Nonstationarity and related measures for time‐dependent hartree–fock and multiconfigurational models

Based on an earlier article (Eberly and Singh, Phys. Rev. D 1973 , 7, 359) and related works on short‐time evolution, this article proposes a many‐electron formulation for the nonstationarity degree which can be assigned to quantum system at each time point. The key measure introduced, , is a nonstationarity index that can be thought of as an inverse nominal lifetime at each instance of time. The index is directly computed from the time derivative of one‐electron density matrix and is a size‐consistent quantity. In this article, the approach is developed for the time‐dependent Hartree–Fock (TDHF), single‐excitation (TDCIS), and time‐dependent full configuration interaction (TDFCI) models. As a rule, nonstationarity effects are more pronounced in correlated electron systems, and a joint analysis of and the multiconfigurational character of wave functions apparently provide a deeper insight into dynamical molecular processes. The performed calculations on small molecules in laser fields show a preference for the TDCIS model when comparing TDCIS and TDHF with the “exact” TDFCI model. © 2013 Wiley Periodicals, Inc.     

Exact relations between the electron density and external potential for systems of interacting and noninteracting electrons

The differential virial theorem (DVT) is an explicit relation between the electron density ρ( r ), the external potential, kinetic energy density tensor, and (for interacting electrons) the pair function. The time‐dependent generalization of this relation also involves the paramagnetic current density. We present a detailed unified derivation of all known variants of the DVT starting from a modified equation of motion for the current density. To emphasize the practical significance of the theorem for noninteracting electrons, we cast it in a form best suited for recovering the Kohn–Sham effective potential v_s( r ) from a given electron density. The resulting expression contains only ρ( r ), v_s( r ), kinetic energy density, and a new orbital‐dependent ingredient containing only occupied Kohn–Sham orbitals. Other possible applications of the theorem are also briefly discussed. © 2012 Wiley Periodicals, Inc.     

Performance of density functional theory in computing nonresonant vibrational (hyper)polarizabilities

A set of exchange‐correlation functionals, including BLYP, PBE0, B3LYP, BHandHLYP, CAM‐B3LYP, LC‐BLYP, and HSE, has been used to determine static and dynamic nonresonant (nuclear relaxation) vibrational (hyper)polarizabilities for a series of all‐trans polymethineimine (PMI) oligomers containing up to eight monomer units. These functionals are assessed against reference values obtained using the Møller–Plesset second‐order perturbation theory (MP2) and CCSD methods. For the smallest oligomer, CCSD(T) calculations confirm the choice of MP2 and CCSD as appropriate for assessing the density functionals. By and large, CAM‐B3LYP is the most successful, because it is best for the nuclear relaxation contribution to the static linear polarizability, intensity‐dependent refractive index second hyperpolarizability, static second hyperpolarizability, and is close to the best for the electro‐optical Pockels effect first hyperpolarizability. However, none of the functionals perform satisfactorily for all the vibrational (hyper)polarizabilities studied. In fact, in the case of electric field‐induced second harmonic generation all of them, as well as the Hartree–Fock approximation, yield the wrong sign. We have also found that the Pople 6–31+G(d) basis set is unreliable for computing nuclear relaxation (hyper)polarizabilities of PMI oligomers due to the spurious prediction of a nonplanar equilibrium geometry. © 2013 Wiley Periodicals, Inc.     

An assessment of pure,hybrid, meta,and hybrid‐meta GGA density functional theory methods for open‐shell systems: The case of the nonheme iron enzyme 8R–LOX

The performance of a range density functional theory functionals combined in a quantum mechanical (QM)/molecular mechanical (MM) approach was investigated in their ability to reliably provide geometries, electronic distributions, and relative energies of a multicentered open‐shell mechanistic intermediate in the mechanism 8R–Lipoxygenase. With the use of large QM/MM active site chemical models, the smallest average differences in geometries between the catalytically relevant quartet and sextet complexes were obtained with the B3LYP^* functional. Moreover, in the case of the relative energies between ⁴II and ⁶II , the use of the B3LYP^* functional provided a difference of 0.0 kcal mol^–1. However, B3LYP^± and B3LYP also predicted differences in energies of less than 1 kcal mol^–1. In the case of describing the electronic distribution (i.e., spin density), the B3LYP^*, B3LYP, or M06‐L functionals appeared to be the most suitable. Overall, the results obtained suggest that for systems with multiple centers having unpaired electrons, the B3LYP^* appears most well rounded to provide reliable geometries, electronic structures, and relative energies. © 2012 Wiley Periodicals, Inc.     

New basis sets for the evaluation of interaction‐induced electric properties in hydrogen‐bonded complexes

Interaction‐induced static electric properties, that is, dipole moment, polarizability, and first hyperpolarizability, of the CO? (HF)_n and N₂? (HF)_n, n = 1–9 hydrogen‐bonded complexes are evaluated within the finite field approach using the Hartree–Fock, density functional theory, Møller–Plesset second‐order perturbation theory, and coupled cluster methods, and the LPol‐n (n = ds, dl, fs, fl) basis sets. To compare the performance of the different methods with respect to the increase of the complex size, we consider as model systems linear chains of the complexes. We analyze the results in terms of the many‐body and cooperative effects. © 2012 Wiley Periodicals, Inc.     

