Centrifugal distortion effects in the microwave spectrum of methylene cyanide

The rotational spectrum of methylene cyanide has been measured up to J = 62 and a total of 82 b-type transitions have been obtained. These data have been analyzed with a semirigid rotor Hamiltonian to give accurate rotational and centrifugal distortion constants. The rotational constants are (in MHz) $\text{A}$ = 20882.7537 ≠ 0.017, $\text{B}$ = 2942.3003. ≠ 0.0031, $\text{C}$ = 2616.7225 ≠ 0.0031 The quartic centrifugal distortion constants are (in MHz)

$\text{Δ}{}_{\mathrm{J}}\text{(1.855455 ≠ 0.014) x 10}{}^{\mathrm{?3}}\text{Δ}{}_{\mathrm{JK}}\text{= (?6.79218 ≠ 0.027) x 10}{}^{\mathrm{?2}}$

$\text{Δ}{}_{\mathrm{K}}\text{(8.621628 ≠ 0.013) x 10}{}^{\mathrm{?1}}\text{δ}{}_{\mathrm{J}}\text{= (4.892607 ≠ 0.016) x 10}{}^{\mathrm{?4}}$

$\text{δ}{}_{\mathrm{K}}\text{= (6.7501 ≠ 0.29) x 10}{}^{\mathrm{?3}}$

The uncertainties are twice the standard deviations in the constants obtained from the least squares analysis, and represent approximately 95% confidence limits.     

A study of the K = 3nA1 - A2 centrifugal splitting in the 3ν2 and 4ν2 states of PH3 using a difference-frequency laser system

A frequency tunable infrared source has been constructed by using the (Ar-laser) - (dyelaser) difference frequency method developed by Pine and applied to the observation of the overtone bands of PH₃ 3ν₂ ← 0 and 4ν₂ ← ν₂ in the 3.4 μm region and 4ν₂ ← 0 in the 1.6-μm region. A Stark modulation method was used to increase the sensitivity of detection. For transitions which were well modulated, the minimum detectable absorption coefficient was estimated to be ～3 × 10^?7 cm^?1 using a 3-m cell. Emphasis was placed on the observation of the A₁-A₂ splitting for K = 3n rotational levels. For the 3ν₂ state splittings were observed for K = 3, 6, and 9 because PH₃ is a very nearly spherical top in this state. The magnitude and the J dependence of the observed K = 3n splittings have been analyzed by using a normal symmetric rotor Hamiltonian and a centrifugal distortion term of the form $\text{τ}{}_{\mathrm{xxxz}}\text{[(J}{}_{\mathrm{+}}{}^3\text{+ J}{}_{\mathrm{?}}{}^3\text{)J}{}_{\mathrm{z}}\text{+ J}{}_{\mathrm{z}}\text{(J}{}_{\mathrm{+}}{}^3\text{+ J}{}_{\mathrm{?}}{}^3\text{)]}\text{4}$.     

Microwave spectrum of divinyl ether: Analysis of doublet splittings in b and c type transitions and internal rotation of vinyl groups

Microwave spectrum of cis, trans-divinyl ether has been remeasured and doublet splittings were observed in most of the b and c type lines and also in a few of the a type transitions. The splittings were analyzed in terms of tunneling motion of the two vinyl groups through the planar configuration in which a steep potential barrier exists due to the repulsion between the α and β hydrogen atoms of trans and cis vinyl groups, respectively. An effective Hamiltonian the form $\text{G}{}_{\mathrm{a}}\text{P}\text{?}{}_{\mathrm{v}}\text{J}\text{?}{}_{\mathrm{a}}\text{+(α}{}_{\mathrm{v}}\text{J}\text{?}{}^2{}_{\mathrm{a}}\text{+β}{}_{\mathrm{v}}\text{J}\text{?}{}^4{}_{\mathrm{a}}\text{+γ}{}_{\mathrm{v}}\text{J}\text{?}{}^2{}_{\mathrm{a}}\text{J}\text{?}{}^2\text{)}$ was used for the analysis where terms in parenthesis apply only for the upper levels of the tunneling doublet. The values of G_a = 2.764, α_v = ?0.391, β_v = ?0.0067, and γ_v = +0.00065 (all in MHz) were derived in addition to the tunneling doubling Δ_v as 27.28 MHz and the refined rotational and centrifugal distortion constants. The potential barrier was approximated by a Gaussian function of the form $\text{V = A}\text{exp}\text{[?a}{}^2\text{(?}{}_1{}^2\text{+ ?}{}_2{}^2\text{)]}$ and its height, A, was estimated to be 580 cm^?1 (1.6 kcal/mole) by way of WKB approximation.The definitions of large-amplitude vibrations in non-planar and non-linear molecules were discussed and a criterion to distinguish internal rotation, pseudo-rotation, inversion, and puckering from each other was derived. The motion reported in this paper was classified as internal rotation by this criterion.     

