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It is well known that the convergence of harmonic frequencies with respect to the basis set size in traditional correlated calculations is slow. We now report that the convergence of cubic and quartic force constants in traditional CCSD(T) calculations on H(2)O with Dunning's cc-pVXZ family of basis sets is also frustratingly slow. As an alternative, we explore the performance of R12-based explicitly correlated methods at the CCSD(T) level. Excellent convergence of harmonic frequencies and cubic force constants is provided by these explicitly correlated methods with R12-suited basis irrespective of the used standard approximation and/or the correlation factor. The Slater type geminal, however, outperforms the linear r(12) for quartic force constants and vibrational anharmonicity constants. The converged force constants from explicitly correlated CCSD(T) calculations succeed in reproducing the fundamental frequencies of water molecule with spectroscopic accuracy after corrections for post-CCSD(T) effects are made.

The high-frequency dielectric varepsilon and the first nonlinear electric susceptibility chi((2)) tensors of crystalline potassium dihydrogen phosphate (KH(2)PO(4)) are calculated by using the coupled perturbed Hartree-Fock and Kohn-Sham methods as implemented in the CRYSTAL code. The effect of basis sets of increasing size on varepsilon and chi((2)) is explored. Five different levels of theory, namely, local-density approximation, generalized gradient approximation (PBE), hybrids (B3LYP and PBE0), and HF are compared using the experimental and theoretical structures corresponding not only to the tetragonal geometry I4d2 at room temperature but also to the orthorhombic phase Fdd2 at low temperature. Comparison between the two phases and their optical behavior is made. The calculated results for the tetragonal phase are in good agreement with the experimental data.

The coupled perturbed Hartree-Fock (CPHF) method for evaluating static first (beta) and second (gamma) hyperpolarizability tensors of periodic systems has recently been implemented in the CRYSTAL code [Bishop et al., J. Chem. Phys. 114, 7633 (2001)]. We develop here an efficient and accurate computational protocol, along with the local basis sets needed for first and second row atoms. Application is made to several high symmetry three-dimensional systems including one (pyrope) with an 80 atom unit cell. CPHF second-order hyperpolarizabilities substantially undershoot experimental values, due to an overestimate of the band gap, but trends are satisfactorily reproduced for beta as well as gamma.

Various periodic piecewise linear potentials for extracting the electronic response of an infinite periodic system to a uniform electrostatic field are examined. It is shown that discontinuous potentials, such as the sawtooth, cannot be used for this purpose. Continuous triangular potentials can be successfully employed to determine both even- and odd-order (hyper)polarizabilities, as demonstrated here for the first time, although the permanent dipole moment of the corresponding long finite chain remains out of reach. Moreover, for typical highly polarizable organic systems, the size of the repeated unit has to be much larger than that of the finite system in order to obtain convergence with respect to system size. All results are illustrated both through extensive model calculations and through ab initio calculations on poly- and oligoacetylenes.

A general reduced dimensionality finite field nuclear relaxation method for calculating vibrational nonlinear optical properties of molecules with large contributions due to anharmonic motions is introduced. In an initial application to the umbrella (inversion) motion of NH(3) it is found that difficulties associated with a conventional single well treatment are overcome and that the particular definition of the inversion coordinate is not important. Future applications are described.

A recently proposed approach for extracting band structures from finite-cluster calculations is improved so that (avoided) band crossings can be handled and the problems related to so-called doublings and holes are reduced. In particular, we demonstrate how the method can be combined with the elongation method for the finite-system calculations and apply it to extracting band structures for polymers from oligomer calculations. As illustrations of the approach we discuss a chain of water molecules, polyacetylene, polyethylene, and a BN nanotube without and with an impurity.

A computational scheme for the evaluation of the static first (beta) and second (gamma) hyperpolarizability tensors of systems periodic in 1D (polymers), 2D (slabs), 3D (crystals), and, as a limiting case, 0D (molecules) has been implemented, within the coupled perturbed Hartree-Fock framework (CPHF), in the CRYSTAL code, which uses a Gaussian type basis set. This generalizes to 2D and 3D the work by Bishop et al. (J. Chem. Phys. 114, 7633 (2001)). CPHF is applied for beta and gamma (the polarizability tensor alpha is also reported for completeness) of LiF in different aggregation states: finite and infinite chains, slabs, and cubic crystal. Correctness of the computational scheme and its numerical efficiency are documented by the trend of beta and gamma for increasing dimensionality: for a finite linear chain containing N LiF units, the hyperpolarizability tends to the infinite chain value at large N, N parallel chains give the slab value when N is sufficiently large, and N superimposed slabs tend to the bulk value. High numerical accuracy can be achieved at relatively low cost, with a dependence on the computational parameters similar to that observed for field-free self-consistent field (SCF) calculations.

