First-principles calculation of local atomic polarizabilities

Common methods of determining atomic polarizabilities suffer from the inclusion of nonlocal effects such as charge polarization. A new method is described for determining fully ab initio atomic polarizabilities based on calculating the response of atomic multipoles to the local electrostatic potential. The localized atomic polarizabilities are then used to calculate induction energies that are compared to ab initio induction energies to test their usefulness in practical applications. These polarizabilities are shown to be an improvement over the corresponding molecular polarizabilities, in terms of both absolute accuracy and the convergence of the multipolar induction series. The transferability of localized polarizabilities for the alkane series is also discussed.     

Coupled-cluster dynamic polarizabilities including triple excitations

Dynamic polarizabilities for open- and closed-shell molecules were obtained by using coupled-cluster (CC) linear response theory with full treatment of singles, doubles, and triples (CCSDT-LR) with large basis sets utilizing the NWChem software suite. By using four approximate CC methods in conjunction with augmented cc-pVNZ basis sets, we are able to evaluate the convergence in both many-electron and one-electron spaces. For systems with primarily dynamic correlation, the results for CC3 and CCSDT are almost indistinguishable. For systems with significant static correlation, the CC3 tends to overestimate the triples contribution, while the PS(T) approximation [J. Chem. Phys. 127, 164105 (2007)] produces mixed results that are heavily dependent on the accuracies provided by noniterative approaches used to correct the equation-of-motion CCSD excitation energies. Our results for open-shell systems show that the choice of reference (restricted open-shell Hartree-Fock versus unrestricted Hartree-Fock) can have a significant impact on the accuracy of polarizabilities. A simple extrapolation based on pentuple-zeta CCSD calculations and triple-zeta CCSDT calculations reproduces experimental results with good precision in most cases.     

How to Predict Excited State Geometry by Using Empirical Parameters Obtained from Franck-Condon Analysis of Optical Spectrum

Excited state geometries of molecules can be calculated with highly reliable wavefunction schemes. Most of such schemes, however, are applicable to small molecules and can hardly be viewed as error-free for excited state geometries. In this study, a theoretical approach is presented in which the excited state geometries of molecules can be predicted by using vibrationally resolved experimental absorption spectrum in combination with the theoretical modelling of vibrational pattern based on Franck-Condon approximation. Huang-Rhys factors have been empirically determined and used as input for revealing the structural changes occurring between the ground and the excited state geometries upon photoexcitation. Naphthalene molecule has been chosen as a test case to show the robustness of the proposed theoretical approach. Predicted 1B_2u excited state geometry of the naphthalene has similar but slightly different bond length alternation pattern when compared with the geometries calculated with CIS, B3LYP, and CC2 methods. Excited state geometries of perylene and pyrene molecules are also determined with the presented theoretical approach. This powerful method can be applied to other molecules and specifically to relatively large molecules rather easily as long as vibrationally resolved experimental spectra are available to use.     

Gaussian induced dipole polarization model

A new induced dipole polarization model based on interacting Gaussian charge densities is presented. In contrast to the original induced point dipole model, the Gaussian polarization model is capable of finite interactions at short distances. Aspects of convergence related to the Gaussian model will be explored. The Gaussian polarization model is compared with the damped Thole-induced dipole model and the point dipole model. It will be shown that the Gaussian polarization model performs slightly better than the Thole model in terms of fitting to molecular polarizability tensors. An advantage of the model based on Gaussian charge distribution is that it can be easily generalized to other multipole moments and provide effective damping for both permanent electrostatic and polarization models. Finally, a method of parameterizing polarizabilities is presented. This method is based on probing a molecule with point charges and fitting polarizabilities to electrostatic potential. In contrast to the generic atom type polarizabilities fit to molecular polarizability tensors, probed polarizabilities are significantly more accurate in terms of reproducing molecular polarizability tensors and electrostatic potential, while retaining conformational transferability.     

Partitioning of higher multipole polarizabilities: numerical evaluation of transferability

In this work, the partitioning of higher multipole polarizabilities, such as dipole-quadrupole, quadrupole-dipole, and quadrupole-quadrupole polarizabilities, into atomic contributions is studied. Partitioning of higher multipole polarizabilities is necessary in the study of accurate interaction energies where dispersion interactions are of importance. The fractional occupation Hirhsfeld-I (FOHI) method is used to calculate the atomic polarizabilities and is briefly explained together with the methodology for partitioning of the polarizabilities. The atomic multipole polarizabilities are calculated for different sets of molecules, linear alkanes, water clusters, and small organic molecules with different functional groups. It is found that the atomic and group contributions of the dipole and quadrupole polarizabilities are transferable as a function of the functional groups.     

