Analytical Model for the Molecular Ionization Energy in an External Electric Field.

A model for the molecular ionization energy in an applied electric field is presented on the basis of a perturbation expansion in the electric field. The leading term arises from the Frenkel approach, which is the same for all molecules normally used in the Poole-Frenkel model for conductivity in an electric field. For a set of test molecules, the quality of the results is comparable to that of previous results using constrained density functional theory. We conclude that the Frenkel term is dominant and sufficient at relatively low fields and that the dipole and polarizability terms, the leading terms dependent on the properties of the individual molecule, make a significant contribution only at high fields and for relatively large molecules. Because the presented model is analytical, quantum chemical calculations are avoided for a variety of electric field strengths and molecular orientations, and the model can therefore be applied directly in coarse-grained models for electronic processes in dielectric condensed phases.

Geometrical flexibility of platinum nanoclusters: impacts on catalytic decomposition of ethylene glycol.

Catalytic decomposition of ethylene glycol on the Pt13 cluster was studied as a model system for hydrogen production from a lignocellulosic material. Ethylene glycol was chosen as a starting material because of two reasons, it is the smallest oxygenate with a 1 : 1 carbon to oxygen ratio and it contains the C-H, O-H, C-C, and C-O bonds also present in biomass. Density functional theory calculations were employed for predictions of reaction pathways for C-H, O-H, C-C and C-O cleavages, and Brønsted-Evans-Polanyi relationships were established between the final state and the transition state for all mechanisms. The results show that Pt13 catalyzes the cleavage reactions of ethylene glycol more favourably than a Pt surface. The flexibility of Pt13 clusters during the reactions is the key factor in reducing the activation barrier. Overall, the results demonstrate that ethylene glycol and thus biomass can be efficiently converted into hydrogen using platinum nanoclusters as catalysts.

Solvent Effects on Optical Rotation: On the Balance between Hydrogen Bonding and Shifts in Dihedral Angles.

Optical rotations of several conformers of four fluorinated molecules containing the 1-naphthalene or 4-(benzyloxy)phenyl group at the stereocenter have been calculated both in the gas phase and in an aqueous environment. For the compounds containing the 4-(benzyloxy)phenyl group, solvent effects on the optical rotations have also been investigated in chloroform as solvent. Optical rotations have been obtained by time-dependent density functional theory (TDDFT) with the CAM-B3LYP functional and the aug-cc-pVDZ basis set at λ = 589 nm. Implicit and explicit solvent effects were investigated through the polarizable continuum model (PCM) and a microsolvation approach in conjunction with PCM, respectively. In the latter model, solvent molecules are considered as an explicit solvent and their positions are obtained by geometry optimizations for different conformers of the chiral molecule. For molecules containing the 1-naphthalene group, this model gives the same optical rotation signs for all conformers as compared to both gas phase and PCM results and reduces absolute deviations between calculations and experiment. Also, the microsolvation model reproduces the sign of the experimental optical rotations for the molecules containing the 4-(benzyloxy)phenyl group using both water and chloroform as solvent. In a microsolvation model, however, the water and chloroform solvent molecules have similar hydrogen bonds but different effects on the conformation and thereby on the optical rotation since one dihedral angle, having a large effect on the optical rotation, is strongly sensitive to hydrogen bonding to water but not to chloroform. Our investigations demonstrate that a microsolvation approach in conjunction with PCM predicts optical rotations in reasonable agreements with experiments for both sign and magnitude.

Optical Rotation Calculations for Fluorinated Alcohols, Amines, Amides, and Esters.

We have calculated the optical rotation at λ = 589 nm for 45 fluorinated alcohols, amines, amides, and esters using both time-dependent density functional theory (TDDFT) with the CAM-B3LYP functional and the second-order approximate coupled-cluster singles and doubles (CC2) method, where the aug-cc-pVDZ basis set was adopted in both methods. Comparison of CAM-B3LYP and CC2 results to experiments illustrates that both methods are able to reproduce the experimental optical rotation results for both sign and magnitude. Several conformers for molecules containing the benzyloxy and naphthalene groups needed to be considered to obtain consistent signs with experiments, and these conformers are discussed in detail. We have also used a two-point inverse power extrapolation of the basis set to investigate the optical rotation in the basis set limit at the CC2 level, however, we only found small differences compared to the aug-cc-pVTZ results. Our results demonstrate that the least computationally expensive method investigated here, the CAM-B3LYP functional with the aug-cc-pVDZ basis set, is a reliable method to predict the optical rotation for large molecules and thereby the absolute configuration of chiral molecules.

Optical Rotation Calculations for a Set of Pyrrole Compounds.

