Dipole moment function and vibration-rotation matrix elements of HCl35 and DCl35

The infrared intensity measurements and molecular beam electric resonance dipole moment measurements for HCl and DCl have been reviewed. A method not previously exploited is used to determine infrared matrix elements from the electric resonance dipole moment measurements. A ‘best’ set of matrix element values was selected for HCl and from these the M_i-coefficients of a polynomial dipole moment approximation were determined; M₀ = 1.0935±0.0007 D, $\text{M}{}_1\text{= 0.947±0.023 D/}\text{A}\text{?}$, $\text{M}{}_2\text{= 0.015±0.041 D/}\text{A}\text{?}{}^2$, $\text{M}{}_3\text{= -0.814± 0.116 D/}\text{A}\text{?}{}^3$. Calculations using this dipole moment function for both HCl and DCl are shown to give good agreement with available band strength and vibration-rotation interaction factor measurements. RKR potentials are also calculated for both molecules.     

Dipole moment function of carbonyl sulphide

Measurements are reported for the infra-red absorption intensity of some overtone and combination bands in carbonyl sulphide. These are interpreted with the aid of an anharmonic force field and some microwave Stark effect measurements on excited vibrational states to give the values for the dipole in the equilibrium configuration, p _e, and the linear and quadratic derivatives for the axial dipole component shown in table 4. These signs are absolute, being tied to the microwave Zeeman effect on isotopically substituted molecules [4].     

Direct fit of experimental ro-vibrational intensities to the dipole moment function: Application to HCl

A dipole moment function (DMF) for hydrogen chloride (HCl) has been obtained using a direct fit approach that fits the best available and appropriately weighted experimental data for individual ro-vibrational transitions. Combining wavefunctions derived from the Rydberg-Klein-Rees (RKR) numerical method and a semi-empirical DMF, line intensities were calculated numerically for bands with Δv=0, 1, 2, 3, 4, 5, 6, 7 up to v′=7. The results have demonstrated the effectiveness of inclusion of rotational dipole moment matrix elements and appropriate weighting of the experimental data in the DMF fitting. The new method is shown to be superior to the common method of fitting only the rotationless dipole moment elements, while at the same time being simple to implement.     

Dipole moment functions of carbon dioxide and nitrous oxide

The vibrational wavefunctions obtained from the direct numerical diagonalization of the vibrational Hamiltonian matrix are used to compute the matrix elements of transition dipole moments for carbon dioxide and nitrous oxide. The computed matrix elements are found very close to those obtained previously by the contact transformation method. The least-squares fit of the dipole moment derivatives up to the second order has been attempted. It is shown that the values as well as the signs of the second derivatives can be determined if the mechanical anharmonicity contributes considerably to the corresponding combination and/or difference bands. The bands selected for N₂O include the fundamentals, first overtones, binary combination, and difference bands as well as the bands coupled with the above by Fermi resonances. The converged set of the dipole moment derivatives of N₂O gives the computed matrix elements very close to the observed. This also demonstrates the wider applicability of the direct diagonalization method.     

Dipole moment of the excited state in indole and tryptophan

The dipole moments of the excited states are derived from the temperature coefficients of the absorption and fluorescence spectra in alcoholic solution.     

Dipole moment studies of the structure of 2,6-diaryl-4-piperidones

Several 2,6-diaryl-4-piperidones were prepared. The configuration and conformation of these piperidones are discussed from the measured values of dipole moments. The influence of substitution on the molecular interactions of these compounds are studied. The results are interpreted in relation to their structure conformation and the charge distribution in groups like N–H and CO. A correlation between the dipole moment values of these compounds with the IR spectral shift and intensities is also attempted.     

Millimeter-wave spectrum of 3-butynenitrile: Dipole moment and centrifugal distortion constants

The molecular rotational spectrum of 3-butynenitrile (3BN, propargyl cyanide), HCCCH₂CN, has been investigated in the vibrational ground state. A total of 222 transitions up to J = 69 have been measured between 8 and 300 GHz. The Hamiltonian used for the spectral analysis was required to include all centrifugal terms of fourth and sixth orders and one term of eighth order in the angular momentum components in order to reproduce the transition frequencies within the experimental error. Significant values for the respective distortion coefficients could be determined. The molecular dipole moment components were calculated from measured Stark effect shifts as |μ_a| = (3.23 ± 0.05) D, |μ_b| = (2.34 ± 0.02) D; μ_tot = (3.99 ± 0.05) D.     