XCC2--a new coupled cluster model for the second-order polarization propagator

A new coupled cluster model of the polarization propagator, denoted as XCC2, is presented. The XCC2 approach employs time-independent coupled cluster theory of polarization propagators of Moszynski et al. [Collect. Czech. Chem. Commun., 2005, 70, 1109] and excitation operators from the time-dependent (TD) CC2 method. The performance of XCC2 was investigated by calculating static and dynamic dipole polarizabilities for a test set of over 20 molecules and comparing them with TD-CCSD results. The quality of XCC2 dispersion coefficients for several noncovalent molecular complexes was also tested against the benchmark values. This numerical study reveals that the average percent error of XCC2 is significantly reduced in comparison to the TD-CC2 method (4-fold reduction for the mean polarizabilities and 2-fold reduction for anisotropic polarizabilities is observed). Since the computational requirements of both XCC2 and TD-CC2 methods are virtually the same, the new XCC2 method can be viewed as a practical alternative for TD-CC2 for property calculations, giving the second-order polarization propagators of near-CCSD quality in many cases, but retaining at the same time the lower computational cost of the TD-CC2 model.     

On the accuracy of computed excited-state dipole moments

The dipole moments of furan and pyrrole in many electronically excited singlet states have been determined using coupled cluster theory including large one-electron basis sets. The inclusion of connected triple excitations is shown to uniformly decrease the equation-of-motion coupled-cluster singles and doubles (EOM-CCSD) excitation energies by 0.04-0.24 eV, with an average reduction of 0.08 eV. Using a basis set larger than DZP (++)D (double-zeta plus polarization augmented with atom- and molecule-centered diffuse functions) uniformly increases the computed EOM-CCSD excitation energies by 0.03-0.29 eV, with an average increase of 0.20 eV. The corresponding shifts in excited-state dipole moments are more erratic. Including connected triple excitations changes the computed dipole moments by an rms amount of 0.17 au. More importantly, using a larger basis set shifts the dipole moments by an rms amount of 0.52 au, with an increase or a decrease being equally likely. The CC dipole moments are compared to those from time-dependent density functional theory (TD-DFT) computed by Burcl, Amos, and Handy [ Chem. Phys. Lett. 2002, 355, 8]. For 29 excited states of furan and pyrrole, the predicted TD-DFT dipole moments differ from the CC results by rms amounts of 1.6 au (HCTH functional) and 1.5 au (B97-1 functional). Including the asymptotic correction to TD-DFT developed by Tozer and Handy [ J. Chem. Phys. 1998, 109, 10180; J. Comput. Chem. 1999, 20, 106] reduces the rms differences for both functionals to 1.2 au. If those Rydberg excited states with very large polarizabilities are excluded, the rms differences from the CC results for the remaining 17 excited states become 1.31 au (HCTH) and 0.88 au (B97-1). For asymptotically corrected functionals and this subset of states, the rms differences from the CC results are only 0.54 au (HCTHc) and 0.34 au (B97-1c). Thus, the Tozer-Handy asymptotic correction for TD-DFT significantly improves the predictions of excited-state dipole moments. For excited states without very large polarizabilities, good agreement is achieved between excited-state dipole moments computed by coupled cluster theory and by the asymptotically corrected B97-1c density functional.     

The calculation of ground and excited state molecular polarizabilities: A simple perturbation treatment

Second order perturbation theory has been coupled with the CNDO/S CI method of Del Bene and Jaffé to calculate the ground and excited state polarizabilities of various molecules. It is found that this treatment produces reasonably good polarizabilities with great computational ease.     