A simple extended finite field nuclear relaxation procedure for calculating vibrational contributions to degenerate four-wave mixing (also known as the intensity-dependent refractive index) is presented. As a by-product one also obtains the static vibrationally averaged linear polarizability, as well as the first and second hyperpolarizability. The methodology is validated by illustrative calculations on the water molecule. Further possible extensions are suggested.

The long-range correction (LC) for treating electron exchange in density functional theory, combined with the Becke-Lee-Yang-Parr (BLYP) exchange-correlation functional, was used to determine (hyper)polarizabilities of polydiacetylene/polybutatriene oligomers. In comparison with coupled-cluster calculations including single and double excitations as well as a perturbative treatment of triple excitations, our values indicate that the tendency of conventional functionals to result in a catastrophic overshoot for these properties is alleviated but not eliminated. No clear-cut preference for LC-BLYP over Hartree-Fock values is obtained. This analysis is consistent with the calculations of Sekino et al. [J. Chem. Phys. 126, 014107 (2007)] on polyacetylene and molecular hydrogen oligomers. Thus, the performance of LC-BLYP with regard to (hyper)polarizabilities of quasilinear conjugated systems is now well characterized.

A method to build accurate band structures of polymers from oligomer calculations has been developed. This method relies on systematic procedures for (i) assigning k values, (2) eliminating strongly localized molecular orbitals, and (iii) connecting bands across the entire Brillouin zone. Illustrative calculations are carried out at the HF/STO-3G level for trans-polyacetylene (PA), poly(para-phenylene) (PPP), and water chains. More stringent tests at several different levels are reported for polydiacetylene/polybutatriene.

The vibrational configuration interaction method used to obtain static vibrational (hyper)polarizabilities is extended to dynamic nonlinear optical properties in the infinite optical frequency approximation. Illustrative calculations are carried out on H(2)O and NH(3). The former molecule is weakly anharmonic while the latter contains a strongly anharmonic umbrella mode. The effect on vibrational (hyper)polarizabilities due to various truncations of the potential energy and property surfaces involved in the calculation are examined.

The response of periodic systems to external electric fields is a challenging theoretical problem. The authors show how the vector potential approach yields a numerically efficient treatment of the combined electronic and nuclear response to a finite static field. Their method is based on a self-consistent reformulation of the charge flow term in the single particle Hamiltonian. Careful numerical implementation yields a treatment whose computational needs are only marginally larger than those of a conventional field-free calculation. To prove the method exemplary polymer calculations are done for a model Hamiltonian. The latter contains all essential elements of an ab initio Kohn-Sham or Hartree-Fock Hamiltonian but allows for extensive testing. The extension to three-dimensional systems is described.

The static polarizability and second hyperpolarizability of increasingly large polydiacetylene and polybutatriene (PBT) chains have been evaluated using the optimized effective potential for exact exchange (OEP-EXX) method developed by Yang and Wu [Phys. Rev. Lett. 89, 143002 (2002)], where the unknown part of the effective potential is expressed as a linear combination of Gaussian functions. Various conventional atomic orbital basis sets were employed for the exchange potential (X basis) as well as for the Kohn-Sham orbitals [molecular orbital (MO) basis]. Our results were compared to coupled-perturbed Hartree-Fock (CPHF) calculations and to ab initio correlated values obtained at various levels of approximation. It turns out that (a) small conventional basis sets are, in general, unsatisfactory for the X basis; (b) the performance of a given X basis depends on the MO basis and is generally improved when using a larger MO basis; (c) these effects are exaggerated for the second hyperpolarizability compared to the polarizability; (d) except for the second hyperpolarizability of PBT chains, using 6-311++G** for the X basis gives reasonable agreement with the CPHF results for all MO basis sets; (e) our results suggest that in the limit of a complete X basis the OEP-EXX values may approach the CPHF data; and (f) in general, the quality of a given conventional X basis degrades with the length of the oligomer, which correlates with the fact that the number of X basis functions becomes a smaller fraction of the number required to reproduce exactly the finite-basis-set Hartree-Fock energies. Linear and especially nonlinear electric field responses constitute a very stringent test for assessing the quality of functionals and potentials; appropriately tailored basis sets are needed to describe the latter. Finally, this study further highlights the importance of electron correlation effects on linear and nonlinear responses, for which correlated functionals with OEP are required.

We have implemented our new procedure for computing Franck-Condon factors utilizing vibrational configuration interaction based on a vibrational self-consistent field reference. Both Duschinsky rotations and anharmonic three-mode coupling are taken into account. Simulations of the first ionization band of ClO(2) and C(4)H(4)O (furan) using up to quadruple excitations in treating anharmonicity are reported and analyzed. A developer version of the MIDASCPP code was employed to obtain the required anharmonic vibrational integrals and transition frequencies.