Optical rotation of 14 molecules containing the pyrrole group is calculated by employing both time-dependent density functional theory (TDDFT) with the CAM-B3LYP functional and the second-order approximate coupled-cluster singles and doubles (CC2) method. All optical rotations have been provided using the aug-cc-pVDZ basis set at λ = 589 nm. The two methods predict similar results for both sign and magnitude for the optical rotation of all molecules. The obtained signs are consistent with experiments as well, although several conformers for four molecules needed to be studied to reproduce the experimental sign. We have also calculated excitation energies and rotatory strengths for the six lowest lying electronic transitions for several conformers of the two smallest molecules and found that each rotatory strength has various contributions for each conformer which can cause different optical rotations for different conformers of a molecule. Our results illustrate that both methods are able to reproduce the experimental optical rotations, and that the CAM-B3LYP functional, the least computationally expensive method used here, is an applicable and reliable method to predict the optical rotation for these molecules in line with previous studies.

Optical Rotation from Coupled Cluster and Density Functional Theory: The Role of Basis Set Convergence.

We have calculated the electronic optical rotation of seven molecules using coupled cluster singles-doubles (CCSD) and the second-order approximation (CC2) employing the aug-cc-pVXZ (X = D, T, or Q) basis sets. We have also compared to time-dependent density functional theory (TDDFT) by utilizing two functionals B3LYP and CAM-B3LYP and the same basis sets. Using relative and absolute error schemes, our calculations demonstrate that the CAM-B3LYP functional predicts optical rotation with the minimum deviations compared to CCSD at λ = 355 and 589.3 nm. Furthermore, our results illustrate that the aug-cc-pVDZ basis set provides the optical rotation in good agreement with the larger basis sets for molecules not possessing small-angle optical rotation at λ = 589.3 nm. We have also performed several two-point inverse power extrapolations for the basis set convergence, i.e., OR(∞) + AX(-n), using the CC2 model at λ = 355 and 589.3 nm. Our results reveal that a two-point inverse power extrapolation with the aug-cc-pVTZ and aug-cc-pVQZ basis sets at n = 5 provides optical rotation deviations similar to those of aug-cc-pV5Z with respect to the basis limit.

A test on reactive force fields for the study of silica dimerization reactions.

We studied silica dimerization reactions in the gas and aqueous phase by density functional theory (DFT) and reactive force fields based on two parameterizations of ReaxFF. For each method (both ReaxFF force fields and DFT), we performed constrained geometry optimizations, which were subsequently evaluated in single point energy calculations using the other two methods. Standard fitting procedures typically compare the force field energies and geometries with those from quantum mechanical data after a geometry optimization. The initial configurations for the force field optimization are usually the minimum energy structures of the ab initio database. Hence, the ab initio method dictates which structures are being examined and force field parameters are being adjusted in order to minimize the differences with the ab initio data. As a result, this approach will not exclude the possibility that the force field predicts stable geometries or low transition states which are realistically very high in energy and, therefore, never considered by the ab initio method. Our analysis reveals the existence of such unphysical geometries even at unreactive conditions where the distance between the reactants is large. To test the effect of these discrepancies, we launched molecular dynamics simulations using DFT and ReaxFF and observed spurious reactions for both ReaxFF force fields. Our results suggest that the standard procedures for parameter fitting need to be improved by a mutual comparative method.

Density Functional Theory Study on the Interactions of Metal Ions with Long Chain Deprotonated Carboxylic Acids.

In this work, interactions between carboxylate ions and calcium or sodium ions are investigated via density functional theory (DFT). Despite the ubiquitous presence of these interactions in natural and industrial chemical processes, few DFT studies on these systems exist in the literature. Special focus has been placed on determining the influence of the multibody interactions (with up to 4 carboxylates and one metal ion) on an effective pair-interaction potential, such as those used in molecular mechanics (MM). Specifically, DFT calculations are employed to quantify an effective pair-potential that implicitly includes multibody interactions to construct potential energy curves for carboxylate-metal ion pairs. The DFT calculated potential curves are compared to a widely used molecular mechanics force field (OPLS-AA). The calculations indicate that multibody effects do influence the energetic behavior of these ionic pairs and the extent of this influence is determined by a balance between (a) charge transfer from the carboxylate to the metal ions which stabilizes the complex and (b) repulsion between carboxylates, which destabilizes the complex. Additionally, the potential curves of the complexes with 1 and 2 carboxylates and one counterion have been examined to higher separation distance (20 Å) by the use of relaxed scan optimization and constrained density functional theory (CDFT). The results from the relaxed scan optimization indicate that near the equilibrium distance, the charge transfer between the metal ion and the deprotonated carboxylic acid group is significant and leads to non-negligible differences between the DFT and MM potential curves, especially for calcium. However, at longer separation distances the MM calculated interaction potential functions converge to those calculated with CDFT, effectively indicating the approximate domain of the separation distance coordinate where charge transfer between the ions is occurring.