Large scale polarizability calculations using the approximate coupled cluster model CC2 and MP2 combined with the resolution-of-the-identity approximation

We present an implementation of static and frequency-dependent polarizabilities for the approximate coupled cluster singles and doubles model CC2 and static polarizabilities for second-order Mo?ller-Plesset perturbation theory. Both are combined with the resolution-of-the-identity approximation for electron repulsion integrals to achieve unprecedented low operation counts, input-output, and disc space demands. To avoid the storage of double excitation amplitudes during the calculation of derivatives of density matrices, we employ in addition a numerical Laplace transformation for orbital energy denominators. It is shown that the error introduced by this approximation is negligible already with a small number of sampling points. Thereby an implementation of second-order one-particle properties is realized, which avoids completely the storage of quantities scaling with the fourth power of the system size. The implementation is tested on a set of organic molecules including large fused aromatic ring systems and the C(60) fullerene. It is demonstrated that exploiting symmetry and shared memory parallelization, second-order properties for such systems can be evaluated at the CC2 and MP2 level within a few hours of calculation time. As large scale applications, we present results for the 7-, 9-, and 11-ring helicenes.     

How Electronic Excitation Can be Used to Inhibit Some Mechanisms Associated to Substituent Effects

Despite the fact that transferability and chemistry go hand in hand, transferability studies in electronically excited states (EESs) are normally omitted, although these states are becoming extremely important in modern processes and applications. In this work, it is shown that this kind of studies can be used to understand how substituent effects can be modified in EESs. Thus, for example, the analysis of the carbonyl oxygen transferability in different HCO‐R molecules allowed us to find that the excitation can be used to break the π conjugation associated to the resonance substituent effect. Moreover, as a direct consequence, the oxygen transferability is enhanced in the first electronically excited state.     

Electronic structure and hyperpolarizability of some conjugated molecules in excited states

For the examples of aromatic and antiaromatic five-membered heterocycles, the static electronic polarizabilities and hyperpolarizabilities are determined in the ground and first singlet- and triplet-excited electronic states. The theoretical calculations are carried out in the SOS formalism and the correlation effects are taken into account using all mono- and biexcited configuration in the PPP approximation. It is shown that the singlet excitation of the molecules for the antiaromatic case is connected to an significant decrease of both polarizabilities and hyperpolarizabilities. Their values are discussed in terms of the index of average bond-order alternation for the ground and excited states and the localization of the electronic transitions in the molecules. © 1993 John Wiley & Sons, Inc.     

Intramolecular Charge Transfer of Carotene‐porphyrin‐fullerene Triad: Sequential or Superexchange Cechanism

As an excellent artificial photosynthetic reaction center, the carotene (C)‐porphyrin (P)‐fullerene (F) triad was extensively investigated experimentally. To reveal the mechanism of the intramolecular charge transfer (ICT) on the mimic of photosynthetic solar energy conversion (such as singlet energy transfer between pigments, and photoinduced electron transfer from excited singlet states to give long‐lived charge‐separated states), the ICT mechanisms of C‐P‐F triad on the exciton were theoretically studied with quantum chemical methods as well as the 2D and 3D real space analysis approaches. The results of quantum chemical methods reveal that the excited states are the ICT states, since the densities of HOMO are localized in the carotene or porphyrin unit, and the densities of LUMO are localized in the fullerene unit. Furthermore, the excited states should be the intramolecular superexchange charge transfer (ISCT) states for the orbital transition from the HOMO whose densities are localized in the carotene to the LUMO whose densities are localized in the fullerene unit. The 3D charge difference densities can clearly show that some excited states are ISCT excited states, since the electron and hole are resident in the fullerene and carotene units, respectively. From the results of the electron‐hole coherence of the 2D transition density matrix, not only 3D results are supported, but also the delocalization size on the exciton can be observed. These phenomena were further interpreted with non‐linear optical effect. The large changes of the linear and non‐linear polarizabilities on the exciton result in the charge separate states, and if their changes are large enough, the ICT mechanism can become the ISCT on the exciton.     

Molecular model with quantum mechanical bonding information

The molecular structure can be defined quantum mechanically thanks to the theory of atoms in molecules. Here, we report a new molecular model that reflects quantum mechanical properties of the chemical bonds. This graphical representation of molecules is based on the topology of the electron density at the critical points. The eigenvalues of the Hessian are used for depicting the critical points three-dimensionally. The bond path linking two atoms has a thickness that is proportional to the electron density at the bond critical point. The nuclei are represented according to the experimentally determined atomic radii. The resulting molecular structures are similar to the traditional ball and stick ones, with the difference that in this model each object included in the plot provides topological information about the atoms and bonding interactions. As a result, the character and intensity of any given interatomic interaction can be identified by visual inspection, including the noncovalent ones. Because similar bonding interactions have similar plots, this tool permits the visualization of chemical bond transferability, revealing the presence of functional groups in large molecules.     