A dipolar-free sum-over-states expression for the diagonal components of the first hyperpolarizability (beta) tensor has been proposed by Kuzyk [Phys. Rev. A 72, 053819 (2005)] as an alternative to the traditional expression. We examine both alternatives for the longitudinal beta of four typical push-pull pi-conjugated systems using the ab initio CIS and CIS(D) schemes to approximate the excited state properties. Since they are each evaluated approximately the two SOS expressions yield different values for beta and it is found that (i) they evolve symmetrically as the number of excited states is increased so that their average is nearly constant; (ii) in the static limit, the two values agree better with one another when their average is close to the "exact" correlated result; and (iii) frequency dispersion can affect the agreement between the alternative expressions. On the basis of (i) and (ii) it appears best for typical push-pull pi-conjugated systems to estimate the static beta, and the error in the value so obtained, by averaging the Kuzyk and traditional results.

Using a new unconventional procedure for calculating Franck-Condon factors with anharmonicity fully included the X 2A2<--X 1A1 band in the photoelectron spectrum of furan (and deuterated furan) was simulated at the second-order perturbation theory level. All 21 vibrational modes were considered but, in the end, only 4 are required to accurately reproduce the spectrum. Except for our own recent work on ethylene such calculations have been previously limited to tri- or tetraatomic molecules. Most of the effect of anharmonicity is accounted for in first order, although second-order corrections to the vibrational frequencies are important. Based on these simulations we were able to improve upon and extend previous assignments as well as suggest further measurements.

The performance of the optimized effective potential procedure for exact exchange in calculating static electric-field response properties of push-pull pi-conjugated systems has been studied, with an emphasis on NO2-(CH=CH)n-NH2 chains. Good agreement with Hartree-Fock dipole moments and (hyper)polarizabilities is obtained; particularly noteworthy is the chain length dependence for beta/n. Thus, the problem that conventional density-functional theory functionals dramatically overestimate these properties is largely solved, although there remains a significant correlation contribution that cannot be accounted for with current correlation functionals.

A variational approach for reliably calculating vibrational linear and nonlinear optical properties of molecules with large electrical and/or mechanical anharmonicity is introduced. This approach utilizes a self-consistent solution of the vibrational Schrodinger equation for the complete field-dependent potential-energy surface and, then, adds higher-level vibrational correlation corrections as desired. An initial application is made to static properties for three molecules of widely varying anharmonicity using the lowest-level vibrational correlation treatment (i.e., vibrational Møller-Plesset perturbation theory). Our results indicate when the conventional Bishop-Kirtman perturbation method can be expected to break down and when high-level vibrational correlation methods are likely to be required. Future improvements and extensions are discussed.

Our new simple method for calculating accurate Franck-Condon factors including nondiagonal (i.e., mode-mode) anharmonic coupling is used to simulate the C2H4+X2B3u<--C2H4X1A(g) band in the photoelectron spectrum. An improved vibrational basis set truncation algorithm, which permits very efficient computations, is employed. Because the torsional mode is highly anharmonic it is separated from the other modes and treated exactly. All other modes are treated through the second-order perturbation theory. The perturbation-theory corrections are significant and lead to a good agreement with experiment, although the separability assumption for torsion causes the C2D4 results to be not as good as those for C2H4. A variational formulation to overcome this circumstance, and deal with large anharmonicities in general, is suggested.

A different localization scheme for the elongation method is developed based on regional molecular orbitals. This scheme is more efficient and more accurate than the previous one especially for covalently bonded systems with strongly delocalized pi electrons. Ab initio test calculations have been performed on three model systems: water chains, polyglycine, and cationic cyanine chains. The dependence on the size of the starting clusters and the effect of the basis set are investigated. Our results are compared with conventional ab initio calculations and it is found in all cases that the error per added unit levels off to a satisfactorily small value as long as the starting cluster is sufficiently large., ((c) 2004 American Institute of Physics.)

Using three typical pi-conjugated molecules (1,3,5-hexatriene, 1-formyl-6-hydroxyhexa-1,3,5- triene, and 1,1-diamino-6,6-dinitrohexa-1,3,5-triene) we investigate the level of ab initio theory necessary to produce reliable values for linear and nonlinear optical properties, with emphasis on the vibrational contributions that are known to be important or potentially important. These calculations are made feasible by employing field-induced coordinates in combination with a finite field procedure. For many, but not all, purposes the MP2/6-31+G(d) level is adequate. Based on our results the convergence of the usual perturbation treatment for vibrational anharmonicity was examined. Although this treatment is initially convergent in most circumstances, a problematic situation has been identified., ((c) 2004 American Institute of Physics)

An efficient new procedure for calculating Franck-Condon factors, based on the direct solution of an appropriate set of simultaneous equations, is presented. Both Duschinsky rotations and anharmonicity are included, the latter by means of second-order perturbation theory. The critical truncation of basis set is accomplished by a build-up procedure that simultaneously removes negligible vibrational states. A successful test is carried out on ClO2 for which there are experimental data and other theoretical calculations., ((c) 2004 American Institute of Physics)