Local Field Factors and Dielectric Properties of Liquid Benzene.

Local electric field factors are calculated for liquid benzene by combining molecular dynamic simulations with a subsequent force-field model based on a combined charge-transfer and point-dipole interaction model for the local field factor. The local field factor is obtained as a linear response of the local field to an external electric field, and the response is calculated at frequencies through the first absorption maximum. It is found that the largest static local field factor is around 2.4, while it is around 6.4 at the absorption frequency. The linear susceptibility, the dielectric constant, and the first absorption maximum of liquid benzene are also studied. The electronic contribution to the dielectric constant is around 2.3 at zero frequency, in good agreement with the experimental value around 2.2, while it increases to 6.3 at the absorption frequency. The π → π* excitation energy is around 6.0 eV, as compared to the gas-phase value of around 6.3 eV, while the experimental values are 6.5 and 6.9 eV for the liquid and gas phase, respectively, demonstrating that the gas-to-liquid shift is well-described.

Lithium ion-water clusters in strong electric fields: a quantum chemical study.

We use density functional theory to investigate the impact that strong electric fields have on the structure and energetics of small lithium ion-water clusters, Li(+)·nH2O, with n = 4 or 6. We find that electric field strengths of ∼0.5 V/Å are sufficient to break the symmetry of the n = 4 tetrahedral energy minimum structure, which undergoes a transformation to an asymmetric cluster consisting of three water molecules bound to lithium and one additional molecule in the second solvation shell. Interestingly, this cluster remains the global minimum configuration at field strengths ≳0.15 V/Å. The 6-coordinated cluster, Li(+)·6H2O, features a similar transition to 5- and 4-coordinated clusters at field strengths of ∼0.2 and ∼0.3 V/Å, respectively, with the tetra-coordinated structure being the global minimum even in the absence of the field. Our findings are relevant to understanding the behavior of the Li(+) ion in aqueous environments under strong electric fields and in interfacial regions where field gradients are significant.

Complex frequency-dependent polarizability through the π → π* excitation energy of azobenzene molecules by a combined charge-transfer and point-dipole interaction model.

The complex frequency-dependent polarizability and π → π* excitation energy of azobenzene compounds are investigated by a combined charge-transfer and point-dipole interaction (CT/PDI) model. To parametrize the model, we adopted time-dependent density functional theory (TDDFT) calculations of the frequency-dependent polarizability extended with excited-state lifetimes to include also its imaginary part. The results of the CT/PDI model are compared with the TDDFT calculations and experimental data demonstrating that the CT/PDI model is fully capable to reproduce the static polarizability as well as the π → π* excitation energy for these compounds. In particular, azobenzene molecules with different functional groups in the para-position have been included serving as a severe test of the model. The π → π* excitation is to a large extent localized to the azo bond, and substituting with electron-donating or electron-attracting groups on the phenyl rings results in charge-transfer effects and a shift in the excitation energy giving rise to azobenzene compounds with a range of different colors. In the CT/PDI model, the π → π* excitation in azobenzenes is manifested as drastically increasing atomic induced dipole moments in the azo group as well as in the adjacent carbon atoms, whereas the shifts in the excitation energies are due to charge-transfer effects.

Thermo-molecular orientation effects in fluids of dipolar dumbbells.

We use molecular dynamics simulations in applied thermal gradients to study thermomolecular orientation (TMO) of size-asymmetric dipolar dumbbells with different molecular dipole moments. We find that the direction of the TMO is the same as in apolar dumbbells of the same size, i.e. the smaller atom in the dumbbell tends to orient towards the colder temperature. The ratio of the electrical polarization to the magnitude of the thermal gradient does not vary much with the magnitude of the molecular dipole moment. We also investigate a novel second order TMO that persists even in size-symmetric dipolar dumbbells where molecules have a slight tendency to orient perpendicular to the gradient except very close to the hot region, where (anti-)parallel orientations are preferred. Finally, we investigate rotational correlation functions and characteristic rotational times in these systems in an attempt to model possible spectroscopic signatures of TMO in experiments. Although we cannot detect any difference in integrated rotational times between equilibrium simulations and simulations in a thermal gradient, more careful modelling of the anisotropic rotational dynamics in the thermal gradient may be more successful.

Structural and electronic properties of the Pt(n)-PAH complex (n = 1, 2) from density functional calculations.