Energy levels of low lying triplet states of N2 from infrared emission studies

A theoretical model used to describe the $\text{B′}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{?}}$ and B³Π_g states of N₂ is presented. Using recently acquired high resolution spectra of the $\text{B′}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{?}}\text{→ B}{}^3\text{Π}{}_{\mathrm{g}}$ (0-0) band, rotational energy levels of the v = 0 vibrational levels of these two states are generated with this model. These levels are in excellent agreement with those obtained using a combination differences technique. The precision of the model generated levels is 0.01 cm^?1. The previously unpublished rotational levels of Dieke and Heath for the $\text{A}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}$, B³Π_g and C³Π_u states are referenced to the $\text{N}{}_2\text{X}{}^1\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{+}}$ (v = 0, J = 0) ground level and tabulated here. Estimates of the precision of their work are made.     

Laser magnetic resonance measurement of rotational transitions in the metastable a1Δg state of oxygen

Laser magnetic resonance (LMR) for five rotational transitions, J = 4 ← 3, 5 ← 4, 7 ← 6, 8 ← 7, 9 ← 8, of the oxygen molecule ¹⁶O¹⁶O in its metastable state, a¹Δ_g, v = 0, are observed using six fir laser lines. Taking the known values of the g factors, their zero-field frequencies are obtained as 340.0085(6), 424.9810(9), 594.870(1), 679.780(1), and 764.658(1) GHz, respectively. They are fit by $\text{(}\text{E}\text{h}\text{) = B}{}_0\text{[J(J + 1) ? 4] + D}{}_0\text{[J(J + 1) ? 4]}{}^2\text{+ (?1)}{}^{\mathrm{J}}\text{(}\text{1}\text{2}\text{)qJ (J + 1)[J(J + 1) ? 2]}$, where B₀ = 42.50457(10) GHz, D₀ = 153.14(110) kHz, and q = 0.050(90) kHz.     

Microwave spectrum of the IO radical

The two lowest rotational transitions of the IO radical in the ${}^2\text{Π}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ ground electronic state have been observed by means of a Stark modulated spectrometer. The effective rotational constants in the ${}^2\text{Π}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ state, the centrifugal distortion constant, the axial component of the magnetic hyperfine interaction, and the nuclear electric quadrupole coupling constant are determined accurately. It was necessary to take into account the second-order effects from the matrix elements off-diagonal in J for the analysis of the hyperfine structure. An equilibrium internuclear distance r_e is calculated to be 1.8677 ± 0.0028 Å from the effective rotational constant $\text{B}{}_0\text{(}{}^2\text{Π}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{)}$, combined with α₃ from the A²Π → X²Π transition.     

The microwave spectrum of the SF radical

The rotational spectrum of the SF radical in the ${}^2\text{Π}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ state was observed by using a source-modulation microwave spectrometer with a 1-m-long discharge cell. The SF radical was generated directly in the cell by a dc discharge in an $\text{OCS}\text{CF}{}_4$ mixture. A previous measurement of the microwave spectrum in the ${}^2\text{Π}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ state was also extended to higher-J transitions. The least-squares analysis of all the observed spectral lines gave the B₀ rotational constant and the D₀ centrifugal distortion constant to be 16 576.9140(46) and 0.02924(10) MHz, respectively, where the values in parentheses denote 2.5 times the standard deviations. The Λ-doubling constant p_v was found to be extremely small, 3.409(44) MHz, and it was presumed that contributions of ²Σ⁺ and ²Σ^? states to the Λ doubling cancel each other. All the four fluorine hyperfine coupling constants were also determined, from which the spin density on the F atom was calculated to be 0.13.     

