of interest, i.e., the selected embedded system, are calculated. This allows an easy analysis and interpretation of the results. In TDDFT calculations, it avoids unphysical results introduced by spurious mixings with the artificially too low charge-transfer excitations which are an artifact of the adiabatic local-density approximation or generalized gradient approximation exchange-correlation kernels currently used. The performance of the frozen-density embedding method is tested for the well-studied solvatochromic properties of the n-->pi(*) excitation of acetone. Further enhancement of the efficiency is studied by constructing approximate solvent densities, e.g., from a superposition of densities of individual solvent molecules. This is demonstrated for systems with up to 802 atoms. To obtain a realistic modeling of the absorption spectra of solvated molecules, including the effect of the solvent motions, we combine the embedding scheme with classical molecular dynamics (MD) and Car-Parrinello MD simulations to obtain snapshots of the solute and its solvent environment, for which then excitation energies are calculated. The frozen-density embedding yields estimated solvent shifts in the range of 0.20-0.26 eV, in good agreement with experimental values of between 0.19 and 0.21 eV.     

Molecular design of flexible liquid crystal oligomers stabilising the chiral frustrated phases

ABSTRACT

Chirality induces structural frustration in liquid crystal systems, producing various kinds of chiral frustrated phases, for example, twist grain boundary (TGB) phases, blue phases (BPs) and dark conglomerate (DC) phases. Almost all molecules exhibiting these frustrated phases have a rigid shape. Especially, a bent–core unit is regarded as a key structure for BPs and DC phases. This paper describes that some flexible liquid crystal oligomers being far from a rigid bent–core molecule stabilise these phases. The LC oligomers have a supermolecular structure in which mesogenic units are connected via flexible spacers. By designing intermolecular interactions, they can exhibit various molecular packing structures in the liquid-crystalline phases as follows: chiral dimers inducing TGB phases, U-shaped and T-shaped oligomers stabilising BPs and achiral liquid crystal trimers exhibiting DC phases. I discuss how the designed liquid crystal oligomers produce the chiral frustrated phases.     

Potential-energy surfaces of local excited states from subsystem- and selective Kohn-Sham-TDDFT

Calculating excited-state potential-energy surfaces for systems with a large number of close-lying excited states requires the identification of the relevant electronic transitions for several geometric structures. Time-dependent density functional theory (TDDFT) is very efficient in such calculations, but the assignment of local excited states of the active molecule can be difficult. We compare the results of the frozen-density embedding (FDE) method with those of standard Kohn-Sham density-functional theory (KS-DFT) and simpler QM/MM-type methods. The FDE results are found to be more accurate for the geometry dependence of excitation energies than classical models. We also discuss how selective iterative diagonalization schemes can be exploited to directly target specific excitations for different structures. Problems due to strongly interacting orbital transitions and possible solutions are discussed. Finally, we apply FDE and the selective KS-TDDFT to investigate the potential energy surface of a high-lying π → π^∗ excitation in a pyridine molecule approaching a silver cluster.     

Chiroptical spectroscopy of surfactants

Three different chiroptical spectroscopic methods, namely, optical rotation, electronic circular dichroism (ECD), and vibrational circular dichroism (VCD) have been evaluated for studying the aggregation of sodium dodecylsulfate (SDS), an achiral surfactant, using garcinia acid disodium salt (GADNa) as a chiral probe. The specific rotation and ECD of GADNa are found to be altered by the aggregation of SDS, suggesting for the first time that achiral surfactants can be characterized with chiroptical spectroscopy using appropriate chiral probes. In addition, a chiral compound, fluorenyl methyloxy carbonyl l-leucine sodium salt (FLNa) is found for the first time to behave as a surfactant in water, with 205 ?(2) surface area per molecule at the air-water interface, critical micelle concentration (CMC) of 0.18 M, and Gibbs energy of micellization of -14 kJ/mol. The specific rotation of FLNa in water is found to increase with concentration beyond CMC, suggesting the formation of chiral aggregates. Different conformations of FLNa amenable to micellization have been identified using quantum chemical conformational analysis and their specific rotations calculated. The formation of lamellar aggregates of FLNa in water is suggested to be the cause for increase in specific rotation with concentration beyond CMC.     

Vibronic contributions to DICD in achiral molecules

The theory of dispersion-induced circular dichroism (the CD induced in a transition of an achiral species through long-range dispersive coupling with a chiral species) is extended to include vibronic terms. Symmetry rules are deduced for DICD-active vibronic states. It is shown that the intensity distribution over DICD-active vibrations within a given electronic band of the achiral species gives both insight into the mechanism through which the DICD appears, and vibronic spectral data not accessible through direct absorption studies. Applications to the carbonyl chromophore and comparison with recent experimental studies suggest that vibronic terms may predominate in certain cases over those expected from the purely electronic case.     

