Nonempirical calculations of dipole moments of molecules in semifloating gaussian basis sets

For the example of the calculation of the dipole moments of the HF, HCl, H₂O, NH₃, CO, H₂CO, CH₃F molecules in two-exponent and three-exponent Gaussian basis sets, we have studied the effect of including floating functions in the basis, directly giving the effect of polarization of the electron shell of the atom in the molecule. We have established a weak dependence of the calculated dipole moment on the dimensionality of the basis, the number of floating functions, and also the orbital exponents of the hydrogen atoms. The correction introduced by the floating functions in molecules with polar bonds is considerably greater than the correlation correction. The proposed approach allows us to decrease the dimensionality of the orbital basis by a factor of 1.5–2 without making the agreement with experiment worse.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 26, No. 4, pp. 481–485, July–August, 1990.     

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.     

Long-range molecular states dissociating to the three or four lowest asymptotes for the ten heteronuclear diatomic alkali molecules

Long-range energy matrix elements have been calculated in the multipolar expansion approximation for all the molecular states dissociating to the three or four lowest asymptotes for the molecules LiNa, LiK, LiRb, LiCs, NaK, NaRb, NaCs, KRb, KCs and RbCs using the semi-empirical perturbative model we proposed recently. Two different assumptions have been investigated: including or excluding the spin-orbit effects within each atom. Full numerical results are presented for NaK and LiCs which have been chosen as examples. For the ten molecules in the non-interacting assumption the long-range coefficients C₆ and C₈ have been found for each state when neglecting atomic spin-orbit effects while the fitted value C^*₆ and C^*₈ are presented for each state when including atomic spin-orbit effects. When considering the interacting states, those dissociating to ns + n′s and to ns + 5d(Cs) are seen to be slightly perturbed while the states dissociating to ns + n′p and to np + n′s are significantly perturbed. The wavefunctions for the interacting ³Σ⁺, ³Π, 0⁺, 0⁻, 1, 2 states for the molecules NaK and LiCs are presented for various internuclear distances.     

Symmetry-adapted-cluster configuration interaction study of the doublet states of HCl+: potential energy curves, dipole moments, and transition dipole moments

The electronic structure of the HCl(+) molecular ion has been calculated using the general-R symmetry-adapted-cluster configuration interaction (SAC-CI) method. The authors present the potential energy curves, dipole moments, and transition dipole moments for a series of doublet states. The data are compared with the previous CASSCF and MCSCF calculations. The SAC-CI results reproduce quite well the data available in literature and extend the knowledge on the HCl(+) electronic structure for several higher states. The calculated R-dependent behavior of both dipole moments and transition dipole moments for a series of bound and unbound states reveals an intricate dissociation process at intermediate distances (R>R(e)). The pronounced maxima in transition dipole moment (TDM) describing transitions into high electronic states (X (2)Pi-->3 (2)Pi, X (2)Pi-->3 (2)Sigma, 2 (2)Pi-->3 (2)Pi, 3 (2)Pi-->4 (2)Pi) occur at different interatomic separations. Such TDM features are promising for selection of excitation pathways and, consequently, for an optimal control of the dissociation products.     

The dipole moments of the excited states of FeC

With the purpose of comparing expectation dipole moment values mu with finite-field obtained dipole moments mu(FF), we recalculated by the finite-field method previously reported mu values of 38 excited states of FeC. In most of the cases mu(FF) is significantly larger than mu.     

Relative magnitudes of singlet and triplet state dipole moments: the lowest nπ* excited states of p-methylbenzaldehyde and p-chlorobenzaldehyde

The molecular dipole moment changes upon ¹nπ* and ³nπ* excitation of p-methylbenzaldehyde and p-chlorobenzaldehyde isolated in p-dimethoxybenzene host crystals have been determined from measurements of the Stark splittings in phosphorescence excitation and phosphorescence spectra. Within the experimental uncertainty, the changes are identical for the corresponding triplet and singlet states. This result contrasts with similar determinations for formaldehyde, benzophenone, and 4,4′-dichlorobenzophenone and with predictions based on simple molecular orbital and electron correlation arguments. The result is considered to be a consequence of a relatively large mixing of ³nμ* and ³μμ* states.     

Berry phase approach to longitudinal dipole moments of infinite chains in electronic-structure methods with local basis sets

The authors provide a reformulation of the modern theory of polarization for one-dimensional stereoregular polymers, at the level of the single determinant Hartree-Fock and Kohn-Sham methods within a basis set of local orbitals. By starting with localization of one-electron orbitals, their approach naturally arrives to the Berry phases of Bloch orbitals. Then they describe a novel numerical algorithm for evaluation of longitudinal dipole moments, computationally more convenient than those presently implemented within the local basis periodic codes. This method is based on the straightforward evaluation of the usual direct space dipole matrix elements between local orbitals, as well as overlap matrices between wave functions at two neighboring k points of the reciprocal space mesh. The practical behavior of the algorithm and its convergence properties with respect to the k-point mesh density are illustrated in benchmark calculations for water chains and fluorinated trans-polyacetylene.     