Revised molecular constants,RKR potential,and long-range analysis for the B3Π(0u+) state of Cl2, and rotationally dependent Franck-Condon factors for Cl2 (BX1Σg+)

Literature data for the line frequencies of the B³Π(0_u⁺) ← X¹Σ_g⁺ transition of Cl₂ are fitted directly by least squares to obtain new molecular constants. The constants from individual bands are merged to obtain single-valued estimates of the rotational constants for each vibrational level of the B state. The results are combined with recent data from the B → X system in emission to obtain new RKR turning points for the B and X states, and Franck-Condon factors for the B-X system. The new constants are also used to provide revised long-range parameters for Cl₂(B) which differ from those of earlier work. In particular, the coefficient C₅ of the leading term in the inverse-power long-range potential is now found to be $\text{C}{}_5\text{= 1.16(2) × 10}{}^5\text{A}\text{?}{}^5\text{cm}{}^{\mathrm{?1}}$. Theoretical results for the variation of centrifugal distortion parameters for levels near dissociation are tested for D_v and H_v, and an extrapolation based on this behavior is used to facilitate determination of reliable B_v and G(v) values for the highest observed B-state levels.     

ΔK = 2 transitions in H2CO and D2CO

Weak transitions of the type ΔJ = ± 1, $\text{Δ}\text{K}{}_{\mathrm{a}}\text{= ? 2}$, ΔK_c = ± 3 have been observed in H₂CO and D₂CO by the millimeterwave double resonance method and also by direct absorption with a Stark modulated spectrometer. The addition of these new transitions in a least-squares analysis, in which all previously known microwave and millimeterwave data are also included, results in an improved set of rotational and distortion constants.     

Low temperature specific heats of nearly one-dimensional antiferromagnet: CuCl2·2NC5H5

Transition temperature to LRO state was found at T_N=1.14K for nearly one-dimensional antiferromagnet CuCl₂ · 2NC₅H₅. Intra- and inter-chain exchange constants J and J′ were estimated, $\text{kT}{}_{\mathrm{<mtext>N</mtext>}}\text{J}\text{=0.082}$ and $\text{J′}\text{J}\text{=3×10}{}^{\mathrm{?3}}$, respectively. Comparison with those of TMMC implies highly one-dimensional character.     

The irreducible Raman scattering tensor operator for the 32 crystallographic point groups and its application to the resonance and electronic Raman effect

The irreducible components of the Raman scattering tensor operator $\text{α}\text{?}{}_{\mathrm{\gamma }}{}^{\mathrm{<mtext>\Gamma </mtext>}}\text{(}\text{Γ}{}_{\mathrm{ks}}\text{Γ}{}_{\mathrm{k\prime s\prime }}\text{)}$ under the symmetry of a general point group are calculated. The unitary transformations U(Γ_γΓ_ksΓ_k′s′, ρσ) from the Cartesian $\text{α}\text{?}{}_{\mathrm{\rho \sigma }}$ and spherical $\text{α}\text{?}{}_{\mathrm{Q}}{}^{\mathrm{K}}$ components, respectively, to the irreducible components $\text{α}\text{?}{}_{\mathrm{\gamma }}{}^{\mathrm{<mtext>\Gamma </mtext>}}\text{(}\text{Γ}{}_{\mathrm{ks}}\text{Γ}{}_{\mathrm{k\prime s\prime }}\text{)}$ for the 32 crystallographic point groups are collected in tables. As an example the unitary transformation U(Γ_γΓ_ksΓ_k′s′, ρσ) is used to discuss the behavior of the scattering tensor in a resonance Raman experiment. With the help of the general formalism the scattering tensor for electronic Raman transitions of transition metal ions is calculated. As an example the scattering tensors of electronic Raman transitions within the ⁵T₂ state of the high-spin trigonal distorted octahedral Fe²⁺ are calculated and the refinement of the selection rules is discussed.     

