High order vibrational matrix elements for diatomic molecules; dipole moment function and transition moments of CO

The fifth and sixth-order contributions to the vibrational matrix elements are obtained for the transitions v→v'(v'?v+4) using an eight power internuclear Dunham potential and a quartic power series expansion of the dipole moment function. The results for the dipole moment coefficients M₀ to M₄ of CO and the transition moments R_v^v' (with v=5, 10, 20) deduced from a calculation including succesively third, fourth, fifth and sixth-order perturbation theory are compared. The validity of these results is discussed.Using a quintic dipole moment function, general expressions for the vibrational matrix elements corresponding to the transitions v→v'(v'? v+5) are also presented and the influence of these contributions on the calculation of the dipole moment coefficients as well as the hot band transition moments of CO is shown.     

Moments de transition vibrationnelle des molecules diatomiques. Intensite des raies rovibrationnelles des bandes 0→2 et 0→3 et fonction dipolaire de CO

General expressions for the radial wavefunctions and the rotationless matrix elements of the dipole moment for the transitions 0→0 to 0→4 are obtained using a fifth-power internuclear potential, a quartic dipole moment function, and third-order perturbation theory. Line intensities in the 0→2 and 0→3 bands of CO have been measured for pressures varying from 2 to 5 atm. Using the values of the vibrational transition moments |R₀²| and |R₀³| deduced from our measurements and the values of |R₀⁰|, |R₀¹| and |R₀⁴| previously given, we evaluate the coefficients M₀ to M₄ of the dipole-moment function for CO.     

Systematics of diatomic molecular transition moments: Encouraging progress—II

Literature absolute transition moments for A-X(0-0) bands have been compiled and used to obtain “best” values of R_e for some 90 transitions. Correlations were sought between R_e and various molecular parameters such as multiplicity, average internuclear separation, etc. None was found. The A-X (and related) R_e have been plotted for isoelectronic molecules against the nuclear charge difference and fitted with simple curves which seem to approach the R_e axis with zero slope. Both of these results are in accord with theory. The concept of isovalence has been clarified to allow for the orbital structure of molecules. It appears that the heavier of two isovalent hydrides has the greater R_e. Graphs of R_e for groups of isovalent molecules can be fitted with simple curves.     

Transition Moments betweenΔg,Πg, andΠuStates of the H2Molecule

Electronic transition moments are computed for dipole transitions between theCandD¹Π_u,IandR¹Π_gandJandS¹Δ_gstates of the hydrogen molecule for internuclear distancesR∈ [1, 15] bohr. The character of the wavefunctions at large internuclear distances is investigated. It is shown that in theDandRstates the asymptotic configurations are strongly mixed forR≤ 15 bohrs. TheSstate has mixed character even atR= 40 bohr.     

Nonempirical and quasi-classical approaches to the calculation of the electronic transition dipole moments

The dependence of the electronic transition dipole moment on the internuclear separation is calculated nonempirically for the Meinel band of the N ₂ ⁺ molecular ion using the Gaussian 98 software package with different basis sets. The results are compared with the dependences obtainedby the semiempirical methods. The basic relationships of the R-centroid method are derived, and the quasi-classical nature of this method is demonstrated. It is confirmed that the dependence of the electronic transition dipole moment on the internuclear separation is described most reliably by using the semiempirical methods. The vibronic transition dipole moment is shown to be an oscillating function of the vibrational quantum number v1 (with v2=const) or v2 (with v1=const).     

Electronic transition moments between excited singlet states of the H2 molecule

The twelve transition moments which connect each of the three ¹Σ_g⁺ states EF, GK, and $\text{H}\text{H}$ with the three ¹Σ_u⁺ states B,B′, $\text{B″}\text{B}$ and with the state C¹Π_u were computed in the range of internuclear distances 1.25 ≤ R ≤ 15 a.u. using accurate electronic wavefunctions. The relative phases of the wavefunctions, which determine the signs of the transition moments, were consistently defined at all R values. The strong R dependences of the transition moments reflect the R-dependent changes in electronic character of the states involved in these transitions. At large R values the ¹Σ_g⁺-¹Σ_u⁺ transition moments are dominated by the two-electron charge resonance in the ionic configuration H⁺ + H^? whose transition moment is $\text{M(R) ? R}$.     

Vibration-rotation matrix elements for diatomic molecules; vibration-rotation interaction functions Fv′v (m) for CO

General expressions for the fourth-order vibrational matrix elements are obtained for the transitions v → v′ (v ? v′ v + 4) using a sixth-power internuclear potential and a quartic dipole moment function. The results for the dipole moment coefficients M₀ to M₄ of CO and for some transition moments R^v′_v deduced from a calculation including successively second, third and fourth order perturbation theory are compared.Using the rotational potential function expanded through the cubic term as a perturbation, we have also obtained general expressions for the vibration-rotation matrix elements. The vibration-rotation interaction functions F^v′_v (m) are calculated for the transitions v → v′ (v = 0, 10, 20 and v ? v′ ? v + 4) of CO and the coefficients C, D, E and G of the quartic polynomials fitting these functions are deduced. Taking account of uncertainties in the matrix elements R⁰₀ to R⁴₀, an error estimate for the coefficients of F²₀(m) and F³₀(m) is given.     

