Determination of transition moments from power saturation

The electric (or magnetic) dipole transition moment may be calculated from the power broadening of saturation spectra if the ratio (T₂/T₁) is known or can be assumed as unity. The transition moment of the (43-0) P(13) R(15) lines of I₂ coincident with the 5145 Å Ar⁺ laser line is calculated from literature data on the power broadening of the saturation spectrum and compared to that obtained from absorption intensity measurements.     

Full configuration interaction benchmark calculations for transition moments

Full configuration-interaction (FCI) calculations have been performed for the ã ¹A₁–b¹B₁and ã ¹A₁–(2)¹A₁transitions in CH₂ and for selected dipole and quadrupole transitions in BeO. The FCI transition moments are compared to those obtained from correlation treatments that truncate the n-particle expansion. The state-averaged MCSCF/SOCI and FCI results agree well, even for BeO, where the CASSCF level nonorthogonal transition moment differs from the state-averaged CASSCF transition moment.     

Configuration mixing effects on molecular dipole transition moments

The behavior of dipole transition matrix elements between adiabatic eigenstates of diatomic molecules is explored in the region of large configuration mixing. It is demonstrated that the matrix element has a lorentzian shape as a function of internuclear distance. The effect of this shape on the spectrum of LiH is investigated. The strong enhancement of the dipole transition moment in the interaction region is suggested as a source for nonthermal population distributions and laser radiation in alkali diatomics and hydrides.     

Calculation of the vibration-rotational transition moments: Matrix method

One version of the matrix method, combination of the analytic representation of wavefunctions and the HEG scheme (J. Chem. Phys.43, 1515 (1965)) was used to calculate the vibration-rotational wavefunctions and infra-red transition moments of OHA ²⁺ state. Besides introducing this method as an alternative to the numerical integration method, it is shown in this report that the calculated transition moments are virtually independent of the nonlinear parameters of the basis functions. This makes optimization of the parameters unnecessary and facilitates its application. The method is also shown to be very reliable.     

Perturbation calculation of transition moments in the ArH+ system

The matrix elements of the transition dipolar momentum IR have been computed between the low-lying states associated to the Lyman–α transition. The orthogonalization of the involved electronic states (obtained by the CIPSI method) has been performed and led to a better value for the asymptotic behavior of the {Ar(3p⁵, 4s) + H⁺} configuration. Position of the satellites in the red and blue wing of the line are deduced from the potential-energy curves in the frame of the quasistatic theory.     

Ab initio vibrational transition dipole moments and intensities of formaldehyde

Vibrational transition dipole moments and absorption band intensities for the ground state of formaldehyde, including the deuterated isotopic forms, are calculated. The analysis is based on ab initio SCF and CI potential energy and dipole moment surfaces. The formalism derives from second-order perturbation theory and involves the expansion of the dipole moment in terms of normal coordinates, as well as the incorporation of point group symmetry in the selection of the dipole moment components for the allowed transitions. Dipole moment expansion coefficients for the three molecule-fixed Cartesian coordinates of formaldehyde are calculated for internal and normal coordinate representations. Transition dipole moments and absorption band intensities of the fundamental, first overtone, combination, and second overtone transitions are reported. The calculated intensities and dipole moment derivatives are compared to experiment and discussed in the context of molecular orbital and bond polarization theory.     

A theoretical study of spectroscopic properties and transition moments of HBr

Relativistic configuration interaction calculations are performed for twelve electronic states of the HBr molecule. Ground-state spectroscopic properties and electronic dipole moment function are calculated and compared with theoretical and experimental data. Electric dipole moments for eleven excited states are presented and discussed. Electronic transition moments between the ground state and seven excited states are presented in the intermediate coupling scheme.     

Possible large magnetic moments in 4d transition metal clusters

The electronic structure and magnetism of 13 atom clusters of ruthenium, rhodium and palladium having face centered cubic(fcc) geometry has been studied using a Gaussian orbital basis and the local spin density approximation. Calculations were done for the lattice spacings relevant to the bulk crystal lattice. Using the fixed moment states as input potentials, as many as 3 self-consistent states were obtained for these clusters. The 3 converged states of Rh₁₃ cluster is found to have magnetic moments of 0.69 _μB , 1.00 _μB and 1.46 _μB . Out of these states, 0.69 _μB moment state is found to be the ground state. But the total energy difference between the 0.69 _μB and 1.00 _μB state is very small. The 1.46 _μB moment state coincides with the state reported previously by other authors which was obtained using the discrete variational method. The experimentally observed moment was around 0.47 _μB . Our calculated moment is closer to the experimentally observed moment than the previously reported moment, but is still a bit larger. Ru₁₃ cluster is also found to have large moments, and 3 self-consistent states are also obtained for this cluster. The 3 magnetic moments of the Ru₁₃ cluster are 0.46 _μB , 0.62 _μB and 1.08 _μB . Out of these states, 0.62 _μB moment state is found to be the ground state. For the Pd₁₃ cluster, in addition to the nonmagnetic state previously reported, a state with magnetic moment of 0.46 _μB is also found to exist indicating possible magnetism in cluster phase.     

Efficient calculation of vibrational magnetic dipole transition moments and rotational strengths

A priori prediction of vibrational magnetic dipole transition moments and vibrational strengths requires the calculation of the overlap integral of the derivatives of the electronic wavefunction with respect to nuclear displacement and an external magnetic field. The efficient calculation of this integral, using coupled Hartree-Fock theory, is described.     

