Geometrical derivatives of dipole moments and polarizabilities

Molecular dipole moments and polarizabilities, as well as their geometrical derivatives, are given analytical expressions for multiconfiguration self-consistent-field and configuration interaction wavefunctions. By considering the response of the electronic wavefunction induced by electric field and geometrical displacement terms in the Hamiltonian, the response of the total electronic energy to these terms is analyzed. The dipole moment and polarizability are then identified through the factors in the energy which are linear and quadratic in the electric field, respectively. Derivatives with respect to molecular deformation are obtained by identifying factors in these moments which are linear, quadratic, etc., in the distortion parameter. The analytical derivative expressions obtained here are compared to those which arise through finite-difference calculations, and it is shown how previous configuration-interaction-based finite difference dipole moment and polarizability derivatives are wrong. The proper means of treating such derivatives are detailed.     

Electric dipole polarizabilities of copper clusters

The static electric dipole polarizabilities of Cu(9)-Cu(61) have been measured via a molecular beam deflection method. The clusters display per-atom polarizabilities that decrease monotonically with size, from approximately 16 A(3) per atom Cu(9-10) to approximately 5 A(3) (Cu(45-61)). Absent are any discernible discontinuities or odd-even alternations due to electronic shell filling or electron pairing effects. For the smallest clusters, the experimental polarizabilities are approximately 3 times larger than those predicted classically for conducting ellipsoids, and approach the classical values only for clusters containing more than approximately 45 atoms.     

The accurate calculation of dipole moments and dipole polarizabilities using Gaussian-based density functional methods

Dipole moments and static dipole polarizabilities have been calculated for a number of small molecules using the linear combination of Gaussian-type orbitals–local spin density method. The effect of augmenting standard orbital basis sets with polarization functions has been investigated. A set of optimum ζ_d, for use in calculating polarizabilities, has been derived for the first-row atoms C, N, O, and F. The results of this optimized doubly polarized double-zeta basis set compare well with results obtained using a double-zeta basis set augmented by four even-tempered ζ_d polarization functions. The results of the optimized basis set, and a basis set augmented with only a single ζ_d polarization function derived from it, compare very favorably with those obtained from Møller–Plesset perturbation theory and with experimental data. They show a marked improvement on results obtained using standard Hartree–Fock self-consistent-field molecular orbital methods where no treatment of electron-correlation is included.     

Excited states dipole moments and polarizabilities of uracil and cytosine 5-halo derivatives

Dipole moments and polarizabilities of different excited states of uracil and cytosine 5-halo derivatives have been calculated using solvent shift methods and CNDO/S calculations. The results are discussed in relation to different solute–solvent interactions and the nature of the electronic transition.     

Calculation of molecular electric polarizabilities and dipole moments. III. BH molecule

We use a previously proposed variation-perturbation method to calculate the electric polarizabilities and the electric dipole moment at equilibrium nuclear distance of the BH molecule. We obtain 3.56 × 10^?24 cm³ for the perpendicular polarizability α_xx and 3.22 × 10^?24 cm³ for the parallel polarizability α_zz. Our result for the electric dipole moment μ₀ is 1.734 debye units; there is no reliable experimental result to compare it with.     

First principles calculation of the dipole moments of small mixed Ge/Te semiconductor clusters

We investigate the structural and electronic properties of the small mixed semiconductor clusters GeTe, Ge₂Te, GeTe₂ and Ge₂Te₂ by means of first principles supercell calculations using the local density approximation and the pseudopotential plane wave method. The cluster geometry is optimized using a conjugate gradient method. For GeTe₂ we confirm the linear structure (D_∞h ) suggested by recent experiments. For Ge₂Te we obtain an equilateral triangle as the equilibrium structure. For Ge₂Te₂ we obtain a deformed tetrahedrom (butterfly C_2v symmetry). For each of these molecules we compute the dipole moment in the equilibrium geometry and in selected geometries near to equilibrium corresponding to states higher in energy by a few tens of meV. For the equilibrium state of Ge₂Te and Ge₂Te₂ we obtain permanent dipole moments smaller than those estimated from recent experiments at room temperature. For selected low lying excited states of these clusters, which have elongated Ge-Te bond length, we obtain enhanced dipole moments, improving the agreement with the ones estimated from experiments.     

Calculation of molecular electric polarizabilities and dipole moments. II. The LiH molecule

We use a variation–perturbation method to calculate the electric polarizabilities and the electric dipole moment of the LiH molecule. We obtain 4.455 for the perpendicular polarizability and 4.001 (×10^?24 cm³) for the parallel polarizability. Our result for the electric dipole moment at equilibrium nuclear distance is 5.866, which is in excellent agreement with the experimental value 5.828 debye units.     