Decomposition of the photoabsorption continuum underlying the Schumann-Runge bands of 16O2—II. Role of the 1 3Πg state and collision-induced absorption

Measurements are presented of molecular oxygen photoabsorption cross-sections and pressure coefficients taken at selected minima between rotational lines of the Schumann-Runge band system. Both room-temperature and liquid-nitrogen-temperature results are presented from 1760–1980 Å, and corrections are applied for the effect of the wings of the rotational lines. Absorption into the B³∑^?_u and A³∑⁺_u⁺ and is found to be insufficient to account for the total observed cross-section, and it is proposed that transitions to the 1³Π_g valence state account for the remainder. The pressure dependence of the cross-sections is consistent with collision-induced enhancement of the intensities of the forbidden transitions X³∑^?_g → A³∑⁺_g and $\text{X}{}^3\text{∑}{}^{\mathrm{?}}{}_{\mathrm{g}}\text{→ 1}{}^3\text{Π}{}_{\mathrm{g}}$, while the temperature dependence of the pressure coefficients is not consistent with absorption due to stable (O₂)₂ dimers.     

Rotational analysis of a red A′ 2Σ+-X 2Πi system of CuO

High dispersion rotational analysis of a red CuO band system has led to the identification of an $\text{A′}{}^2\text{Σ}{}^{\mathrm{+}}\text{-X}{}^2\text{Π}{}_{\mathrm{i}}$ transition. The anomalous appearance of the branches is due to a very large spin splitting of the ²Σ upper state. The influence of centrifugal distortion effects on this spin splitting (γ_D and γ_H parameters) is essential for explaining the band structure. A reassignment of electronic symmetries of all the ²Σ states of CuO is proposed.     

Two-photon excitation of the C̃1B2 state of sulfur dioxide

The two-photon excitation (TPE) spectrum of sulfur dioxide is reported in the region of the $\text{C}\text{?}{}^1\text{B}{}_2\text{←}\text{X}\text{?}{}^1\text{A}{}_1\text{[2b}{}_1\text{(π}{}^1\text{) ← 1a}{}_2\text{(π)]}$ transition. The spectrum shows considerable rovibronic structure; the band contours are identified as arising from ΔK_?1 = ± 1 transitions and rotational features are assigned by comparison with synthetic spectra generated from known rotational constants. The vibronic structure observed in TPE is quite similar to that observed in the one-photon spectrum: no zero-rank tensor transitions to levels with odd v₃ are identified, though they are allowed in the presence of vibronic coupling. The vibronic intensity distribution in the TPE spectrum below the dissociation limit is similar to that in one-photon absorption. However, near the dissociation threshold (5.63–5.67 eV), marked intensity redistribution occurs, from which it is concluded that the lowest energy photo-dissociation process proceeds through asymmetric stretching of the SO bonds.     

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).     

Resolution of the discrepancies concerning the optical and microwave values for B0 and D0 of the X 3Σg− state of O2

The discrepancies concerning the optical and microwave values of B₀ and D₀ for the X${}^3\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{?}}$ state of O₂ have been removed by a nonlinear least-squares fit to all of the lines of the O₂, $\text{b}{}^1\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{+}}\text{-X}{}^3\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{?}}$ Red Atmospheric bands recorded by Babcock and Herzberg (Astrophys. J., 108, 167, 1948). The resulting values for B₀″ and D₀″ are in excellent agreement with the Raman and microwave values. Improved values are determined for B₁″, D₁″, γ₁″ (spin-rotation), and ?₁″ (spin-spin). Both γ_v″ and ?_v″ increase in magnitude from v″ = 0 to v″ = 1. Improved Dunham Y_i0 and Y_i1 expansion coefficients are determined for the $\text{b}{}^1\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{+}}$ state, from which the Rydberg-Klein-Rees potential is constructed.     

