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Previously we have shown how to obtain the electric properties of a polymer or other periodic system at the coupled Hartree-Fock level by direct, analytical calculation rather than by extrapolation of oligomer results. Here we add computationally simpler noniterative formulas and test the methodology for the longitudinal dipole moment (μ), polarizability (α), first hyperpolarizability (β), and second hyperpolarizability (γ) of five quasilinear polymers: (LiH)[sub n], (FH)[sub n], (H[sub 2]O)[sub n], trans-polymethineimine (-CNH-)[sub n], and trans-polyacetylene (-CH=CH-)[sub n]. The polymer values are in good agreement with large-oligomer calculations. In this connection the role of phase factors, particularly in determining the dipole moment, is elucidated. We are now in a good position to include electron correlation using methods analogous to those employed for molecular systems. © 2001 American Institute of Physics. [ABSTRACT FROM AUTHOR]

For the computation of rovibrational levels and their spectroscopic intensities, the Eckart conditions are essential to achieve the optimal separation between rotation and vibration. Dymarsky and Kudin [J. Chem. Phys. 122, 124103 (2005)] proposed a procedure for a simplified calculation of the Eckart rotation matrix. In the present work, we have adapted their approach to obtain a kinetic energy operator in curvilinear coordinates using a numerical but exact procedure without resorting tofinite differences. Furthermore, we have modified this approach for the study of molecular systems with several minima, for which several Eckart reference geometries are required. The HONO molecular system has been used to show the efficiency of our implementation. Using the Eckart conditions with multi-reference geometries allows for a calculation of the rotational levels as well as frequencies and intensities of the infrared spectra of both HONO isomers with a single calculation. [ABSTRACT FROM AUTHOR]

We describe our implementation of a fully analytical scheme, based on the 2n + 1 rule, for computing the coupled perturbed Hartree Fock and Kohn-Sham dynamic first hyperpolarizability tensor β(-σ;ω1,ω2) of periodic 1D (polymer), 2D (slab), and 3D (crystal) systems in the CRYSTAL code [R. Dovesi et al., Int. J. Quantum Chem. 114, 1287 (2014)], which utilizes local Gaussian type basis sets. The dc-Pockels (dc-P) and second harmonic generation (SHG) tensors are included as special cases. It is verified that (i) symmetry requirements are satisfied; (ii) using LiF as an example, the infinite periodic polymer result agrees with extrapolated finite oligomer calculations and, likewise, for the build-up to a 2D slab and a 3D crystal; (iii) the values converge to the static case for low frequencies; and (iv) the Bishop-deKee dispersion formulas relating dc-P, SHG, and general processes are reproduced through quartic terms. Preliminary SHG calculations on multi-layer MoS2 satisfactorily reproduce experimental data. [ABSTRACT FROM AUTHOR]

The response to an electrostatic field is determined through simple model calculations, within both the restricted Hartree-Fock and density functional theory methods, for long, finite as well as infinite, periodic chains. The permanent dipole moment, μ0, the polarizability, α, and the hyperpolarizabilities β and γ , calculated using a finite-field approach, are extensively analyzed. Our simple model allows for treatment of large systems and for separation of the properties into atomic and unit-cell contributions. That part of the response properties attributable to the terminations of the finite system change into delocalized current contributions in the corresponding infinite periodic system. Special emphasis is placed on analyzing the reasons behind the dramatic overestimation of the response properties found with density functional theory methods presently in common use. [ABSTRACT FROM AUTHOR]

The high-frequency dielectric ε and the first nonlinear electric susceptibility χ(2) tensors of crystalline potassium dihydrogen phosphate (KH2PO4) 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 ε and χ(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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

A computational scheme for the evaluation of the static first (β) and second (γ) 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 β and γ (the polarizability tensor α 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 β and γ 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. [ABSTRACT FROM AUTHOR]

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 Schrödinger 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 Mo\ller–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. [ABSTRACT FROM AUTHOR]

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 ClO[sub 2] for which there are experimental data and other theoretical calculations. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

A treatment of nuclear vibrational motions in two-photon absorption is laid out in detail. Perturbation theory is used to develop working formulas for diatomic molecules and tested for the X[sup 1]&sigma[sup +]-A[sup 1]π transition of carbon monoxide. The results are compared with the exact numerical values. Certain vibrational contributions, not previously recognized, are found to make an important contribution to the two-photon absorption probability. [ABSTRACT FROM AUTHOR]

Ab initio static and dynamic (hyper)polarizability calculations at the time-dependent coupled-perturbed Hartree–Fock level have been carried out on polyyne, all-trans polyacetylene (PA), and trans-transoi¨d polymethineimine by a noniterative method. The dependence on basis set and on the number of neighboring unit cells exactly included has been investigated. The 6-31G basis set with nine neighboring unit cells, and long-range Coulomb interactions taken into account, was utilized in the final calculations. Although in many instances our results are the first that have been obtained we compare with oligomer calculations wherever possible. For PA the theoretical result is also compared with experiment and the main reasons for the existing discrepancy are addressed. © 2001 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Although the static first hyperpolarizability β of graphene and chiral carbon nanotubes (CNTs) vanishes by symmetry, that is no longer true for frequency-dependent fields in which case there is a unique nonzero component. We evaluate that component for the dc-Pockels effect and second harmonic generation of several CNTs by means of the coupled perturbed Kohn-Sham method with the CAM-B3LYP functional as implemented in the CRYSTAL code. Both electronic and vibrational contributions are considered. Of particular interest is the frequency dependence in the region below the first resonance. Our results for the role of band gap, type of chirality, CNT radius and effect of orbital relaxation are analyzed using the conventional sum-over-states formulation in conjunction with the calculated band structure and density of states. [ABSTRACT FROM AUTHOR]

CRYSTAL is a periodic ab initio code that uses a Gaussian-type basis set to express crystalline orbitals (i.e., Bloch functions). The use of atom-centered basis functions allows treating 3D (crystals), 2D (slabs), 1D (polymers), and 0D (molecules) systems on the same grounds. In turn, all-electron calculations are inherently permitted along with pseudopotential strategies. A variety of density functionals are implemented, including global and range-separated hybrids of various natures and, as an extreme case, Hartree–Fock (HF). The cost for HF or hybrids is only about 3–5 times higher than when using the local density approximation or the generalized gradient approximation. Symmetry is fully exploited at all steps of the calculation. Many tools are available to modify the structure as given in input and simplify the construction of complicated objects, such as slabs, nanotubes, molecules, and clusters. Many tensorial properties can be evaluated by using a single input keyword: elastic, piezoelectric, photoelastic, dielectric, first and second hyperpolarizabilities, etc. The calculation of infrared and Raman spectra is available, and the intensities are computed analytically. Automated tools are available for the generation of the relevant configurations of solid solutions and/or disordered systems. Three versions of the code exist: serial, parallel, and massive-parallel. In the second one, the most relevant matrices are duplicated on each core, whereas in the third one, the Fock matrix is distributed for diagonalization. All the relevant vectors are dynamically allocated and deallocated after use, making the code very agile. CRYSTAL can be used efficiently on high performance computing machines up to thousands of cores. [ABSTRACT FROM AUTHOR]