A detailed density functional study of the Pt atom and the Pt dimer adsorption on a polyaromatic hydrocarbon (PAH) is presented. The preferred adsorption site for a Pt atom is confirmed to be the bridge site. Upon adsorption of a single Pt atom, however, it is found here that the electronic ground state changes from the triplet state (5d(9)6s(1) configuration) to the closed-shell singlet state (5d(10)6s(0) configuration), which consequently will affect the catalytic activity of Pt when single Pt atoms bind to a carbon surface. The preferred adsorption site for the Pt dimer in the upright configuration is the hollow site. In contrast to the adsorption of a single Pt atom, the formation of a Pt-C bond in the adsorption of a Pt dimer is not accompanied by a change in the spin state, so the most stable electronic state is still the triplet state. While the atomic charge on the Pt atoms and dimers (in parallel configuration) in the Ptn-PAH complex is positive, a negative charge is found on the upper Pt atom for the upright configuration, indicating that single layers of Pt atoms will have a different catalytic activity as compared to Pt clusters on a carbon surface. Comparing the Pt-C bond length and the charge transfer on different sites, the magnitude of the charge transfer decreases with bond elongation, indicating that the catalytic activity of the Pt atom and dimer can be changed by modifying its chemical surroundings. The adsorption energy for the Pt dimer on a PAH surface is larger than that for two individual Pt atoms on the surface indicating that aggregation of Pt atoms on the PAH surface is favorable.

Quantitative structure-property relationship modeling of Grätzel solar cell dyes.

With fossil fuel reserves on the decline, there is increasing focus on the design and development of low-cost organic photovoltaic devices, in particular, dye-sensitized solar cells (DSSCs). The power conversion efficiency (PCE) of a DSSC is heavily influenced by the chemical structure of the dye. However, as far as we know, no predictive quantitative structure-property relationship models for DSSCs with PCE as one of the response variables have been reported. Thus, we report for the first time the successful application of comparative molecular field analysis (CoMFA) and vibrational frequency-based eigenvalue (EVA) descriptors to model molecular structure-photovoltaic performance relationships for a set of 40 coumarin derivatives. The results show that the models obtained provide statistically robust predictions of important photovoltaic parameters such as PCE, the open-circuit voltage (V(OC)), short-circuit current (J(SC)) and the peak absorption wavelength λ(max). Some of our findings based on the analysis of the models are in accordance with those reported in the literature. These structure-property relationships can be applied to the rational structural design and evaluation of new photovoltaic materials.

Nonmetallic electronegativity equalization and point-dipole interaction model including exchange interactions for molecular dipole moments and polarizabilities.

The electronegativity equalization model (EEM) has been combined with a point-dipole interaction model to obtain a molecular mechanics model consisting of atomic charges, atomic dipole moments, and two-atom relay tensors to describe molecular dipole moments and molecular dipole-dipole polarizabilities. The EEM has been phrased as an atom-atom charge-transfer model allowing for a modification of the charge-transfer terms to avoid that the polarizability approaches infinity for two particles at infinite distance and for long chains. In the present work, these shortcomings have been resolved by adding an energy term for transporting charges through individual atoms. A Gaussian distribution is adopted for the atomic charge distributions, resulting in a damping of the electrostatic interactions at short distances. Assuming that an interatomic exchange term may be described as the overlap between two electronic charge distributions, the EEM has also been extended by a short-range exchange term. The result is a molecular mechanics model where the difference of charge transfer in insulating and metallic systems is modeled regarding the difference in bond length between different types of system. For example, the model is capable of modeling charge transfer in both alkanes and alkenes with alternating double bonds with the same set of carbon parameters only relying on the difference in bond length between carbon sigma- and pi-bonds. Analytical results have been obtained for the polarizability of a long linear chain. These results show that the model is capable of describing the polarizability scaling both linearly and nonlinearly with the size of the system. Similarly, a linear chain with an end atom with a high electronegativity has been analyzed analytically. The dipole moment of this model system can either be independent of the length or increase linearly with the length of the chain. In addition, the model has been parametrized for alkane and alkene chains with data from density functional theory calculations, where the polarizability behaves differently with the chain length. For the molecular dipole moment, the same two systems have been studied with an aldehyde end group. Both the molecular polarizability and the dipole moment are well described as a function of the chain length for both alkane and alkene chains demonstrating the power of the presented model.

Molecular dynamics simulations of the interactions between platinum clusters and carbon platelets.