Determination of molecular properties by the method of moments

Some precautions needed in the choice of weight functions when calculating wave functions by the method of moments are analysed. It appears that an important criterion for good weight functions is that the difference between the total and the truncated overlaps (both defined in the paper) be high.The method of moments is applied to wave functions involving Hylleraas-type correlation factors using weight functions made up of products of single-particle orbitals. The aim of the calculations is partly to test the criteria for good weight functions, partly a preparation of more extended calculations of a similar type.The new name of the institute is: Computer Application Research and Development Center of the Chemical Industries.     

Determination of molecular properties by the method of moments

The method of moments and the method of least squares is applied to electron scattering on a simple model potential. Some general problems connected with treatment of scattering problems by the method of moments and the method of least squares are discussed. The calculations give an example of the random sampling type error estimates discussed in previous papers of the series, and present a possible way of optimizing nonlinear parameters in the framework of the method of moments and the method of least squares.

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Zusammenfassung Die Momentenmethode und die Methode der kleinsten Quadrate wird auf die Elektronenstreuung an einem einfachen Modellpotential angewandt. Einige allgemeine Probleme bei der Anwendung dieser beiden Methoden auf Streuprobleme wurden diskutiert. Die Berechnungen geben ein Beispiel der Fehlerabschätzung vom Stichproben-Typ, der in vorhergehenden Artikeln dieser Serie untersucht wurde; sie stellen eine Möglichkeit der Optimierung nicht-linearer Parameter bei den genannten zwei Methoden dar.

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Résumé La méthode des moments et la méthode des moindres carrés sont appliquées à l'étude de la diffusion électronique sur un potentiel modèle simple. Discussion de certains problèmes généraux liés à l'emploi de ces méthodes à l'étude de la diffusion. Les calculs donnet un exemple de l'estimation d'erreur par échantillonage discutée dans les articles précédents, et présentent une méthode pour optimiser des paramètres non linéaires dans le cadre des méthodes des moments et des moindres carrés.

     

Determination of molecular properties by the method of moments

Basic principles of a possibility of simplifying the unrestricted spin-projected Hartree-Fock equations by means of the method of moments are outlined.     

Computation of electronic transition moments: the length versus the velocity representation

Summary We have compared transition moments (TMs) obtained using the length and velocity representations for transitions from the ground state of H₂ to the lowest two¹ _u and two¹ _u ⁺ Rydberg states, theA ¹–X ¹⁺ transition in BH, and theA ¹ _u –X ¹ _g ⁺ transition in C₂. For H₂, the TMs in the length and velocity representations agree well even in cases where the one-particle basis is incomplete and the TM has not converged. For BH and C₂ the TM in the length representation converges rapidly with improvements in the one-particle basis set and is insensitive to inner-shell correlation. In contrast, in the velocity representation convergence with improvements in the one-particle basis is much slower, especially for C₂, and the TMs are significantly changed by inner-shell correlation. Thus the difference between the TMs in the length and velocity representations would not appear to be a viable diagnostic of TM convergence.     

Determination of dipole moments and stability constants for molecular complexex

Conclusions Dipole moments and stability constants have been determined for various molecular complexes through measurements of the dielectric constants over a single series of solution concentrations, following the proposed method of equivalent concentrations. The results obtained for a series of 11 complexes have been checked against the theory.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 10, pp. 2283–2287, October, 1978.The authors wish to thank A. A. Kryuchkov for his help in carrying out the spectrophotometric measurements.     

On the calculation of transition moments between states described in different orbital basis

The organization of a computer code to compute transition moments between states described in different orbital basis sets (a nonorthogonal transition moment) is described. The code is organized to minimize redundant work and allow efficient threshold checking. Three sample calculations are presented.     

Determination of the glass transition temperature

The definition of the glass transition temperature, T _g, is recalled and its experimental determination by various techniques is reviewed. The diversity of values of T _g obtained by the different methods is discussed, with particular attention being paid to Differential Scanning Calorimetry (DSC) and to dynamic techniques such as Dynamic Mechanical Thermal Analysis (DMTA) and Temperature Modulated DSC (TMDSC). This last technique, TMDSC, in particular, is considered in respect of ways in which the heterogeneity of the glass transformation process can be quantified.     

Determination of molecular properties by the method of moments. III

The wave functions of the water and the ammonia molecules have been determined for many nuclear configurations by both the method of moments and the method of energy variation. The accuracy of the results obtained by the two methods is similar although the method of moments requires considerably less integrational work. Some technical problems connected with the use of the method of moments are discussed.

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Zusammenfassung Die Wellenfunktionen des Wasser- und Ammoniakmoleküls wurden für mehrere molekulare Konfigurationen nach der Momentenmethode und der Methode der Energievariation bestimmt. Die Genauigkeit beider Methoden ist ungefähr gleich, obwohl bei der Momentenmethode weniger Aufwand an Integration benötigt wird. Einige technische Probleme bei der Verwendung der Momentenmethode werden diskutiert.

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Résumé Les fonctions d'onde de l'eau et de l'ammoniac ont été déterminées pour de nombreuses configurations nucléaires par la méthode des moments et la méthode variationnelle. Les précisions atteintes par les deux méthodes sont comparables quoique la méthode des moments nécessite un moindre effort sur le plan des intégrations. Discussion de certains problèmes techniques liés à l'emploi de la méthode des moments.

     

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.