A theoretical study of calcium monohydride, CaH: low-lying states and their permanent electric dipole moments

Potential energy curves, energy parameters, and spectroscopic values for the X (2)Sigma(+), A (2)Pi, B (2)Sigma(+), a (4)Pi, and b (4)Sigma(+), states of CaH have been calculated using the multireference configuration interaction and coupled cluster levels of theory, while employing quantitative basis sets (of augmented quintuple-zeta quality) and taking also into account core/valence correlation and one-electron relativistic effects. For the ground (X (2)Sigma(+)) and the first two following excited states (A (2)Pi, B (2)Sigma(+)) of CaH, the permanent electric dipole moments have been calculated. Our best finite field dipole moment of the A (2)Pi state of 2.425 D (upsilon = 0) is in very good agreement with the experimental literature value of 2.372(12) D. However, a discrepancy is observed in the dipole moment of the X (2)Sigma(+) state. Our most extensive calculation gives mu = 2.623 D (upsilon = 0), which is considerably smaller than the experimental value of mu = 2.94(16) D (upsilon = 0). Small van der Waals minima were found for both "repulsive" quartet states. Spectroscopic constants and energy parameters for all states are in remarkable agreement with available experimental values.     

RMS dipole moments of the valence excited states of linear polyenes

Asymmetrical vibrations induce small oscillating dipole moments in the ground states of linear all-trans polyenes. Upon vertical excitation into one of the two low-lying valence excited states the induced in-plane dipole moments are increased 3 times and more. The rms dipole moments increase with the chain length. The inducing modes are the CCC skeletal bending and the CC stretching vibrations. CH stretching vibrations are also found to contribute non-negligible polarization.     

Calculation of the electronic structure and dipole moments of 4-substituted tetrabromopyridines

It is demonstrated from the results of a quantum-chemical calculation by the CNDO/2 (complete neglect of differential overlap/2) method and the experimental dipole moments for a number of 4-substituted tetrabromopyridines that the character of the intramolecular interactions in the investigated compounds differs little from that observed for 4-substituted nonhalogenated pyridines. A linear relationship between the charge on the heteroatom and the p constants for the substituents in the 4 position was observed. A similar relationship was obtained for the experimental dipole moments and the substituent constants.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 7, pp. 927–931, July, 1981.     

Small basis sets for calculations of barrier heights, energies of reaction, electron affinities, geometries, and dipole moments

Beginning with the MIDI! basis set (also called MIDIX), we introduce the MIDIX+, MIDIY, and MIDIY+ basis sets. Using correlated ab initio and hybrid density functional theory, we compare their performance to that of several existing basis sets for electronic structure calculations. The new basis sets are tested with databases of 358 energies of reactions, 44 barrier heights, 31 electron affinities, 18 geometries, and 29 dipole moments. The MIDI!, MIDIX+, MIDIY, and MIDIY+ basis sets are shown to be cost-efficient methods for calculating relative energies, geometries, and dipole moments. The MIDIX+ basis is shown to be particularly efficient for calculating electron affinities of large molecules.Contribution to the Jacopo Tomasi Honorary Issue     

Calculation of electric dipole transition moments using quasi-degenerate variational perturbation theory and averaged coupled-pair functional theory

Results are reported from calculations of electric dipole transition moments for various electronic transitions in Be, CH₂, and A1H using multireference singles and doubles configuration interaction, quasi-degenerate variational perturbation theory, and multireference averaged coupled pair functional theory. A simple normalization scheme is used for the quasi-degenerate variational perturbation theory and multireference averaged coupled pair functional theory wave functions. In all cases, comparison is made with full configuration interaction results in the valence space. For Be and CH₂, all methods are of comparable quality in calculating the transition moments and excitation energies, with averaged coupled-pair functional theory yielding slightly quicker convergence of the excitation energies and transition moments in most cases. For AlH, multireference singles and doubles configuration interaction is somewhat more accurate for the calculation of the transition moment. Factors that affect the accuracy of the methods are discussed. © 1994 John Wiley & Sons, Inc.     