On the theory of pyro- and ferroelectrics: Dipole moment density and polarization

The physical origin of the ambiguity related to the dependence of the polarization on the choice of the unit cell in a crystal is established in the framework of classical electrodynamics. It is shown that the electric polarization of a crystal is determined not only by the charge distribution in the unit cell (dipole moment density) but also by the microscopic mechanism of symmetry breaking in the polar phase. An approach to the calculation of the polarization invariant with respect to the choice of the unit cell is suggested. It is demonstrated that the dependence of the polarization on the mechanism of formation of the polar phase exists in the “modern topological theory” of polarization too.     

The Green's function moment method

This paper develops a modified moment method for the numerical solution of two “Pocklington Type” integral equations. The first equation arises from the problem of scalar diffraction through a slot; the second from scattering by a straight, thin-wire. Numerical results and comparison with a more conventional method are given.     

Dipole moment of the HO2 radical from its microwave spectrum

Stark effects are measured for the 1₀₁ ← 0₀₀, 7₁₇ ← 8₀₈, and 9₀₉ → 8₁₈ transitions of the HO₂ free radical. The unresolved Stark patterns of the b-type transitions are analyzed by the use of computer simulation. Second-order perturbation theory, including the effect of spin-doublings in the denominators, is used for the calculation of the Stark effect coefficients. The dipole moment determined is μ_a = 1.412 ± 0.033 D, μ_b = 1.541 ± 0.016 D, and μ_total = 2.090 ± 0.034 D.     

Magnetic properties and molecular quadrupole moment of HF and HCl by molecular-beam electric-resonance spectroscopy

The radio-frequency spectra of HF and H³⁵Cl in an external electric and magnetic field are measured using a high-resolution molecular-beam electric-resonance spectrometer. The measurements are in the lowest vibrational state (v = 0) and the first rotational state (J = 1). The spectra are analyzed using a standard Hamiltonian. The magnetic properties of the molecules are derived using methods introduced by Ramsey. The results, corrected for the effects of molecular vibrations, are:

     

14.

Dipole moment functions for electronic transitions from ion-pair states of the second tier of molecular iodine     

M. E. Akopyan  I. Yu. Novikova  S. A. Poretsky  A. M. Pravilov  A. G. Smolin  T. V. Fedorova 《Optics and Spectroscopy》2005,99(1):36-42

The emission spectra caused by the transitions from the ion-pair states and f0 _g ⁺ and G1_g of the I₂ molecule are obtained by excitation of individual rovibronic levels of the molecule by the method of optical-optical double resonance. The emission spectra from the state F0 _u ⁺ populated due to collisions I₂(f) + I₂(X) are also measured. By modeling the experimental emission spectra, the dipole moment functions for the electronic transitions f _g ⁺ -B0 _u ⁺ , A0 _u ⁺ , and B″0 _u ⁺ ; G1_g-A0 _u ⁺ and B″0 _u ⁺ ; and F0 _u ⁺ -X0 _g ⁺ and a′0 _g ⁺ of the iodine molecule are reconstructed.     

15.

Microwave spectra of deuterated ethylenes: Dipole moment and r_z structure     

Eizi Hirota  Yasuki Endo  Shuji Saito  Kazuhiko Yoshida  Ichiro Yamaguchi  Katsunosuke Machida 《Journal of Molecular Spectroscopy》1981,89(1):223-231

The pure rotational spectra of three deuterated ethylenes, CH₂CD₂, CH₂CHD, and cis-CHDCHD, were observed by microwave spectroscopy, and the rotational and centrifugal distortion constants were determined precisely. The dipole moment of CH₂CD₂ was calculated from the Stark effects to be 0.0091 ± 0.0004 D. From the observed rotational constants the average structure was calculated to be $\text{r}{}_{\mathrm{z}}\text{(CC)}\text{= 1.3391 ± 0.0013}\text{A}\text{?}$, $\text{r}{}_{\mathrm{z}}\text{(CH)}\text{= 1.0869 ± 0.0013}\text{A}\text{?}$, θ_z(CCH) = 121.28 ± 0.10°, and $\text{r}{}_{\mathrm{z}}\text{(CH)}\text{- r}{}_{\mathrm{z}}\text{(CD)}\text{= 0.00137 ± 0.00037}\text{A}\text{?}$, where the errors include one standard deviation in the fitting and errors due to an uncertainty (±0.03°) in θ_z(CCH) - θ_z(CCD).     

16.

Dipole moment effects in e+e--->Z-->bb-barg with polarized and unpolarized beams     

Atwood D  Bar-Shalom S  Soni A 《Physical review D: Particles and fields》1995,51(3):1034-1039

     

17.

