Nonlinear optical property calculations of polyynes with long-range corrected hybrid exchange-correlation functionals

Polarizabilities (alpha), second-hyperpolarizabilities (gamma), and the gamma scaling factors (c) of polyynes [H-(C[triple bond]C)(n)-H, n = 1-8] were evaluated using the long-range corrected (LC) density functional theory (DFT) and LC-DFT with a short-range Gaussian attenuation (LCgau), as well as high quality wavefunction methods. We show that the c values obtained from LC- and LCgau-DFT are consistent with those from CCSD(T) calculations. Furthermore, the polyyne c values we obtained are seen to be smaller than the c values derived from previously calculated polyene gamma values [Sekino et al., J. Chem. Phys. 126, 014107 (2007)] in all the methods we consider. We compare our results with those obtained experimentally [Shepkov et al., J. Chem. Phys. 120, 6807 (2004).] from end-capped polyynes [i-Pr(3)Si-(C[triple bond]C)(n)-Sii-Pr(3)], which show larger c values for polyynes than polyenes. Our alpha and gamma calculations with i-Pr(3)Si-(C[triple bond]C)(n)-Sii-Pr(3) (n = 4, 5, 6, and 8) show that i-Pr(3)Si- may participate in pi molecular orbital delocalization, which can unexpectedly affect the c value. We also confirm the importance of molecular geometry in these nonlinear optical calculations. We find that while LC- and LCgau-DFT excellently reproduce experimental geometries and bond length alternation (BLA), MP2 optimized geometries have a BLA that is too short to be used for accurate alpha and gamma calculations.     

Nonlinear optical materials by the sol-gel method

The sol-gel method, because of the use of homogeneous liquid solutions and the ability to form gels at room temperature, is uniquely suited for the preparation of many nonlinear optical (NLO) materials, especially films. The preparations of NLO crystalline solids, such as ferroelectrics, oxide glasses, and amorphous ferroelectrics, are described. The preparation of NLO nanocomposites can be made by a number of approaches. These include the mixing of optically active organics into the sol-gel liquid solution, the impregnation of organics into the interconnecting pores of a stabilized oxide gel, and the direct chemical bonding of optically active organics and inorganics to form new hybrid NLO nanocomposites.     

Density functional calculations of optical excitation energies by a transition-state method

Optical excitation energies of MnO⁻₄, CrO²⁻₄, and RuO₄ are calculated using the density functional methodology. A short outline of some important developments in this theory for the determination of excited-state properties is given. A practical working procedure for the calculation of transition energies including multiplet splitting is described. This method is based on a transition-state approach which is connected, as will be shown, to Slater's transition-state concept. Results obtained by this working procedure are compared to the energy differences between separately converged configurations of ground and excited states and the corresponding multiplet structure, denoted as the ΔSCF calculation in the following. © 1997 John Wiley & Sons, Inc.     

Linear response and quasiparticle calculations as probes of the Kohn-Sham eigenvalues in metals

The Kohn-Sham eigenvalues were formally introduced into density functional theory as Lagrange multipliers in the implementation of the minimum principle for the total energy of a many-electron system. No general results are available concerning the physical significance of these one-electron eigenvalues (with the exception of the highest occupied level, which equals the Fermi energy). Recent ab initio calculations of dynamical response in metals make explicit use of the Kohn-Sham band structure, and associated wave functions, through the use of spectral representations. This opens up the possibility of examining the significance of the eigenvalues at an “empirical” level, i.e., through direct comparison with the results of spectroscopic measurements. A particularly interesting example is afforded by new inelastic x-ray scattering experiments on A1. For a special wave vector transfer, q_o ≈︂ 1.5k_F, the measured spectrum provides a direct mapping of the Kohn-Sham noninteracting spectrum. For a range of wave vectors about q_o, the bare Kohn-Sham spectrum still reproduces all the main features of the measurements; this suggests that, in this metal, the Kohn-Sham eigenvalues are good approximations to the quasiparticle energies. We also discuss the interplay between Kohn-Sham bands and the energy of the “anomalous” plasmon in Cs, whose dispersion bears a signature of the excited-state band structure. Finally, and in a more formal framework, we outline the results of a first-principles comparison between quasiparticle amplitudes and Kohn-Sham wave functions at a jellium surface; the latter turn out to be excellent approximations to the former. © 1996 John Wiley & Sons, Inc.     

A hierarchic sparse matrix data structure for large-scale Hartree-Fock/Kohn-Sham calculations

A hierarchic sparse matrix data structure for Hartree-Fock/Kohn-Sham calculations is presented. The data structure makes the implementation of matrix manipulations needed for large systems faster, easier, and more maintainable without loss of performance. Algorithms for symmetric matrix square and inverse Cholesky decomposition within the hierarchic framework are also described. The presented data structure is general; in addition to its use in Hartree-Fock/Kohn-Sham calculations, it may also be used in other research areas where matrices with similar properties are encountered. The applicability of the data structure to ab initio calculations is shown with help of benchmarks on water droplets and graphene nanoribbons.     