Ab Initio Diabatic energies and dipole moments of the electronic states of RbLi molecule

For all states dissociating below the ionic limit Li^? Rb⁺, we perform a diabatic study for ¹Σ⁺ electronic states dissociating into Rb (5s, 5p, 4d, 6s, 6p, 5d, 7s, 4f) + Li (2s, 2p, 3s). Furthermore, we present the diabatic results for the 1–11 ³σ, 1–8 ^1,3Π, and 1–4 ^1,3Δ states. The present calculations on the RbLi molecule are complementary to previous theoretical work on this system, including recently observed electronic states that had not been calculated previously. The calculations rely on ab‐initio pseudopotential, core polarization potential operators for the core‐valence correlation and full valence configuration interaction approaches, combined to an efficient diabatization procedure. For the low‐lying states, diabatic potentials and permanent dipole moments are analyzed, revealing the strong imprint of the ionic state in the ¹Σ⁺ adiabatic states. The transition dipole moment is used to evaluate the radiative lifetimes of the vibrational levels trapped in the 2 ¹Σ⁺ excited states for the first time. In addition to the bound–bound contribution, the bound–free term has been evaluated using the Franck–Condon approximation and also exactly added to the total radiative lifetime. © 2013 Wiley Periodicals, Inc.     

Quadrupole moments of the alkali dimers,Li2, Na2, and K2

The quadrupole moments (Θ) of Li₂, Na₂, and K₂ have been determined using SCF, B3LYP, and CCSD(T). Included in this study is the effect of valence and core–valence correlation. The variation of Θ as a function of bond length has also been evaluated from which vibrational contributions have been determined. Additionally, the shape and relative magnitude of Θ vs. bond length are attributed to the s–s nature of the bonding. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

An accurate lower-bound calculation of the lowest triplet states of he and its isoelectronic series

Accurate lower bounds for the nonrelativistic lowest triplet states of ⁴He and ^∞He and the He isoelectronic series up to Z = 10 were calculated by the method of variance minimization using wave functions with logarithmic terms. Furthermore, the method of Lehmann/Goerisch was extended to self-adjoint operators with an essential spectrum. Both methods were compared for ⁴He. © 1992 John Wiley & Sons, Inc.     

Radiative transition probabilities, lifetimes and dipole moments for the vibrational levels of the X1Sigma+ ground state of 39K85Rb

Using a potential energy curve (based primarily on the RKR potential of Amiot and Verges [J. Chem. Phys. 112, 7068 (2000)]) and a dipole moment function (based primarily on ab initio calculations of Park et al. [Chem. Phys. 257, 135 (2000)]), we have calculated radiative transition probabilities (Einstein A coefficients), radiative lifetimes, and dipole moment expectation values involving all vibrational levels (for several rotational quantum numbers) of the X1Sigma+ ground state of 39K85Rb. We observe that the radiative lifetimes of vibrationally excited levels, in particular, are approximately 10(3)-10(6) seconds, far too long to be significant in most ultracold experiments involving 39K85Rb or its isotopomers. Comparison with other molecules (LiH and HF) suggests that simple scaling (A approximately mu2nu3 approximately tau(-1)) will predict similarly long lifetimes for many other heteronuclear molecules, e.g., RbCs.     

AB initio calculations of the dipole moments in low-lying electronic states of the ccn radical

The structures and dipole moments of the four low-lying electronic states (X²Π, A²Δ, B²Σ⁻ and C²Σ⁺) of the linear CCN radical are investigated by ab initio calculations at SDCI/DZP and TZP levels. For all the electronically excited states, the dipole moments are calculated to be ≈ 3.0 D. However, a significantly smaller dipole moment, ≈ 0.6 D, is predicted for the ground state. This result is consistent with the recent experiment by Suzuki, Saito and Hirota, where the MODR signals are observed for the A state CCN but not for the X state. Electronic correlation is important in determining both equilibrium bond lengths and dipole moments.     

Approximate wave functions for excited states: Energies and dipole moments of the 2pσ state of HeH+2

The problem of calculating approximate wave functions for an excited state, which is not the lowest of a symmetry species, has been investigated for the first excited -state of the HeH²⁺ ion. The results of calculations using explicitly orthogonalized variational trial functions are compared with results based on the linear combination of molecular Orbitals (LCMO) procedure, and with the exact values. Our values of the electronic energy and of the dipole moment are in good agreement with the exact values.

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Zusammenfassung Das Problem der Berechnung eines angeregten Zustands, der nicht der niedrigste seiner Rasse ist, wird am Beispiel des ersten angeregten -Zustands von HeH⁺² diskutiert. Energien, Dipolmomente und Übergangsmomente, erhalten mit nichtorthogonalisierten und orthogonalisierten Variationsstörungsfunktionen 0. und 1. Ordnung und mit LCMO-Funktionen, werden mit den exakten Werten verglichen.

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Résumé On étudie le problème du calcul d'une fonction d'onde approchée pour un état excité qui n'est pas le plus bas pour sa classe de symétrie, sur l'exemple du premier état excité de l'ion HeH⁺². Les résultats du calcul par utilisation de fonctions d'essai variationnelles explicitement orthogonalisées sont comparés à ceux fondés sur un procédé de combinaison linéaire des orbitales moléculaires (LCMO) et aux valeurs exactes. Nos valeurs pour l'énergie électronique et le moment dipolaire sont en bon accord avec les valeurs exactes.