Potential-energy surface for the electronic ground state of NH3 up to 20,000 cm-1 above equilibrium

Ab initio coupled cluster calculations with single and double substitutions and a perturbative treatment of connected triple excitations [CCSD(T)] with the augmented correlation-consistent polarized valence triple-zeta aug-cc-pVTZ basis at 51 816 geometries provide a six-dimensional potential-energy surface for the electronic ground state of NH3. At 3814 selected geometries, CBS+ energies are obtained by extrapolating the CCSD(T) results for the aug-cc-pVXZ(X=T,Q,5) basis sets to the complete basis set (CBS) limit and adding corrections for core-valence correlation and relativistic effects. CBS** ab initio energies are generated at 51,816 geometries by an empirical extrapolation of the CCSD(T)/aug-cc-pVTZ results to the CBS+ limit. They cover the energy region up to 20,000 cm-1 above equilibrium. Parametrized analytical functions are fitted through the ab initio points. For these analytical surfaces, vibrational term values and transition moments are calculated by means of a variational program employing a kinetic-energy operator expressed in the Eckart-Sayvetz frame. Comparisons against experiment are used to assess the quality of the generated potential-energy surfaces. A "spectroscopic" potential-energy surface of NH3 is determined by a slight empirical adjustment of the ab initio potential to the experimental vibrational term values. Variational calculations on this refined surface yield rms deviations from experiment of 0.8 cm-1 for 24 inversion splittings and 0.4 (3.0) cm-1 for 34 (51) vibrational term values up to 6100 (10,300) cm-1.     

Ab initio potential energy and dipole moment surfaces of (H2O)2

A full-dimensional ab initio potential energy surface (PES) and dipole moment surface (DMS) are reported for the water dimer, (H2O)2. The CCSD(T)-PES is a very precise fit to 19,805 ab initio energies obtained with the coupled-cluster (CCSD(T)) method, using an aug-cc-pVTZ basis. The standard counterpoise correction was applied to approximately eliminate basis set superposition errors. The fit is based on an approach that incorporates the permutational symmetry of identical atoms [Huang, X.; Braams, B.; Bowman, J. M. J. Chem.Phys. 2005, 122, 044308]. The DMS is a fit to the dipole moment obtained with M?ller-Plesset (MP2) theory, using an aug-cc-pVTZ basis. The PES has an RMS fitting error of 31 cm(-1) for energies below 20,000 cm(-1), relative to the global minimum. This surface can describe various internal floppy motions, including various monomer inversions, and isomerization pathways. Ten characteristic stationary points have been located on the surface, four of which are transition structures and the rest are higher order saddle points. Their geometrical and vibrational properties are presented and compared with available previous theoretical work. The CCSD(T)-PES and MP2-DMS dissociate correctly (and symmetrically) to two H2O monomers, with D(e) = 1665.7 cm(-1) (19.93 kJ/mol). Accurate quantum calculations of the zero-point energy of the dimer (using diffusion Monte Carlo) and the monomers (using a vibrational configuration interaction approach) are reported, and these together with D(e) give a value of D0 of 1042 cm(-1) (12.44 kJ/mol). A best estimated value is 1130 cm(-1) (13.5 kJ/mol).     

Highly accurate potential-energy and dipole moment surfaces for vibrational state calculations of methane

Full-dimensional ab initio potential-energy surface (PES) and dipole moment surface are constructed for a methane molecule at the CCSD(T)/cc-pVTZ and MP2/cc-pVTZ levels of theory, respectively, by the modified Shepard interpolation method based on the fourth-order Taylor expansion [MSI(4th)]. The reference points for the interpolation have been set in the coupling region of CH symmetric and antisymmetric stretching modes so as to reproduce the vibrational energy levels related to CH stretching vibrations. The vibrational configuration-interaction calculations have been performed to obtain the energy levels and the absorption intensities up to 9000 cm(-1) with the use of MSI(4th)-PES. The calculated fundamental frequencies and low-lying vibrational energy levels show that MSI(4th) is superior to the widely employed quartic force field, giving a better agreement with the experimental values. The absorption bands of overtones as well as combination bands, which are caused by purely anharmonic effects, have been obtained up to 9000 cm(-1). Strongly coupled states with visible intensity have been found in the 6500-9000 cm(-1) region where the experimental data are still lacking.     