A new form of electric-field-dependent basis functions for the calculation of electric polarizabilities and dipole moments

An ab-initio molecular orbital theory of electrical polarization is presented in which the molecular orbitals are written as linear combinations of atomic functions which depend explicitly on the strength of a uniform external electric field. The wavefunctions in the presence of such a field are determined using self-consistent field perturbation theory. It is shown that the use of field-dependent atomic functions provides an efficient technique for the calculation of electric polarizability tensors. Polarizability tensors and electric-dipole moments calculated using both a minimal and a split-valence-shell basis set are compared with experimental results. Both polarizability-tensor components and dipole moments are seriously underestimated at the minimal bases-set level. The split-valence basis approach yields substantially better results; the calculated values at this level are in reasonable agreement with the corresponding experimental values. The experimental ordering of isotropic polarizabilities for a set of small molecules is duplicated quite closely by both the minimal and the split-valence-shell calculations.     

Electric dipole polarizabilities and C6 dipole-dipole dispersion coefficients for sodium clusters and C60

The frequency-dependent polarizabilities of closed-shell sodium clusters containing up to 20 atoms have been calculated using the linear complex polarization propagator approach in conjunction with Hartree-Fock and Kohn-Sham density functional theories. In combination with polarizabilities for C(60) from a previous work [J. Chem. Phys. 123, 124312 (2005)], the C(6) dipole-dipole dispersion coefficients for the metal-cluster-to-cluster and cluster-to-buckminster-fullerene interactions are obtained via the Casimir-Polder relation [Phys. Rev. 73, 360 (1948)]. The B3PW91 results for the polarizability of the sodium dimer and tetramer are benchmarked against coupled cluster calculations. The error bars of the reported theoretical results for the C(6) coefficients are estimated to be 5%, and the results are well within the error bars of the experiment.     

Excited state dipole moments and polarizabilities of centrosymmetric and dimeric molecules. II. Polyenes, polyynes and cumulenes

Electro-optical absorption spectra are measured for a series of polyenes, polyynes and cumulenes with centrosymmetric π-chromophores in cyclohexane solution at 298 K. For all molecules the long-axis component of the polarizability tensor is considerably larger in the first dipole-allowed singlet state compared to the ground state. The transition moments are found to be parallel to the long molecular axis. All polyenes and one cumulene show a linear Stark component indicating a long-axis excited state dipole moment. Both the dipole moments and the polarizabilities are corrected within the extended Onsager model for solvent cavity and reaction field effects. It is suggested that symmetry lowering solvent perturbations are the reason for the apparent excited state dipole moments.     

Static dipole polarizabilities of open-shell negative ions

Summary Dipole polarizability estimates at have been calculated for the 2p and 3p open-shell negative ions in their ground and valence excited states. To complete the sequence such estimates for F^– and Cl^– in their ground¹ S state have also been made. Single configuration based linear response theory has been adopted presently with a view to study the effect of RPA-type correlations on the polarizabilities of such systems. For the 3p open-shell systems the innermost 1s core has been kept frozen. Most of the results are reported for the first time. Agreement with existing data, wherever available, is reasonable. The convergence of the polarizability estimates towards basis sets has been studied.     

Molecular dipole moments and electronegativity

As suggested by acharge-transfer model based on Mulliken's definition of electronegativity, the dipole moments of various diatomic molecules and certain photoemission chemical shifts are shown to depend on the normalized electronegativity differences, [(x_B ? x_A)/$\text{x}$], and not simply on (x_B ? x_A).     

Excited state dipole moments and polarizabilities of centrosymmetric and dimeric molecules. I. Model study of a bichromophoric molecule

Refractometric, dielectric and electro-optical absorption measurements are reported for 1-dimethylamino-2,6-dicyano-4-methyl-benzene (I) and 1,4-bis(4′-dimethylamino-3′,5′-dicyanophenyl)bicyclo[2.2.2]octane (II). The evaluation leads to dipole moments and polarizabilities of the ground state as well as the first dipole allowed singlet state. The experimental res excellently substantiate the method of electro-optical absorption measurements in solution. It is shown that the excited dimer wavefunctions of the bichromophoric molecule II localize by solvent induced local site perturbations.     

Static dipole and quadrupole polarizabilities of alkaline earth atoms

Static dipole and quadrupole polarizability (α_d and α_q, respectively) values of coupled Hartree–Fock quality have been calculated for the alkaline earth atoms Be(2s), Mg(3s), Ca(4s), and Sr(5s) using a method based on the many-body perturbation theory. The present values of α_d and α_q for Be and α_d for Mg are in excellent agreement with the other available results of similar accuracy. The CHF calculations of α_d for Sr and α_q for Mg, Ca, and Sr are being reported for the first time.     

Calculations of electric dipole polarizabilities of polyatomic molecules

Coupled and uncoupled Hartree–Fock theories are used to compute the electric dipole polarizability of water, ammonia, and methane with three different GTO basis sets. Bounds for the geometric approximation to uncoupled polarizabilities are also computed to examine the accuracy of calculated values. The results are compared with those obtained by a variational-perturbation method proposed by Rebane. The numerical tests provide some information on the correlation terms affecting total computed polarizabilities. The computed values are shown to be in fair or good agreement with experimental data for the largest basis sets. The reliability of Rebane's method with respect to coupled HF procedure is also discussed.