Understanding the electronic energy transfer pathways in the trimeric and hexameric aggregation state of cyanobacteria phycocyanin within the framework of Förster theory

In the present study, the electronic energy transfer pathways in trimeric and hexameric aggregation state of cyanobacteria C‐phycocyanin (C‐PC) were investigated in term of the Förster theory. The corresponding excited states and transition dipole moments of phycocyanobilins (PCBs) located into C‐PC were examined by model chemistry in gas phase at time‐dependent density functional theory (TDDFT), configuration interaction‐singles (CIS), and Zerner's intermediate neglect of differential overlap (ZINDO) levels, respectively. Then, the long‐range pigment‐protein interactions were approximately taken into account by using polarizable continuum model (PCM) at TDDFT level to estimate the influence of protein environment on the preceding calculated physical quantities. The influence of the short‐range interaction caused by aspartate residue nearby PCBs was examined as well. Only when the protonation of PCBs and its long‐ and short‐range interactions were properly taken into account, the calculated energy transfer rates (1/K) in the framework of Förster model at TDDFT/B3LYP/6‐31+G* level were in good agreement with the experimental results of C‐PC monomer and trimer. Furthermore, the present calculated results suggested that the energy transfer pathway in C‐PC monomer is predominant from β‐155 to β‐84 (1/K = 13.4 ps), however, from α‐84 of one monomer to β‐84 (1/K = 0.3–0.4 ps) in a neighbor monomer in C‐PC trimer. In C‐PC hexamer, an additional energy flow was predicted to be from β‐155 (or α‐84) in top trimer to adjacent β‐155 (or α‐84) (1/K = 0.5–2.7 ps) in bottom trimer. © 2013 Wiley Periodicals, Inc.     

NMR shielding constants of CuX,AgX, and AuX (X = F,Cl, Br,and I) investigated by density functional theory based on the Douglas–Kroll–Hess Hamiltonian

Two‐component relativistic density functional theory (DFT) with the second‐order Douglas–Kroll–Hess (DKH2) one‐electron Hamiltonian was applied to the calculation of nuclear magnetic resonance (NMR) shielding constant. Large basis set dependence was observed in the shielding constant of Xe atom. The DKH2‐DFT‐calculated shielding constants of I and Xe in HI, I₂, CuI, AgI, and XeF₂ agree well with those obtained by the four‐component relativistic theory and experiments. The Au NMR shielding constant in AuF is extremely more positive than in AuCl, AuBr, and AuI, as reported recently. This extremely positive shielding constant arises from the much larger Fermi contact (FC) term of AuF than in others. Interestingly, the absolute values of the paramagnetic and the FC terms are considerably larger in CuF and AuF than in others. The large paramagnetic term of AuF arises from the large d‐components in the Au d_π –F p_π and Au sd_σ–F p_σ molecular orbitals (MOs). The large FC term in AuF arises from the small energy difference between the Au sd_σ + F p_σ and Au sd_σ–F p_σ MOs. The second‐order magnetically relativistic effect, which is the effect of DKH2 magnetic operator, is important even in CuF. This effect considerably improves the overestimation of the spin‐orbit effect calculated by the Breit–Pauli magnetic operator. © 2013 Wiley Periodicals, Inc.     

Structure and spectroscopic aspects of water‐halide ion clusters: A study based on a conjunction of stochastic and quantum chemical methods

In this article, we propose a stochastic search based method, namely genetic algorithm in conjunction with density functional theory to evaluate structures of water‐halide microclusters, with the halide ion being Cl^?, Br^?, and I^?. Once the structures are established, we evaluate the infrared spectroscopic modes, vertical detachment energies and natural population analysis based charges. We compare our results with available experimental and theoretical results. © 2012 Wiley Periodicals, Inc.     

Effect of Rough Nanoparticle Orientation on DLVO Energy Interaction

This study investigated the effect of the orientation of rough nanoparticles on Derjaguin and Landau, Verwey and Overbeek (DLVO) energy interaction. Rippled sphere model was used to survey van der Waals attraction energy and repulsive double-layer interaction energy between nanoparticles. The effect of particle size, asperity size, number of asperities, and concentration was studied for different orientations. Spherical coordinates were used to evaluate the effect of changes in orientation under controlled conditions. Surface element integral method was used to calculate DLVO energy interactions between rough particles at specific orientations. The DLVO energy results show that a change in orientation significantly affected the stability of the nanoparticles. The stability of dispersion varied as the contact surface between nanoparticles changed.     

A New Association Term for SAFT Equation of State

This work is devoted to present a new expression for association part of SAFT equation of state. This expression is obtained by calculating the mole fraction of not bonded molecules through a general chemical theory of association. The new equation of state is named CSAFT and has one adjustable parameter less than original SAFT for pure associating fluids. The performance of CSAFT is investigated by PVT calculations for pure fluids and LLE calculations for binary and ternary mixtures. Results show that CSAFT correlates vapor pressure and liquid density data of pure associating components more accurate than SAFT. Also the accuracy of CSAFT model is much better than SAFT for LLE prediction of binary and ternary mixtures, considering SAFT has one pure component parameter more than CSAFT.