Accurate ab initio structure, dissociation energy, and vibrational spectroscopy of the F(-)-CH4 anion complex

Accurate equilibrium structure, dissociation energy, global potential energy surface (PES), dipole moment surface (DMS), and the infrared vibrational spectrum in the 0-3000 cm(-1) range of the F(-)-CH4 anion complex have been obtained. The equilibrium electronic structure calculations employed second-order M?ller-Plesset perturbation theory (MP2) and coupled-cluster (CC) method up to single, double, triple, and perturbative quadruple excitations using the aug-cc-p(C)VXZ [X = 2(D), 3(T), 4(Q), and 5] correlation-consistent basis sets. The best equilibrium geometry has been obtained at the all-electron CCSD(T)/aug-cc-pCVQZ level of theory. The dissociation energy has been determined based on basis set extrapolation techniques within the focal-point analysis (FPA) approach considering (a) electron correlation beyond the all-electron CCSD(T) level, (b) relativistic effects, (c) diagonal Born-Oppenheimer corrections (DBOC), and (d) variationally computed zero-point vibrational energies. The final D(e) and D0 values are 2398 +/- 12 and 2280 +/- 20 cm(-1), respectively. The global PES and DMS have been computed at the frozen-core CCSD(T)/aug-cc-pVTZ and MP2/aug-cc-pVTZ levels of theory, respectively. Variational vibrational calculations have been performed for CH4 and F(-)-CH4 employing the vibrational configuration interaction (VCI) method as implemented in Multimode.     

Xe-N2O复合物的分子间势能面和振转光谱的理论研究

采用CCSD(T)方法研究了范德华分子体系Xe—N2O复合物的势能面和振转光谱性质,研究表明,该势能面有两个极小点,分别对应T构型和线性Xe—ONN构型,采用离散变量表象和Lanczos算法计算了体系的振转能级,计算结果表明,CCSD(T)势能面支持97个振动束缚态,并对能级进行了指认,计算得到的Xe—N2O转动跃迁频率与实验值吻合得很好。     

CCSD(T) study of dimethyl-ether infrared and Raman spectra

CCSD(T) state-of-the-art ab initio calculations are used to determine a vibrationally corrected three-dimensional potential energy surface of dimethyl-ether depending on the two methyl torsions and the COC bending angle. The surface is employed to obtain variationally the lowest vibrational energies that can be populated at very low temperatures. The interactions between the bending and the torsional coordinates are responsible for the displacements of the torsional overtone bands and several combination bands. The effect of these interactions on the potential parameters is analyzed. Second order perturbation theory is used as a help for the understanding of many spectroscopic parameters and to obtain anharmonic fundamentals for the 3N - 9 neglected modes as well as the rotational parameters. To evaluate the surface accuracy and to verify previous assignments, the calculated vibrational levels are compared with experimental data corresponding to the most abundant isotopologue. The surface has been empirically adjusted for understanding the origin of small divergences between ab initio calculations and experimental data. Our calculations confirm previous assignments and show the importance of including the COC bending degree of freedom for computing with a higher accuracy the excited torsional term values through the Fermi interaction. Besides, this work shows a possible lack of accuracy of some available experimental transition frequencies and proposes a new assignment for a transition line. As an example, the transition 100 → 120 has been computed at 445.93 cm(-1), which is consistent with the observed transition frequency in the Raman spectrum at 450.5 cm(-1).     

Communication: convergence of anharmonic infrared intensities of hydrogen fluoride in traditional and explicitly correlated coupled cluster calculations

It is shown that the convergence of anharmonic infrared spectral intensities with respect to the basis set size is much enhanced in explicitly correlated calculations as compared to traditional configuration interaction type wave function expansion. Explicitly correlated coupled cluster (CC) calculations using Slater-type geminal correlation factor (CC-F12) yield well-converged dipole derivatives and vibrational intensities for hydrogen fluoride with basis set involving f functions on the heavy atom. Combination of CC-F12 with singles, doubles, and non-iterative triples (CCSD(T)-F12) with small corrections due to quadruple excitations, core-electron correlation, and relativistic effects yields vibrational line positions, dipole moments, and transition dipole matrix elements in good agreement with the best experimental values.     