Reexamination of the I2 spectrum near the B(3Π0u+) state dissociation limit

The disagreement of Danyluk and King's (Chem. Phys.25, 343 (1977)) rotational constants for levels lying near the dissociation limit of B-state I₂ with the mechanical behavior predicted by near-dissociation theory is investigated. The discrepancies are shown to be much too large to be explained by either the neglect of centrifugal distortion effects in the original analysis or by rotational or spin-rotation coupling to a nearby repulsive 1_u state. These differences are therefore attributed to experimental error, a conclusion which is confirmed by more recent experimental results. A reanalysis of the best available data for levels near the dissociation limit of B-state I₂ then yields improved values for the B-state dissociation limit $\text{D}$ = 20 043.16 (±0.02) cm^?1 of the vibrational index at dissociation v_$\text{D}$ = 87.32 (±0.04) and of the long-range potential constant $\text{C}{}_5\text{= 2.88 (±0.03) × 10}{}^5\text{cm}{}^{\mathrm{?1}}\text{A}\text{?}{}^5$. This in turn implies a slightly improved ground-state dissociation energy of $\text{D}$₀ = 12 440.18 (±0.02) cm^?1.     

Centrifugal distortion in weakly bound linear triatomic molecules

A simple formula is derived for the centrifugal distortion constant of a linear triatomic molecule in which one of the chemical bonds is much weaker than the other. The derivation is in complete analogy with the standard semiclassical diatomic derivation and results in the equation $\text{D}{}_{\mathrm{J}}\text{= [}\text{4B}{}_{\mathrm{e}}{}^3\text{(hv)}{}^2\text{][1 ? (}\text{B}{}_{\mathrm{e}}\text{b}{}_{\mathrm{e}}\text{)]}$, where B_e, ν, and b_e are, respectively, the triatomic rotational constant, the low stretching frequency, and the rotational constant of the strongly bound diatomic part of the triatomic molecule.     

l-type doubling transitions in Δ states of OCS

Molecular beam electric resonance spectroscopy has been used to measure the l-type doubling transitions in carbonyl sulfide. Transitions in J = 4 to J = 20 have been observed for the (02²0) vibrational state and for J = 1 and J = 2 for the (03¹0) state. The data has been analyzed to give the v = 2 energy separation $\text{E}{}_{\mathrm{<mtext>\Delta </mtext>}}{}^0\text{- E}{}_{\mathrm{<mtext>\Sigma </mtext>}}{}^0\text{= ?5.7861(2) + 8.36(1) × 10}{}^{\mathrm{?5}}\text{J(J + 1)}\text{cm}{}^{\mathrm{?1}}$, and the vibrational dependence of q to be 86.52(9)(v₂ + 1) KHz. The dipole moment of the (02²0) vibrational state is 0.6936(3) D.     

Some effects of spin-orbit interaction on rotational levels and rotational line intensities in vibrationally unexcited 2A, 2E, and 2F electronic states of open-shell XY4 molecules

Rotational energy levels in vibronic ground states of ²A, ²E, and ²F electronic states of open-shell XY₄ molecules, as well as rotational line intensities for allowed transitions between such states, are discussed, including the effects of spin-orbit interaction and tetrahedral splittings. Jahn-Teller effects are assumed to be small, and are only taken into account implicitly, through their contributions to various parameters in the effective Hamiltonian. Qualitative information is obtained by considering several limiting-case coupling schemes among the electron spin angular momentum S, the electron orbital angular momentum L, and the pure rotational angular momentum R. These limiting cases are similar in spirit to Hund's coupling cases in diatomic molecules, but differ sufficiently from the latter to make detailed correspondences unhelpful. Quantitative information on rotational energy levels and line intensities is obtained numerically by diagonalizing a Hamiltonian matrix set up in a basis set characterized by uncoupled moleculefixed projections of S, L, and the total angular momentum J, and symmetrized so that all basis set functions belong to a definite species in the subgroup D_2d of the true point group T_d. Hamiltonian matrix elements are determined by ladder operator techniques. Three sample calculated spectra, corresponding to $\text{p(}{}^2\text{F}{}_2\text{)-s(}{}^2\text{A}{}_1\text{)}$, $\text{d(}{}^2\text{E)-p(}{}^2\text{F}{}_2\text{)}$, and $\text{d(}{}^2\text{F}{}_2\text{)-p(}{}^2\text{F}{}_2\text{)}$ are presented. As one might expect, when the spin-orbit constant A is set equal to zero, then both qualitative and quantitative aspects of the rotational-electronic problem in open-shell XY₄ molecules can be mapped easily onto discussions of the rotation-vibration problem from the CH₄ literature.