Ab Initio Molecular Wavefunctions Research Articles

NaK Λ doubling and permanent electric dipoles in low-lying1Πstates: Experiment and theory

The paper presents \ensuremath{\Lambda} splittings and q factors in the NaK $D{}^{1}\ensuremath{\Pi}$ state, directly measured from the electric radio-frequency-optical double resonance (RF-ODR) in laser-induced fluorescence (LIF) for a number of vibrational states $v=1--22$ with definite rotational levels J between 7 and 46. Permanent electric dipole moment values (d) have been obtained by measuring in LIF spectra the relative intensities of ``forbidden'' lines caused by dc Stark effect induced $e/f$ mixing in the ${}^{1}\ensuremath{\Pi}$ state, with their subsequent processing, which allowed us to obtain the $q/d$ ratio. A possible influence of the hyperfine structure on the RF-ODR signal and relative intensities has been calculated, showing that this influence can be neglected. The $q(v)$ values exhibited a decrease from $q(1)=1.529\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}{\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ to $q(22)=1.171\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}{\mathrm{cm}}^{\mathrm{\ensuremath{-}}1},$ which has been explained by an increase of the difference potential between $D{}^{1}\ensuremath{\Pi}$ and $C{}^{1}{\ensuremath{\Sigma}}^{+}$ states with internuclear distance (R); the respective L-uncoupling matrix element was evaluated as 1.87. It was shown, both by semiempirical treatment and population analysis of ab initio molecular wave functions, that considerable $\ensuremath{\pi}d$ and $\ensuremath{\sigma}d$ configuration admixtures are present in the $D{}^{1}\ensuremath{\Pi}$ and the $C{}^{1}{\ensuremath{\Sigma}}^{+}$ states. For the $B{}^{1}\ensuremath{\Pi}$ state, it was demonstrated that \ensuremath{\Lambda} doubling is caused by two competing perturbers $(A{}^{1}{\ensuremath{\Sigma}}^{+}$ and $C{}^{1}{\ensuremath{\Sigma}}^{+}),$ yielding q factors of $\ensuremath{\sim}\ensuremath{-}2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}{\mathrm{cm}}^{\mathrm{\ensuremath{-}}1},$ in agreement with high-resolution spectroscopy data given in the literature; single-configuration approximation is valid for interacting $B{}^{1}\ensuremath{\Pi}(\ensuremath{\sigma}{3s}_{\mathrm{Na}},\ensuremath{\pi}{4p}_{\mathrm{K}})\ensuremath{\sim}A{}^{1}{\ensuremath{\Sigma}}^{+}(\ensuremath{\sigma}{3s}_{\mathrm{Na}},\ensuremath{\sigma}{4p}_{\mathrm{K}})$ states. The measured $d(v)$ values, which varied from 6.6 to 4.6 D, have been used to obtain the empirical $D{}^{1}\ensuremath{\Pi}$ state $d(R)$ function for $R=6--12\mathrm{a}.\mathrm{u}.$ by means of an improved instability-free inversion procedure exploiting a special functional form. Two independent series of ab initio all-electron calculations of $d(R)$ and $d(v)$ have been performed for the $D{}^{1}\ensuremath{\Pi}$ and $B{}^{1}\ensuremath{\Pi}$ states of NaK. First, d values were computed as expectation values of the electric dipole operator with conventional multireference configuration-interaction wave functions. Second, the finite-field (FF) technique, combined with a multipartitioning perturbation theory (MPPT) treatment of electronic eigenstates, was applied for the calculation of $d(R)$ functions. The FF-MPPT calculations showed excellent agreement with experimental $D{}^{1}\ensuremath{\Pi}d(v)$ values obtained in the present work, as well as the proximity to experimental $B{}^{1}\ensuremath{\Pi}d(v)$ values given in the literature, thus showing that, as distinct from the ground state, it is important to account correctly for effective interactions of valence electrons arising from core-valence correlations, which could not be done properly with previously used pseudopotential techniques. The experimental d and q values dropping out from a smooth $v$ dependence have been considered as perturbed by $D{}^{1}\ensuremath{\Pi}\ensuremath{\sim}d{}^{3}\ensuremath{\Pi}$ interaction and exploited to evaluate respective ${d}_{t}$ and ${c}_{t}$ values for the perturbing $d{}^{3}\ensuremath{\Pi}$ state.

Calculation of nuclear spin-spin coupling constants with ab initio molecular orbital wave functions

We investigate the use of ab initio molecular wave functions to evaluate the Fermi contact contribution to nuclear spin-spin coupling constants n J AB (A, B=C, H) for a data set of 19 molecules having well-defined experimental geometry and coupling values. We critically examine the theoretical and numerical problems associated with the Dirac δ function operator and its perturbation-theoretic treatment. We show that the common approximation of neglecting basis orbitals not centered on the coupled nuclei is a major source of error in previous calculations

Modeling the diffraction process of molecular crystals: computation of X-ray scattering intensities from ab initio electron densities

An algorithm for calculating the scattering factors of atomic fragments in molecules as defined by the Stockholder recipe is presented. This method allows the calculation, from ab initio molecular wave functions, of structure factors including individual anisotropic atomic temperature factors. These structure factors agree with the model used in most least-squares multipole-refinement procedures. Calculations on the H2O molecule illustrate the method.