Vibrational spectra of cyclooctatetraenyl alkali metal complexes [C8H8M2 (M = Na, K)]: A theoretical study

The cyclooctatetraenyl dianion (C₈H₈²⁻) π-conjugated system forms a stable complex system with alkali and some transition metals. The results of vibrational analysis for C₈H₈M₂ (M = Na, K) complexes were reported here. The geometries of C₈H₈M₂ (M = Na, K) were optimized using ab initio (HF, MP2, CCSD(T)) and DFT (B3LYP) methods with 6-311G** and 6-311++G** basis sets and the harmonic frequencies were obtained. To reproduce and compare with the experimental values the structurally similar molecules C₅H₅M (M = Na, K) and benzene were studied. The scale factors obtained from these systems were applied to predict the experimental frequencies of C₈H₈M₂ (M = Na, K). The force field and vibrational spectra are analyzed and the most probable assignments are proposed for all the fundamentals based on the potential energy distribution.     

Calculation of the O-H stretching vibrational overtone spectrum of the water dimer

The O-H stretching vibrational overtone spectrum of the water dimer has been calculated with the dimer modeled as two individually vibrating monomer units. Vibrational term values and absorption intensities have been obtained variationally with a computed dipole moment surface and an internal coordinate Hamiltonian, which consists of exact kinetic energy operators within the Born-Oppenheimer approximation of the monomer units. Three-dimensional ab initio potential energy and dipole moment surfaces have been calculated using the internal coordinates of the monomer units using the coupled cluster method including single, double, and perturbative triple excitations [CCSD(T)] with the augmented correlation consistent valence triple zeta basis set (aug-cc-pVTZ). The augmented correlation consistent valence quadruple zeta basis set (aug-cc-pVQZ), counterpoise correction, basis set extrapolation to the complete basis set limit, relativistic corrections, and core and valence electron correlations effects have been included in one-dimensional potential energy surface cuts. The aim is both to investigate the level of ab initio and vibrational calculations necessary to produce accurate results when compared with experiment and to aid the detection of the water dimer under atmospheric conditions.     

Theoretical study on the structures, isomerization and stability of SiC3H isomers

The calculations of the geometry optimizations, energies, dipole moments, vibrational spectra, rotational constants, and isomerization of doublet SiC₃H species were performed using density functional theory and ab initio methods. Four types of isomers, a total of 18 minima, connected by 16 interconversion transition states, were located on the potential energy surface (PES) at the B3LYP/6-311G (d, p) level. More accurate energies were obtained at the CCSD(T)/6-311G(2df, 2p), and G3(MP2) levels. With the highest isomerization barrier, the lowest lying structure, linear A1 possesses the largest kinetic stability. Besides, the isomerization barriers of A2, A4, C2, F1, F4 and F5 are over 10 kcal/mol, and these isomers are also considered to be higher kinetically stable. Other isomers cannot be kinetically stabilized with considerably low isomerization barriers. Investigation on the bonding properties and the computations of vibrational spectra, dipole moments, and rotational constants for SiC₃H isomers are helpful for understanding their structures and also valuable for their detections in the interstellar space and laboratory.     

Vibrational energies of PH3 calculated variationally at the complete basis set limit

The potential energy surface for the electronic ground state of PH(3) was calculated at the CCSD(T) level using aug-cc-pV(Q+d)Z and aug-cc-pVQZ basis sets for P and H, respectively, with scalar relativistic corrections included. A parametrized function was fitted through these ab initio points, and one parameter of this function was empirically adjusted. This analytical PES was employed in variational calculations of vibrational energies with the newly developed program TROVE. The convergence of the calculated vibrational energies with increasing vibrational basis set size was improved by means of an extrapolation scheme analogous to the complete basis set limit schemes used in ab initio electronic structure calculations. The resulting theoretical energy values are in excellent agreement with the available experimentally derived values.     

The structures,binding energies and vibrational frequencies of Ca3 and Ca4 — An application of the CCSD(T) method

Summary The Ca₃ and Ca₄ metallic clusters have been investigated using state-of-the-artab initio quantum mechanical methods. Large atomic natural orbital basis sets have been used in conjunction with the singles and doubles coupled-cluster (CCSD) method, a coupled-cluster method that includes a perturbational estimate of connected triple excitations, denoted CCSD(T), and the multireference configuration interaction (MRCI) method. The equilibrium geometries, binding energies and harmonic vibrational frequencies have been determined with each of the methods so that the accuracy of the coupled-cluster methods may be assessed. Since the CCSD(T) method reproduces the MRCI results very well, cubic and quartic force fields of Ca₃ and Ca₄ have been determined using this approach and used to evaluate the fundamental vibrational frequencies. The infrared intensities of both thee mode of Ca₃ and thet ₂ mode of Ca₄ are found to be small. The results obtained in this study are compared and contrasted with those from our earlier studies on small Be and Mg clusters.Dedicated to Prof. Klaus Ruedenberg on the occasion of his 70th birthday     