Induced chirality upon crocetin binding to human serum albumin: origin and nature

Binding to human serum albumin (HSA) of the natural, achiral carotenoid crocetin, having hypocholesterolemic and antitumour effects, was investigated in detail by circular dichroism (CD) and absorption spectroscopy. It has been shown that in the visible absorption region the crocetin–HSA complex exhibits a well-defined induced circular dichroic spectrum with two major bands of opposite sign, proving excitonic interaction between carotenoids bound in a left-handed chiral arrangement on the albumin molecule. In the course of CD titration experiments, palmitic acid gradually decreased the exciton band intensities indicating that crocetin and palmitic acid have common binding sites on HSA. To investigate potential sources of the intermolecular excitonic interaction, molecular modeling studies were performed fitting crocetin molecules to the long-chain fatty acid binding sites of HSA, determined recently by X-ray crystallographic measurements. The results suggest that binding of crocetin to domain III of the albumin might be responsible for the observed intermolecular exciton coupling. Crocetin binding was accompanied by a significant red shift in the visible absorption spectrum which has showed no excitonic contribution but rather indicates the higher polarizability of the protein environment.     

Molecular Chirality Recognized by Achiral Compounds

Abstract

Three cases are described where chirality is recognized by achiral molecules, where chirality is induced into achiral compounds through interactions with chiral compounds, and lastly where induced chirality in the solid-state is utilized for an enantio-selective photoreaction. In the first instance, the thermodynamically and kinetically preferred diastereoisomer of an optically labile chromium complex depended on the nature of the achiral solvent. In the second case, for the first time 1,2-chloroethane was trapped and observed in a chiral near-eclipsed form and 1-chloropropane in the truly eclipsed form at room temperature in a 1:1 inclusion complex with an optically active host molecule. Finally, induced chirality in a prochiral compound in the solid-state was successfully employed in an enantio-selective photoreaction. In the two cases, solid-state CD provided valuable information.     

First-principles calculation of electronic spectra of light-harvesting complex II

We report on a fully quantum chemical investigation of important structural and environmental effects on the site energies of chlorophyll pigments in green-plant light-harvesting complex II (LHC II). Among the tested factors are technical and structural aspects as well as effects of neighboring residues and exciton couplings in the chlorophyll network. By employing a subsystem time-dependent density functional theory (TDDFT) approach based on the frozen density embedding (FDE) method we are able to determine site energies and electronic couplings separately in a systematic way. This approach allows us to treat much larger systems in a quantum chemical way than would be feasible with a conventional density functional theory. Based on this method, we have simulated a series of mutagenesis experiments to investigate the effect of a lack of one pigment in the chlorophyll network on the excitation properties of the other pigments. From these calculations, we can conclude that conformational changes within the chlorophyll molecules, direct interactions with neighboring residues, and interactions with other chlorophyll pigments can lead to non-negligible changes in excitation energies. All of these factors are important when site energies shall be calculated with high accuracy. Moreover, the redistribution of the oscillator strengths due to exciton coupling has a large impact on the calculated absorption spectra. This indicates that modeling mutagenesis experiments requires us to consider the entire set of chlorophyll molecules in the wild type and in the mutant, rather than just considering the missing chlorophyll pigment. An analysis of the mixing of particular excitations and the coupling elements in the FDEc calculation indicates that some pigments in the chlorophyll network act as bridges which mediate the interaction between other pigments. These bridges are also supported by the calculations on the "mutants" lacking the bridging pigment.     

Solute-solvent interactions and chiral induction in liquid crystals

The induction of a cholesteric phase by doping an achiral nematic liquid crystal with an enantiopure solute is a phenomenon that, as in all general supramolecular phenomena of chiral amplification, depends in a subtle way on intermolecular interactions. The micrometric helical deformation of the phase director in the cholesteric phase is generated by the interplay of anisotropy and chirality of probe-medium interactions. In the case of a flexible chiral dopant, the solvent can influence the twisting power in two ways, difficult to disentangle: it is responsible for the solute orientational order, an essential ingredient for the emergence of phase chirality; but also it can affect the dopant conformational distribution and then the chirality of the structures present in the solution. In this work we have investigated methyl phenyl sulfoxide, a flexible, chiral molecule that, when dissolved in different nematics, can produce cholesteric phases of opposite handedness. This peculiar, intriguing sensitivity to the environment makes MPS a suitable probe for a thorough investigation of the effects of solute-solvent interactions on chiral induction in liquid crystals. NMR experiments in various nematic solvents have been performed in addition to twisting power measurements. From the analysis of partially averaged 1H-1H and 13C-1H dipolar couplings, the effects of solvent on solute conformation and orientational order are disentangled, and this information is combined with the modeling of the chirality of intermolecular interactions, within a molecular field theory. The integration of different techniques allows an unprecedented insight into the role of solvent in mediating the chirality transfer from molecule to phase.     

Laser-operated chiral molecular switch: quantum simulations for the controlled transformation between achiral and chiral atropisomers

We report quantum dynamical simulations for the laser controlled isomerization of 1-(2-cis-fluoroethenyl)-2-fluorobenzene based on one-dimensional electronic ground and excited state potentials obtained from (TD)DFT calculations. 1-(2-cis-fluoroethenyl)-2-fluorobenzene supports two chiral and one achiral atropisomers, the latter being the most stable isomer at room temperature. Using a linearly polarized IR laser pulse the molecule is excited to an internal rotation around its chiral axis, i.e. around the C-C single bond between phenyl ring and ethenyl group, changing the molecular chirality. A second linearly polarized laser pulse stops the torsion to prepare the desired enantiomeric form of the molecule. This laser control allows the selective switching between the achiral and either the left- or right-handed form of the molecule. Once the chirality is "switched on" linearly polarized UV laser pulses allow the selective change of the chirality using the electronic excited state as intermediate state.