Dipole moment of a small water cluster. The effect of size,temperature, and electric field     

D. Yu. Dubov  A. A. Vostrikov 《JETP Letters》2010,92(1):28-32

A molecular dynamics simulation of neutral clusters (H₂O) _{n ≤ 21} has been performed in the framework of the flexible polarized model. The formation and evolution of the dipole moment of the cluster have been investigated with a change in the size and temperature of the cluster and an external electric field. It has been shown that at low electric fields corresponding to the experiments on the deflection of clusters in the transverse inhomogeneous electrostatic field (Moro et al., 2006), the induced polarization of the cluster is determined by the orientational polarizability of the “rigid” cluster, rather than by the intracluster reorientation of the molecules. The calculated dependence of the effective polarizability of the cluster in the low field on n qualitatively reproduces the experimental results, but the calculated polarizability is numerically much higher than the experimental value by, e.g., a factor of 4 for n ≈ 20.     

18.

Isotopically invariant dunham parameters and the potential function of the HCl molecule     

T. I. Velichko  S. N. Mikhailenko 《Optics and Spectroscopy》2002,92(6):871-876

The isotopically invariant Dunham parameters U _mj , Δ _mj ^H and Δ _mj ^Cl were determined by simultaneously fitting the line centers of vibration-rotation transitions of six isotopic HCl forms in the ground electronic state. Fitting included relations between U _mj values. The parameters of the isotopically invariant potential of HCl were determined using independent U _m0 and U _m1 values. The contributions to the vibrational terms of H³⁵Cl caused by violation of the Born-Oppenheimer approximation were calculated.     

19.

Dipole moment and far infra-red absorption of quinuclidine (1-aza-bicyclo-[2-2-2]-octane)     

B. Lassier  C. Brot  N. Dat-Xuong 《Molecular physics》2013,111(6):1697-1700

Incoherent quasi-elastic neutron-scattering spectra have been measured on powder samples of D-BPBAC in its smectic E, B and A phases using the high-resolution backscattering technique. The data have been analysed in terms of translational diffusion and a localized rotational motion. It has been found that the apparent translational diffusion constant has a temperature dependent value of ～1 × 10^-6 cm² s^-1 in the smectic A phase but is smaller by at least an order of magnitude in the smectic B and E phases. Comparison of the widths of the rotational components of the spectra with other measurements suggests that simple rotational models are not adequate to explain the experimental data.     

20.

Dipole soliton-vortices     

Kartashov YV  Ferrando A  García-March MA 《Optics letters》2007,32(15):2155-2157

On universal symmetry grounds, we analyze the existence of a new type of discrete-symmetry vortex solitons that can be considered as coherent states of dipole solitons carrying a nonzero topological charge. Remarkably, they can be also interpreted as excited angular Bloch states. The stability of new soliton states is elucidated numerically.     

	HF	H35Cl
$\text{g}{}_{\mathrm{J}}$	0.74104(15)	0.45935(9)
$\text{χ}{}_{\mathrm{|}}\text{- χ}{}_{\mathrm{\delta }}\text{(}\text{kHz/(kG)}{}^2\text{)}$	0.132(6)	?0.048(18)
$\text{(χ}{}_{\mathrm{|}}\text{- χ}{}_{\mathrm{\delta }}\text{)}{}^{\mathrm{d}}\text{(10}{}^{\mathrm{?6}}\text{erg/G}{}^2\text{·mole}\text{)}$	1.342(25)	3.49(10)
$\text{(σ}{}_{\mathrm{|}}\text{- σ}{}_{\mathrm{\delta }}\text{)}{}_{\mathrm{H}}\text{(}\text{ppm}\text{)}$	24(9)	21(5)
$\text{(σ}{}_{\mathrm{|}}\text{- σ}{}_{\mathrm{\delta }}\text{)}{}_{\mathrm{H}}{}^{\mathrm{d}}\text{(}\text{ppm}\text{)}$	?96(9)	?148(7)
$\text{(σ}{}_{\mathrm{|}}\text{- σ}{}_{\mathrm{\delta }}\text{)}{}_{\mathrm{<mtext>hal</mtext>}}\text{(}\text{ppm}\text{)}$	108(9)	300(24)
$\text{(σ}{}_{\mathrm{|}}\text{- σ}{}_{\mathrm{\delta }}\text{)}{}_{\mathrm{<mtext>hal</mtext>}}{}^{\mathrm{d}}\text{(}\text{ppm}\text{)}$	?1(9)	?4(25)
$\text{θ (10}{}^{\mathrm{?26}}\text{esu cm}{}^2\text{)}$	2.36(3)	3.74(12)