Franck-Condon factors based on anharmonic vibrational wave functions of polyatomic molecules

Franck-Condon (FC) integrals of polyatomic molecules are computed on the basis of vibrational self-consistent-field (VSCF) or configuration-interaction (VCI) calculations capable of including vibrational anharmonicity to any desired extent (within certain molecular size limits). The anharmonic vibrational wave functions of the initial and final states are expanded unambiguously by harmonic oscillator basis functions of normal coordinates of the respective electronic states. The anharmonic FC integrals are then obtained as linear combinations of harmonic counterparts, which can, in turn, be evaluated by established techniques taking account of the Duschinsky rotations, geometry displacements, and frequency changes. Alternatively, anharmonic wave functions of both states are expanded by basis functions of just one electronic state, permitting the FC integral to be evaluated directly by the Gauss-Hermite quadrature used in the VSCF and VCI steps [Bowman et al., Mol. Phys. 104, 33 (2006)]. These methods in conjunction with the VCI and coupled-cluster with singles, doubles, and perturbative triples [CCSD(T)] method have predicted the peak positions and intensities of the vibrational manifold in the X 2B1 photoelectron band of H2O with quantitative accuracy. It has revealed that two weakly visible peaks are the result of intensity borrowing from nearby states through anharmonic couplings, an effect explained qualitatively by VSCF and quantitatively by VCI, but not by the harmonic approximation. The X 2B2 photoelectron band of H2CO is less accurately reproduced by this method, likely because of the inability of CCSD(T)/cc-pVTZ to describe the potential energy surface of open-shell H2CO+ with the same high accuracy as in H2O+.     

Conventional strain energies of 1,2-dihydroazete, 2,3-dihydroazete, 1,2-dihydrophosphete, and 2,3-dihydrophosphete

The conventional strain energies of 1,2-dihydroazete, 2,3-dihydroazete, 1,2-dihydrophosphete, and 2,3-dihydrophosphete are determined within the isodesmic, homodesmotic, and hyperhomodesmotic models. Optimum equilibrium geometries, harmonic vibrational frequencies, and corresponding electronic energies and zero-point vibrational energies are computed for all pertinent molecular systems using SCF theory, second-order perturbation theory, and density functional theory and employing the correlation consistent basis sets cc-pVDZ, cc-pVTZ, and cc-pVQZ. Single-point fourth-order perturbation theory, CCSD, and CCSD(T) calculations employing the cc-pVTZ and the cc-pVQZ basis sets are computed using the MP2/cc-pVTZ and MP2/cc-pVQZ optimized geometries, respectfully, to ascertain the contribution of higher order correlation. Three DFT functionals, B3LYP, wB97XD, and M06-2X, are employed to determine whether they can yield results similar to those obtained at the CCSD(T) level.     

Semispectroscopic and quantitative structure-property relationship estimates of the equilibrium and vibrationally averaged structure and dipole moment of 1-buten-3-yne

Systematic quantum chemical calculations have been performed to obtain precise estimates of the equilibrium and vibrationally averaged molecular structure and electric dipole moment of vinylacetylene (VA, 1-buten-3-yne). Anharmonic (cubic and semi-diagonal quartic) MP2/cc-pVTZ force fields in normal coordinates were computed to account for anharmonic vibrational effects, including zero-point contributions to the rotational constants and the electric dipole moment. A simultaneous weighted least-squares structural refinement was performed, resulting in the best semispectroscopic estimate of the re structure of VA. The refinement was based on experimentally measured ground-state rotational constants of two isotopologs of VA corrected to equilibrium values using MP2/cc-pVTZ vibration-rotation interaction constants and all-electron CCSD(T)/aug-cc-pVTZ structural constraints. The semispectroscopic re structure of VA agrees excellently with the high-level CCSD(T)/aug-cc-pVTZ ab initio structure. The most dependable, CCSD(T)/cc-pVQZ//CCSD(T)/aug-cc-pVTZ equilibrium electric dipole moment of VA, in D, is mua= 0.4088, mub= 0.0004, and muc= 0. The vibrationally corrected a-component of 0.4214 D is in excellent agreement with one of the available experimental values. The present analysis shows that mub is negligible even after vibrational correction. A simple quantitative structure-property relationship (QSPR) model resulted in a highly similar estimate, 0.45 D, for the electric dipole moment of VA.     