Quantitative frontier orbital theory: Part II. A theoretical interpretation of the rules for ring closure

The ‘Sphere Charge’ technique for obtaining charge densities in defined regions of space from ab initio molecular wavefunctions is employed to derive preferred approach angles for nucleophilic attack on digonal, trigonal and tetrahedral systems. The values obtained are related to Baldwin's rules for ring closure.

The concept of bond order

A method for obtaining precise charge densities in defined regions of space from ab initio molecular wavefunctions is employed to place the concept of bond order on a firm theoretical footing. The bond orders obtained for carboncarbon bonds in a range of organic compounds are assessed: those for buta-1,3-diene confirm that it consists of essentially localised double and single bonds.

The concept of bond order: Part II

We recently suggested [l] a method for the computation of bond orders from ab initio molecular wavefunctions, based on the Dean and Richards charge-partition technique [ 21. A calibration for carbon-carbon bonds was obtained by calculating the charge per unit volume in spheres in the internuclear regions of ethane, ethylene and acetylene (where the carbon-carbon distance was a diameter), This is illustrated in Fig. l(a). While the excellent linear correlation with formal bond order is pleasing, it does not however prove the validity of the method since there is no independent verification that the intercept on the charge axis corresponds with a zero bond order. With this in mind we have performed calculations on the molecular fragments CH3, CH,? and CH, having the same geometries as in the reference molecules (Fig. 2). Wavefunctions were obtained using the Gaussian 70 program [ 31 with an STO-3G basis set [4], allowing the maximum multiplicity in each case (i.e. 2, 3 and 4 respectively). Charges were then calculated, by the Dean and Richards method [ 51, in analogous spheres to those used for the cahbration calculations. The results are presented in Table 1 and Fig. l(b). By analogy with the simple picture of bond formation between two atoms, we hoped that twice the value of the charge per unit volume (i.e. the sum for two identical fragments without interaction) would correspond to a zero bond order, the bond strength being due to the extra internuclear localisation resulting from the interaction between fragments. Remarkably, for the methyl fragments, this value does indeed correspond quite closely to the “zero-bond order” charge of the calibration. For the ethylenic and acetylenic fragments a progressively greater charge is observed. This is hardly surprising since one could not expect a diatomic analogy to apply to compounds having unsaturation. However a further point of interest is that the progression of fragment charge again produces an excellent straight line. We believe that this confirmation of the significance of the zero of our bond order scale lends further support to the method, and indicates the viability of its use in the study of molecular properties.

A comparison of the theoretical and experimental electron density distribution in the cyanide and thiocyanate group

Electron density distributions, derived from ab initio molecular wavefunctions, have been calculated for CN − and SCN − ions. From these dynamic densities were calculated assuming rigid body thermal vibrations of the molecules. Comparison with the difference density in NaCN - 2H 2O, NaSCN and NH 4SCN, observed by X-ray diffraction, is fair. Remaining differences between theory and experiment are discussed. The Hartree-Fock method gives a better correspondence with the observed electron density distribution in the thiocyanate ion than the Hartree-Fock-Slater method.

Ab initiocalculation of spin-orbit coupling constants for gaussian lobe and gaussian-type wave functions

The spin-orbit coupling constants of a series of diatomic compounds containing first row atoms have been calculated using ab initio molecular wave functions with gaussian lobe and gaussian-type basis sets. In most cases, fair agreement with the experimental values has been achieved. It is pointed out that multicentre terms have almost no effect on the spin-orbit coupling constant. Furthermore, suggestions for a one-electron approximation using effective nuclear charges are presented.

Ab initio computations of spin‐orbit interactions in polyatomic molecules. Splitting of sulfur LII,III states and singlet–triplet transitions in SO2

AbstractSpin‐orbit interactions among the ground and the first few excited electronic states of SO2, are computed with ab initio molecular wave functions and Gaussian atomic orbitals. All spin‐other orbits contributions to the matrix elements are included.The computed intensity of the first singlet–triplet transition is found to be in broad agreement with experiment and sensitive to an extension of the configuration interaction expansion of molecular wave functions. Also, the splitting of sulfur LII,III states in SO2 is derived as an example of large spin‐orbit interactions among electronic states.

Transition moments, band strengths, and line strengths for NaH

Electronic transition moments, as functions of internuclear separation, are calculated for the A1Σ+ → X1Σ+, B1Π → X1Σ+, B1Π → A1Σ+, c3Σ+ → a3Σ+, b3Π → a3Σ+, and b3Π → c3Σ+ transitions in NaH from ab initio molecular wavefunctions. Reduced line strengths, band strengths, band oscillator strengths, and band Einstein coefficients are calculated for the observed A1Σ+ → X1Σ+ transition, and are compared to experimental band intensities. Also calculated are Franck–Condon factors and R centroids, and the effects of various approximations used in treating experimental data are analyzed.

One‐Electron properties from approximate LCAO‐SCF wave functions

AbstractApproximate and ab initio molecular wave functions are obtained using Gaussian expansions of different length for the Slater orbitals. The expectation values of several one‐electron operators are obtained and the accuracy of different wave functions discussed.