Dipole Moment Function of Hydrogen Halides

A new semi-empirical method for constructing the dipole moments of diatomic molecules as functions of the internuclear distance R $\varepsilon$ [0, ∞) is suggested. The dipole moment is described by a piecewise continuous function specified by a power-law polynomial with the asymptotic μ(R) → R ³ for small R, the dipole moment and its derivatives for equilibrium positions of nuclei in the molecule, and the results of ab initio calculations of the dipole moment for large R. The method is hydrogen halide molecules.     

Vibronic-spin-orbit coupling in octachlorodibenzo-p-dioxin

The dipole moments of vibronic transitions P _0R caused by vibronic-spin-orbit coupling along the coordinates of out-of-plane vibration modes R (to which the most intense vibronic lines of the fine-structure phosphorescence spectrum correspond) were calculated for the ³ B _1u (π π*) → S ₀ electronic transition in an octachlorodibenzo-p-dioxin molecule. The dependence of distribution (P _0R )² over R on the constant of spin-orbit coupling ?_A in different atomic groups (A = C, O, α-Cl, and β-Cl) of the molecule is ascertained. The contribution of these atomic groups (related to ?_A) to the value of P _0R ⁱ for the transitions from various triplet i-sublevels of the electronic state is determined. The obtained results about the different effect of the α-Cl and β-Cl atoms on the vibronic P _0R ⁱ and pure electronic transition dipole moments are discussed in connection with experimental data on the weak influence of the amount of chlorine atoms in polychlorinated dioxins on the phosphorescence decay time.     

Ab initio calculation of electronic transition moments for singlet excited states of the H2 molecule

Ab initio CI electronic dipole transition moments have been calculated for the transitions between singlet states of the hydrogen molecule correlating asymptotically with H(nl)+H(1s) (n=1,2,3). The investigated singlet-singlet transitions include the 30 (n=3) inter-Rydberg transitions and the 32 transitions which may contribute to absorption in the far wings of the Balmer α line of atomic hydrogen perturbed by another hydrogen atom in its ground state. Results are presented for internuclear distances 1.0a₀?R?12a₀. The present results compare well with the previous theoretical calculations available for about half of the transitions treated in the present work. Thirty eight new transitions are presented. Adiabatic potential energies for the and and improved energies for the and states are reported as well.     

Variation of Dipole Moment Function of O-H Bond of t-Butanol with the Nature of Solvent and Its Temperature

The intermolecular influence on dipole moment function is evaluated for O-H bond of t-butanol in different nonpolar solvents at temperatures ranging from 10° to 60°C employing IR band intensities of fundamental and first overtone bands. Two sets of dipole moment derivatives have been calculated corresponding to – and +- combinations of the transition moment matrix elements R₁₀ and R₂₀, the values for ++ and -+ combinations are equal in magnitude to those for - and +- combinations, respectively and opposite in signs. In general the dipole moment derivatives increase on lowering the temperature as well as with increasing molecular interactions with the solvent molecules. Dipole moment plots with dimensionless coordinate ξ [=(r-r_e)/r_e, where r and r_e are internuclear distances during vibration and at equilibrium, respectively] are reported for various systems considered. It is found that for +- combination the dipole moment maximum shifts to higher internuclear distances when polarisation of the solute molecules is increased by lowering of temperature or increase in molecular interactions between solute and solvent molecules. A reverse trend is observed for – combination.- The OH band of t-butanol vapor has been measured.     

The microwave spectrum and dipole moment of heptafulvene

The microwave spectrum of heptafulvene (C₈H₈) has been investigated in the frequency range from 26 to 40 GHz. The following rotational constants have been obtained from a least-squares fit of the measured transition frequencies: A = 3665.972(66)MHz, B = 2004.3165(59)MHz, and C = 1297.5029(90)MHz. From the corresponding moments of inertia it was concluded that heptafulvene has a planar equilibrium structure. The quantitative measurement of the Stark splittings of three transitions have yielded a dipole moment of 0.477(5) D along the a principal axis. A series of satellite transitions accompanied each rotational transition. The satellites have been assigned to the lowest out-of-plane vibration ν₄₂ (B₂) for which a frequency of 70(11) cm^?1 has been determined from relative intensity measurements.     

A possible interpretation of enhanced raman scattering in the vicinity of a nanotip

Theoretical and experimental studies on Raman scattering in a space with small bodies are briefly reviewed. Probabilities of radiative transitions for atoms (molecules) in the vicinity of bodies with dimensions much smaller than a wavelength are calculated. It is shown that in the vicinity of a nanosphere with |ε|?1, the probability of a single-photon electric dipole transition increases by a factor of 9, and the probability of a two-photon transition—by a factor of 81. In the vicinity of a conical needle resting on a plane (the needle and plane have |ε|?1), the radiative transition probability increases by a factor (λ/R _in)² and (λ/R _in)⁴ for single-and two-photon transitions, respectively (R _in is the radius of the needle tip curvature). This theoretical result is offered to interpret the enhancement of radiative processes experimentally observed in the referenced studies.     