The trust-region self-consistent field method in Kohn-Sham density-functional theory

The trust-region self-consistent field (TRSCF) method is extended to the optimization of the Kohn-Sham energy. In the TRSCF method, both the Roothaan-Hall step and the density-subspace minimization step are replaced by trust-region optimizations of local approximations to the Kohn-Sham energy, leading to a controlled, monotonic convergence towards the optimized energy. Previously the TRSCF method has been developed for optimization of the Hartree-Fock energy, which is a simple quadratic function in the density matrix. However, since the Kohn-Sham energy is a nonquadratic function of the density matrix, the local energy functions must be generalized for use with the Kohn-Sham model. Such a generalization, which contains the Hartree-Fock model as a special case, is presented here. For comparison, a rederivation of the popular direct inversion in the iterative subspace (DIIS) algorithm is performed, demonstrating that the DIIS method may be viewed as a quasi-Newton method, explaining its fast local convergence. In the global region the convergence behavior of DIIS is less predictable. The related energy DIIS technique is also discussed and shown to be inappropriate for the optimization of the Kohn-Sham energy.     

Simplified accurate approximation for the Kohn-Sham potential using the KLI method

The method of Krieger, Li, and Iafrate (KLI) [Phys. Rev. A46, 5453 (1992) and A47, 165 (1993)] is employed to calculate the Kohn-Sham (KS) potential, V_κσ, for the exchange-only case in which the electron-electron interaction between “core” electrons in the Hartree-Fock exchange energy functional is treated in the local-spin-density (LSD) approximation with and without self-interaction-correction (SIC). The resulting V_κσ(r) maintains the important analytic properties exhibited by the exact KS potential. When the core is taken to include all occupied states except those in the last two occupied subshells of the atom, we find that properties strongly dependent on the valence electron states continue to be accurately approximated. In particular, when the LSDSIC approximation is employed, we find the results of self-consistent calculations of the ionization potential and electron affinity are within 0.3 mRy of the exact KS results and that the energy eigenvalue corresponding to the highest energy occupied orbital and <r²> have an average error of a few tenths of 1% for both atoms and negative ions for Z ≤ 20. Similarly, slightly less accurate results are obtained when the LSD approximation is employed. These results suggest that the KLI method may be accurately and more easily applied to multiatom systems when this additional approximation is made. © 1997 John Wiley & Sons, Inc.     

A non-orthogonal Kohn-Sham method using partially fixed molecular orbitals

A density functional theory method using partially fixed molecular orbitals (PFMOs) is presented. The PFMOs, which have some fixed molecular orbital coefficients and are non-orthogonal, are a generalization of the extreme localized orbitals (ELMOs) of Couty, Bayse, and Hall (1997) Theor Chem Acc 97:96. A non-orthogonal Kohn-Sham method with these PFMOs is derived, and is applied to molecular calculations on the ionization potential of pyridine, the energy difference between cis- and trans-butadiene, the reaction barrier height of the cyclobutene-cis-butadiene interconversion, and the potential energy curve of the hydrogen shift reaction of hydroxycarbene to formaldehyde. The PFMO Kohn-Sham method reproduces well the results of the full Kohn-Sham method without having a restriction on the molecular orbital coefficients. The difference is less than 0.1 eV in the ionization potential and about 0.1 kcal/mol in the barrier height and in the potential energy calculations.     

Accurate calculations of free-energy differences by the distribution method

We employ the strategy used in the successive umbrella sampling method [P. Virnau and M. Muller, J. Chem. Phys. 120, 10925 (2004)] to obtain the energy-difference distribution over its desired range. This is very helpful in calculating free-energy differences, where the source of the error is well recognized as the insufficient sampling over the relevant tail region in the energy-difference distribution. The distribution method proposed here employs the idea of restricting the sampling within an appropriate energy range, as was presented by Shing and Gubbins in their restricted umbrella sampling method [Mol. Phys. 46, 1109 (1982)]. We demonstrate the efficiency of the distribution method by calculating the free-energy difference of a model of harmonic oscillators where the systems exhibit nonoverlap features in their important phase spaces through the original Metropolis sampling. For this particular case, we show that the distribution method outperforms the free-energy perturbation method and even the Bennett's acceptance ratio method [J. Comput. Phys. 22, 245 (1976)] with the fastest convergence and the smallest relative errors. We further demonstrate the application of the distribution method with a simple point charge water model.     

Hydration free energy calculations by the acceptance ratio method

The hydration energy difference between the alanine and glycine zwitter ions was calculated by both the free energy perturbation method and the acceptance ratio method. The calculations were carried out by using different increments of the mutation parameter λ, δλ = ? 0.05, ?0.10, and ?0.20. The free energy difference calculated by the acceptance ratio method was found to be approximately the same as an average of the two free energy differences in the forward and the backward directions calculated by the perturbation method. The results by the perturbation method were significantly affected by large δλ as compared with that by the acceptance ratio method. The statistical error caused by decreasing the simulation time for sampling equilibrium configurations is discussed.     