Dipole moment functions for electronic transitions from ion-pair states of the second tier of molecular iodine

The emission spectra caused by the transitions from the ion-pair states and f0 _g ⁺ and G1_g of the I₂ molecule are obtained by excitation of individual rovibronic levels of the molecule by the method of optical-optical double resonance. The emission spectra from the state F0 _u ⁺ populated due to collisions I₂(f) + I₂(X) are also measured. By modeling the experimental emission spectra, the dipole moment functions for the electronic transitions f _g ⁺ -B0 _u ⁺ , A0 _u ⁺ , and B″0 _u ⁺ ; G1_g-A0 _u ⁺ and B″0 _u ⁺ ; and F0 _u ⁺ -X0 _g ⁺ and a′0 _g ⁺ of the iodine molecule are reconstructed.     

Microwave spectra of deuterated ethylenes: Dipole moment and rz structure

The pure rotational spectra of three deuterated ethylenes, CH₂CD₂, CH₂CHD, and cis-CHDCHD, were observed by microwave spectroscopy, and the rotational and centrifugal distortion constants were determined precisely. The dipole moment of CH₂CD₂ was calculated from the Stark effects to be 0.0091 ± 0.0004 D. From the observed rotational constants the average structure was calculated to be $\text{r}{}_{\mathrm{z}}\text{(CC)}\text{= 1.3391 ± 0.0013}\text{A}\text{?}$, $\text{r}{}_{\mathrm{z}}\text{(CH)}\text{= 1.0869 ± 0.0013}\text{A}\text{?}$, θ_z(CCH) = 121.28 ± 0.10°, and $\text{r}{}_{\mathrm{z}}\text{(CH)}\text{- r}{}_{\mathrm{z}}\text{(CD)}\text{= 0.00137 ± 0.00037}\text{A}\text{?}$, where the errors include one standard deviation in the fitting and errors due to an uncertainty (±0.03°) in θ_z(CCH) - θ_z(CCD).     

Dipole moment of a small water cluster. The effect of size,temperature, and electric field

A molecular dynamics simulation of neutral clusters (H₂O) _{n ≤ 21} has been performed in the framework of the flexible polarized model. The formation and evolution of the dipole moment of the cluster have been investigated with a change in the size and temperature of the cluster and an external electric field. It has been shown that at low electric fields corresponding to the experiments on the deflection of clusters in the transverse inhomogeneous electrostatic field (Moro et al., 2006), the induced polarization of the cluster is determined by the orientational polarizability of the “rigid” cluster, rather than by the intracluster reorientation of the molecules. The calculated dependence of the effective polarizability of the cluster in the low field on n qualitatively reproduces the experimental results, but the calculated polarizability is numerically much higher than the experimental value by, e.g., a factor of 4 for n ≈ 20.     

Isotopically invariant dunham parameters and the potential function of the HCl molecule

The isotopically invariant Dunham parameters U _mj , Δ _mj ^H and Δ _mj ^Cl were determined by simultaneously fitting the line centers of vibration-rotation transitions of six isotopic HCl forms in the ground electronic state. Fitting included relations between U _mj values. The parameters of the isotopically invariant potential of HCl were determined using independent U _m0 and U _m1 values. The contributions to the vibrational terms of H³⁵Cl caused by violation of the Born-Oppenheimer approximation were calculated.     

Dipole moment and far infra-red absorption of quinuclidine (1-aza-bicyclo-[2-2-2]-octane)

Incoherent quasi-elastic neutron-scattering spectra have been measured on powder samples of D-BPBAC in its smectic E, B and A phases using the high-resolution backscattering technique. The data have been analysed in terms of translational diffusion and a localized rotational motion. It has been found that the apparent translational diffusion constant has a temperature dependent value of ～1 × 10^-6 cm² s^-1 in the smectic A phase but is smaller by at least an order of magnitude in the smectic B and E phases. Comparison of the widths of the rotational components of the spectra with other measurements suggests that simple rotational models are not adequate to explain the experimental data.     

Dipole soliton-vortices

On universal symmetry grounds, we analyze the existence of a new type of discrete-symmetry vortex solitons that can be considered as coherent states of dipole solitons carrying a nonzero topological charge. Remarkably, they can be also interpreted as excited angular Bloch states. The stability of new soliton states is elucidated numerically.