Molecule‐specific determination of atomic polarizabilities with the polarizable atomic multipole model

Recently, many polarizable force fields have been devised to describe induction effects between molecules. In popular polarizable models based on induced dipole moments, atomic polarizabilities are the essential parameters and should be derived carefully. Here, we present a parameterization scheme for atomic polarizabilities using a minimization target function containing both molecular and atomic information. The main idea is to adopt reference data only from quantum chemical calculations, to perform atomic polarizability parameterizations even when relevant experimental data are scarce as in the case of electronically excited molecules. Specifically, our scheme assigns the atomic polarizabilities of any given molecule in such a way that its molecular polarizability tensor is well reproduced. We show that our scheme successfully works for various molecules in mimicking dipole responses not only in ground states but also in valence excited states. The electrostatic potential around a molecule with an externally perturbing nearby charge also exhibits a near‐quantitative agreement with the reference data from quantum chemical calculations. The limitation of the model with isotropic atoms is also discussed to examine the scope of its applicability. © 2012 Wiley Periodicals, Inc.     

Effect of electronic polarization on charge-transport parameters in molecular organic semiconductors

Theoretical investigations of charge transport in organic materials are generally based on the "energy splitting in dimer" method and routinely assume that the transport parameters (site energies and transfer integrals) determined from monomer and dimer calculations can be reliably used to describe extended systems. Here, we demonstrate that this transferability can fail even in molecular crystals with weak van der Waals intermolecular interactions, due to the substantial (but often ignored) impact of polarization effects, particularly on the site energies. We show that the neglect of electronic polarization leads to qualitatively incorrect values and trends for the transfer integrals computed with the energy splitting method, even in simple prototypes such as ethylene or pentacene dimers. The polarization effect in these systems is largely electrostatic in nature and can change dramatically upon transition from a dimer to an extended system. For example, the difference in site energy for a prototypical "face-to-edge" one-dimensional stack of pentacene molecules is calculated to be 30% greater than that in the "face-to-edge" dimer, whereas the site energy difference in the pentacene crystal is vanishingly small. Importantly, when computed directly in the framework of localized monomer orbitals, the transfer integral values for dimer and extended systems are very similar.     

Dynamic polarizabilities of Zn and Cd and dispersion coefficients involving group 12 atoms

The refractive index data for Zn and Cd measured by Goebel and Hohm are analyzed with a three-term Maxwell-Sellmeier expression which incorporates the experimental oscillator strengths of the first two dipole transitions. These expressions are extended to imaginary frequencies for the determination of the upper and lower bounds of the dynamic polarizabilities α(iω), from which the van der Waals coefficients of two-body interactions and the non-additive three-body interactions are generated. The determined C(6) values for Zn(2) (359±8?a.u.) and Cd(2) (686±10?a.u.) are much larger than those originally estimated by Goebel and Hohm. This is because their one-term approximation of α(ω), which fits the measurements very well in the normal frequency range, greatly underestimates α(iω) when the frequency is extended into the imaginary domain. On the other hand, the present results of heteronuclear interactions verify once again that Tang's one-term approximation of α(iω) leads to accurate combining rules. The two- and three-body interaction coefficients between group 12 atoms (Zn, Cd, Hg) and the alkali, alkaline-earth, rare-gas atoms, and some molecules are estimated with these combining rules.     

Determination of extremely localized molecular orbitals in the framework of density functional theory

Extremely localized molecular orbitals are rigorously localized on only a preselected set of atoms and do not have any tails outside the localization region. The importance of these orbitals lies in their ability to be transferred from one molecule to another one. A new algorithm to determine extremely localized molecular orbitals in the framework of the density functional theory method is presented. This could also be a valuable tool in the quantum mechanics/molecular mechanics methodology where localized molecular orbitals are used to describe covalent bonds across the frontier region. The present approach is used to build up the electron density of thymopentin, a polypeptide constituted by five residues, starting from extremely localized molecular orbitals determined on a set of model molecules. The results obtained confirm good transferability properties for these orbitals.Proceedings of the 11th International Congress of Quantum Chemistry satellite meeting in honor of Jean-Louis Rivail