Electronic polarization in quasilinear chains

Starting with a finite $k$-mesh version of a well-known equation by Blount, we show how various definitions proposed for the polarization of long chains are related. Expressions used for infinite periodic chains in the 'modern theory of polarization' are thereby obtained along with a new single particle formulation. Separate intracellular and intercellular contributions to the polarization are identified and, in application to infinite chains, the traditional sawtooth definition is found to be missing the latter. For a finite open chain the dipole moment depends upon how the chain is terminated, but the intracellular and intercellular polarization do not. All of these results are illustrated through calculations with a simple H\"uckel-like model.Comment: 5 page

First-Principles Calculation of the Optical Rotatory Power of Periodic Systems: Modern Theory with Modern Functionals

An analysis of orbital magnetization in band insulators is provided. It is shown that a previously proposed electronic orbital angular-momentum operator generalizes the ``modern theory of orbital magnetization'' to include non-local Hamiltonians. Expressions for magnetic transition dipole moments needed for the calculation of optical rotation (OR) and other properties are developed. A variety of issues that arise in this context are critically analyzed. These issues include periodicity of the operators, previously proposed band dispersion terms as well as, if and where needed, evaluation of reciprocal space derivatives of orbital coefficients. Our treatment is used to determine the optical rotatory power of band insulators employing a formulation that accounts for electric dipole - electric quadrupole (DQ), as well as electric dipole-magnetic dipole, contributions. An implementation in the public \textsc{Crystal} program is validated against a model finite system and applied to the $\alpha$-quartz mineral through linear-response time-dependent density functional theory with a hybrid functional. The latter calculations confirmed the importance of DQ terms. Agreement against experiment was only possible with i) use of a high quality basis set, ii) inclusion of a fraction of non-local Fock exchange, and iii) account of orbital-relaxation terms in the calculation of response functions

Factors Governing Nuclear Geometry and Bond-Orbital Directions in Second Row AH2 Molecules

We have obtained valence bond waivefunctions for the neutral, positive ion, and lower excited states of second row AH2 molecules. A number of simple rules emerge which govern the nuclear geometry and bond-orbital directions. These are explained in terms of valence bond orbital characteristics as well as an analysis of energy components

How much can donor/acceptor-substitution change the responses of long push-pull systems to DC fields?

Mathematical arguments are presented that give a unique answer to the question in the title. Subsequently, the mathematical analysis is extended using results of detailed model calculations that, in addition, throw further light on the consequences of the analysis. Finally, through a comparison with various recent studies, many of the latter are given a new interpretation.Comment: Accepted by Chem. Phys. Let

Calculation of the Infrared Intensity of Crystalline Systems. A Comparison of Three Strategies Based on Berry Phase, Wannier Function, and Coupled-Perturbed Kohn–Sham Methods

Three alternative strategies for the calculation of the IR intensity of crystalline systems, as determined by Born charges, have been implemented in the Crystal code, using a Gaussian type basis set. One uses the Berry phase (BP) algorithm to compute the dipole moment; another does so, instead, through well localized crystalline orbitals (Wannier functions, WF); and the third is based on a coupled perturbed Hartree–Fock or Kohn–Sham procedure (CP). In WF and BP, the derivative of the dipole moment with respect to the atomic coordinates is evaluated numerically, whereas in CP it is analytical. In the three cases, very different numerical schemes are utilized, so that the equivalence of the obtained IR intensities is not ensured a priori but instead is the result of the high numerical accuracy of the many computational steps involved. The main aspects of the three schemes are briefly recalled, and the dependence of the results on the computational parameters (number of k points in reciprocal space, tolerances for the truncation of the Coulomb and exchange series, and so on) is documented. It is shown that in standard computational conditions the three schemes produce IR intensities that differ by less than 1%; this difference can be reduced by an order of magnitude by acting on the parameters that control the accuracy of the calculation. A large unit cell system (80 atoms per cell) is used to document the relative cost of the three schemes. Within the current implementation the BP strategy, despite its seminumerical nature, is the most efficient choice. That is because it is the oldest implementation, and it is based on the simplest of the three algorithms. Thus, parallelism and other schemes for improving efficiency have, so far, been implemented to a lesser degree in the other two cases

Anharmonic vibrational analysis of water with traditional and explicitly correlated coupled cluster methods

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