On the direct determination of constrained pure state one-electron density matrices: II. A modified algorithm and its applications

An algorithm recently proposed by us for the direct determination of pure state one-electron density matrices (P) under externally imposed constraints has been remodelled. The modified algorithm is applied to the construction of ground state potential energy curve of lithium hydride molecule usingknown values of dipole moments of LiH at various internuclear distances as theexternal constraint. The equilibrium internuclear distances (R _c) is seen to be unaffected by the constraint, but the force constant improves remarkably. The relevant features of the constrained density vis-a-vis those of the unconstrained one are analyzed revealing some of the improved features of the constrained density.     

Systematics of vibrational intensities for “diatomic” molecules: Approximate formulas

Several approximations are discussed which enable one to estimate electric dipole moment transition matrix elements for diatomic molecules based on a very limited amount of experimental data. For strongly polar molecules, a simplistic point-charge dipole model in which there is no vibrational charge flux predicts a simple relation between the permanent moment, M₀, and its derivative with respect to internuclear separation, M₁. This is found to be approximately valid for a surprisingly large number of polar molecules. Next, approximate matrix elements for the fundamental and overtone bands are presented for a linear dipole moment function. Finally, systematic trends for molecules having similar electronic structures are investigated and combined with the approximations discussed above in order to estimate the transition moments for several molecules of astrophysical interest. An extension to the ν₃ fundamental and overtone bands of CH₄ is suggestive that some of these ideas may be applicable to certain polyatomic molecules as well.     

A theoretical study of the electronic transition moment for the C2 swan band system

Self-consistent-field plus configuration-interaction calculations have been performed on the a³Π_u and d³Π_g states of C₂. Good agreement is obtained between the theoretical potential energy curves and these obtained by a Klein-Dunham analysis of measured molecular constants. The sum of the squares of the theoretical transition moments Σ|R_e|² between these states at 2.44 bohr is 4.12, a.u. which is in good agreement with the range of values of 3.3–3.6 a.u. obtained from shock tube measurements. The computed variation of the Σ|R_e|² with internuclear distance is in remarkably good agreement with the relative measurements by Danylewych and Nicholls.     

Gamma-gamma directional correlations in the decay of206Po

Directional correlations of gamma-gamma cascades in the decay of²⁰⁶Po have been measured for the first time. Using a multichannel goniometer with 2 Ge(Li) and 6 NaI(Tl) detectors theA ₂ andA ₄ coefficients have been measured for five cascades in²⁰⁶Bi. From the results,E2/M1 mixing ratios of nine transitions are determined. Upper limits of the transition strengths are presented. Three of the measured mixing ratios are compared with theoretical estimates based on magnetic dipole and electric quadrupole moments of neighbouring nuclei.     

Quasi-relativistic treatment of the low-lying KCs states

The potential energy curves, permanent and transition dipole moments as well as spin-orbit and angular coupling matrix elements between the KCs electronic states converging to the lowest three dissociation limits were evaluated in the basis of the spin-averaged wavefunctions corresponding to pure Hund’s coupling case (a). The quasi-relativistic matrix elements have been obtained for a wide range of internuclear distance by using of small (9-electrons) effective core pseudopotentials of both atoms. The core-valence correlation has been accounted for a large scale multi-reference configuration interaction method combined with semi-empirical core polarization potentials. The static dipole polarizabilities of the ground X¹Σ⁺ and a³Σ⁺ states were extracted from the closed-shell coupled-cluster energies by the finite-field method. Among the singlet and triplet Σ⁺ states manifold the pronounced avoided crossing effect between repulsive walls of the (2,3)³Σ⁺ states has been discovered and analyzed by finite-difference calculation of radial coupling matrix elements. The resulting transition dipole moments and potentials were used to predict radiative lifetimes and emission branching ratios of excited vibronic states while the calculated angular coupling matrix elements were transformed to Λ-doubling constants of the (1,2)¹Π states and magnetic g-factor of the ground state. The accuracies of the present results are discussed by comparing with experimental data and preceding calculations.     

Microwave spectrum,structure, dipole moment,and quadrupole coupling constants of isopropylamine

The microwave spectra of (CH₃)₂CHNH₂, (CH₃)₂CHNHD, and (CH₃)₂CHND₂ have been assigned and analyzed. Only c-type, R-branch transitions were identified. The observed spectra correspond to the trans rotamer, as shown by planar moments, the deuterium isotope effect, dipole moment components, and the N quadrupole coupling constants. The CN bond distance is shorter than that observed in methyl amine, as expected, and significantly longer than that in the analogous closed-ring compound cyclopropylamine.     

On excited states of the Au<Subscript>3</Subscript> cluster: an <Emphasis Type="Italic">ab initio</Emphasis> study

Excited electronic states of the Au₃ cluster are studied within the shape-consistent small-core relativistic pseudopotential model using many-body multipartitioning perturbation theory. Vertical transition energies and dipole moments are evaluated. For highly symmetric isomer, these theoretical results are in reasonable agreement with spectroscopic data from experiments.