Molecular dynamics simulations have been performed with two reactive force fields to investigate the structure of a Pt100 cluster adsorbed on the three distinct sides of a carbon platelet. A revised Reax force field for the carbon-platinum system is presented. In the simulations, carbon platelet edges both with and without hydrogen termination have been studied. It is found that the initial mismatch between the atomic structure of the platelet egde and the adsorbed face of the Pt100 cluster leads to a desorption of a few platinum atoms from the cluster and the subsequent restructuring of the cluster. Consequently, the average Pt-Pt bond length is enlarged in agreement with experimental results. This change in the bond length is supposed to play an important role in the enhancement of the catalytic activity, which is demonstrated by studying the changes in the bond order of the platinum atoms. We found an overall shift to lower values as well as a loss of the well-defined peak structure in the bond-order distribution.

Quantitative prediction of the absorption maxima of azobenzene dyes from bond lengths and critical points in the electron density.

The relationship between the molecular electronic structure and the position of the absorption maxima in 191 azobenzene dyes has been studied by quantitative structure-property relations. A strong linearity is observed between the nitrogen-nitrogen bond length and the absorption wavelength with a squared correlation coefficient of 0.90. Bond lengths and properties of the critical points located on the electron density distribution are used to build partial least squares regression models for quantitative prediction of absorption wavelengths. Fifty of the azobenzene dyes were used as an external test set to evaluate the overall performance of the models. The simplest model where only the nitrogen-nitrogen bond length is used as a descriptor gives a root mean square error of prediction of 12.6 nm. When the value, laplacian and ellipticity of the electron density in all comparable bond critical points are used, the error of prediction is reduced to 5.4 nm. However, this model is less general and robust to prediction of novel molecular structures. It is demonstrated that the nitrogen-nitrogen bond in the azobenzene compounds relates to the colour of the dyes and in particular the nitrogen-nitrogen bond length plays a central role.

Validation of critical points in the electron density as descriptors by building quantitative structure-property relationships for the atomic polar tensor.

A crucial component of research in the field of quantitative structure-activity/property relationships is the identification of molecular descriptors relevant to the activity or property of interest. Descriptors based on the topology of the electron density as formulated in Bader's theory of atoms in molecules are investigated in detail in this work. In a model study, the authors investigate their ability to predict the atomic polar tensor (the gradient of the molecular dipole moment), which contains information on the vibrational intensities in infrared spectroscopy and constitutes a scheme for partitioning the total charge distribution into atomic charges. The atomic polar tensor may therefore be used to investigate whether the descriptors give adequate information on the local electronic structure in the molecule. Both the trace of the atomic polar tensor and for planar molecules its out-of-plane component may be interpreted as definitions of atomic charges suitable for prediction. Hydrogen and carbon atoms in a set of 60 aromatic compounds with various substituents have been studied. Excellent results for prediction of hydrogen and carbon charges have been achieved with cross-validated squared correlation coefficients between predicted and theoretical values varying from 0.92 and 0.977 for the most complex set of substituents when the value, Laplacian, and ellipticity of the electron density in the bond critical points are used as descriptors. The carbon charges defined from the trace of the atomic polar tensor are correlated with its out-of-plane component whereas such relationship is not observed for the hydrogen charges studied in this work.

Statistical mechanically averaged molecular properties of liquid water calculated using the combined coupled cluster/molecular dynamics method.

Liquid water is investigated theoretically using combined molecular dynamics (MD) simulations and accurate electronic structure methods. The statistical mechanically averaged molecular properties of liquid water are calculated using the combined coupled cluster/molecular mechanics (CC/MM) method for a large number of configurations generated from MD simulations. The method includes electron correlation effects at the coupled cluster singles and doubles level and the use of a large correlation consistent basis set. A polarizable force field has been used for the molecular dynamics part in both the CC/MM method and in the MD simulation. We describe how the methodology can be optimized with respect to computational costs while maintaining the quality of the results. Using the optimized method we study the energetic properties including the heat of vaporization and electronic excitation energies as well as electric dipole and quadrupole moments, the frequency dependent electric (dipole) polarizability, and electric-field-induced second harmonic generation first and second hyperpolarizabilities. Comparisons with experiments are performed where reliable data are available. Furthermore, we discuss the important issue on how to compare the calculated microscopic nonlocal properties to the experimental macroscopic measurements.

Refractive index of liquid water in different solvent models.

We present a combined molecular dynamics/quantum chemical perturbation method for calculating the refractive index of liquid water at different temperatures. We compare results of this method with the refractive index obtained from other solvent models. The best agreement with the experimental refractive index of liquid water and its temperature dependence is obtained using correlated gas-phase polarizabilities in the classical Lorentz-Lorenz expression. Also, the iterative self-consistent reaction field approach in the semicontinuum implementation matches the experimental refractive index reasonably well.