Nonlinear optical properties of dicyanomethylene‐derived heteroaromatic dyes: Semiempirical molecular orbital calculations and experimental investigations

The effect of conformation (E/Z isomerism), nature (donor/acceptor) of substituents, and endgroups (indandione, pyrazolone, pyrazoledione) on the molecular hyperpolarizability β_vec of dicyanomethylene (hetero)aromatic dyes is investigated by means of semiempirical (AM1, ZINDO) molecular orbital calculations. Unless Z isomers are stabilized by intramolecular hydrogen bonding, generally E conformers have larger β_vec's. Replacement of one nitrile group of the dicyanomethylene moiety by p‐aminoaryl rather than p‐R‐arylamino (R=NMe₂, MeO, H, NO₂) is found to be advantageous. Increasing the acceptor strength of 29 by successively replacing the carbonyl with dicyanovinyl groups leads to a maximum of β_vec for the derivative with one rather than two C(CN)₂ groups. With respect to endgroups, the indandione moiety generally is the least active group. Solvent effects are treated within the framework of the self‐consistent reaction field approximation. In most cases gas‐phase tendencies are either parallel or even reinforced if solvent effects are taken into account. The calculated results are compared with electric field induced second harmonic generation (EFISH) measurements. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 79: 253–266, 2000     

Nonlinear optical response of chloroaluminiumphthalocyanine encapsulated by silica core-shell particles

We report for the first time on the synthesis of core-shell particles containing chloroaluminiumphthalocyanine (ClAlPc) prepared using a sol-gel technique. These particles have the dye molecules at the core, encapsulated by silica shell. The mean size of the particle is determined from HRTEM studies and is found to be approximately 0.08 microm. The surface and bulk compositions of the core-shell particles are studied by XPS and EDAX measurements, respectively. Time-resolved fluorescent measurements indicate a decrease in fluorescence lifetime for the core-shell particles as compared to that of bare dye dissolved in ethanol. This is analyzed on the basis of available theoretical models. Third-order nonlinear optical effects are investigated by the Z-scan technique using 8 ns pulses at a wavelength of 532 nm from a frequency-doubled Nd:YAG laser. The analysis indicates that both singlet and triplet excited-state absorption contribute to nonlinear absorption.     

Two-electron valence indices from the Kohn-Sham orbitals

The recent Hartree-Fock (HF) difference approach to the chemical valence indices (ionic and covalent), formulated in the framework of the pair-density matrix, is implemented within the Kohn-Sham (KS) density functional theory (DFT). The valence numbers are quadratic in terms of displacements of the molecular spin-resolved charge-and-bond-order (CBO) matrix elements, relative to values in the separated atoms limit (SAL). It is shown that the global valence represents a generalized “distance” quantity measuring a degree of similarity between the two CBO matrices: the molecular and SAL. Numerical values for typical molecules exhibiting single and multiple bonds demonstrate that the KS orbitals give rise to these new bond valences in good agreement with both chemical and HF predictions. This KS bond multiplicity analysis is applied to the chemisorption system including the allyl radical and a model surface cluster of molybdenum oxide. It is concluded that the quadratic valence analysis represents a valuable procedure for extracting useful chemical information from standard DFT calculations. © 1997 John Wiley & Sons, Inc.     

Configuration interaction by the method of bonded functions,some preliminary calculations

A resumé of Boys' approach to configuration interaction calculations is presented, and a program suitable to perform such calculations is described in some detail. The results of a preliminary calculation on water, together with some timings are presented.     

Atomic approximation to the projection on electronic states in the Douglas-Kroll-Hess approach to the relativistic Kohn-Sham method

We suggest an approximate relativistic model for economical all-electron calculations on molecular systems that exploits an atomic ansatz for the relativistic projection transformation. With such a choice, the projection transformation matrix is by definition both transferable and independent of the geometry. The formulation is flexible with regard to the level at which the projection transformation is approximated; we employ the free-particle Foldy-Wouthuysen and the second-order Douglas-Kroll-Hess variants. The (atomic) infinite-order decoupling scheme shows little effect on structural parameters in scalar-relativistic calculations; also, the use of a screened nuclear potential in the definition of the projection transformation shows hardly any effect in the context of the present work. Applications to structural and energetic parameters of various systems (diatomics AuH, AuCl, and Au(2), two structural isomers of Ir(4), and uranyl dication UO(2) (2+) solvated by 3-6 water ligands) show that the atomic approximation to the conventional second-order Douglas-Kroll-Hess projection (ADKH) transformation yields highly accurate results at substantial computational savings, in particular, when calculating energy derivatives of larger systems. The size-dependence of the intrinsic error of the ADKH method in extended systems of heavy elements is analyzed for the atomization energies of Pd(n) clusters (n相似文献