Structure and Stability of Isomers of the Promising Interstellar Molecule PC3O

DFT/B3LYP/6-311G(d) and CCSD(T)/6-311G(2d) single-point calculations are carried out for exploring the doublet potential energy surface (PES) of PC₃O, a molecule of potential interest in interstellar chemistry. A total of 29 minima connected by 65 interconversion transition states are located. The structures of the most relevant isomers and transition states are further optimized at the QCISD level followed by CCSD(T) single-point energy calculations. At the CCSD(T)/6-311G(2df)//QCISD/6-311G(d)+ZPVE level, the global minimum is the quasi-linear structure PCCCO 1 (0.0 kcal/mol) with a great kinetic stability of 47.9 kcal/mol, and the cumulenic form features largely in its resonance structures. Moreover, the chainlike isomer OPCCC 3 (64.5) and five-membered-ring species cPCCCO 19 (77.8) possess considerable kinetic stability of about 18.0 kcal/mol. All these three isomers are very promising candidates for future experimental and astrophysical detection. Additionally, a three-membered-ring isomer CC-cCOP 10 (69.6) has slightly lower kinetic stability of around 15 kcal/mol and may also be experimentally observable. Possible formation mechanisms of the four stable isomers in interstellar space are discussed. The present research is the first attempt to study the isomerization and dissociation mechanisms of PC _n O series. The predicted spectroscopic properties, including harmonic vibrational frequencies, dipole moments and rotational constants for the relevant isomers, are expected to be informative for the identification of PC₃O in laboratory and interstellar medium.     

Silaacetylene: A possible target for experimental studies

The equilibrium geometries and transition states for interconversion of the CSiH₂ isomers in the singlet electronic ground state are optimized at the MP2 and CCSD(T) levels of theory using a TZ2P basis set. The heats of formation, vibrational frequencies, infrared intensities, and rotational constants are also predicted. There are three energy minima on the CSiH₂ potential energy surface. Energy calculations at CCSD(T)/TZ2P(fd) + ZPE predict that the global energy minimum is silavinylidene (1), which is 34.1 kcal mol⁻¹ lower in energy than trans-bent silaacetylene (2) and 84.1 kcal mol⁻¹ more stable than the vinylidene isomer (3). The barrier for rearrangement 2→1 is calculated at the same level of theory to be 5.1 kcal mol⁻¹, while for the rearrangement 3→2 a barrier of 2.7 kcal mol⁻¹ is predicted. The natural bond orbital (NBO) population scheme indicates a clear polarization of the C(SINGLE BOND)Si bonds toward the carbon end. A significant ionic contribution to the C(SINGLE BOND)Si bonds of 1 and 2 is suggested by the NBO analysis. The C(SINGLE BOND)Si bond length of trans-bent silaacetylene (2) is longer than previously calculated [1.665 Å at CCSD(T)/TZ2P)]. The calculated carbon-silicon bond length of 2 is in the middle between the C(SINGLE BOND)Si double bond length of 1 (1.721 Å) and the C(SINGLE BOND)Si triple bond of the linear form HCSiH (4), which is 1.604 Å. Structure 4 is a higher-order saddle point on the potential energy surface. © 1996 by John Wiley & Sons, Inc.     

Relativistic effects on inversion barriers of pyramidal group 15 hydrides

Quantum chemistry is an important tool for determining general molecular properties, although relativistic corrections are usually required for systems containing heavy and super heavy elements. Non‐relativistic along with relativistic two‐ and four‐component electronic structure calculations done with the CCSD‐T method and the new RPF‐4Z basis set have therefore been applied for determining inversion barriers, corresponding to the change from a pyramidal (C_3v) ground‐state structure to the trigonal planar (D_3h) transition state, TS, of group 15 hydrides, XH₃ (X= N, P, As, Sb, and Bi). The ground‐state structure of the McH₃ molecule, which contains the super heavy element Moscovium, is also predicted as pyramidal (C_3v), with an atomization energy of 90.8 kcal mol⁻¹. However, although non‐relativistic calculations still provided a D_3h planar TS for McH₃, four‐component relativistic calculations based on single‐reference wave functions are unable to elucidate the definitive TS geometry in this case. Hence, the results show that relativistic effects are crucial for this barrier determination in those hydrides containing Bi and Mc. Moreover, while the scalar relativistic effects predominate, increasing barrier heights by as much as 17.6 kcal mol⁻¹ (32%) in BiH₃, the spin‐orbit coupling cannot be disregarded in those hydrides containing the heaviest group 15 elements, decreasing the barrier by 2.5 kcal mol⁻¹ (4.5%) in this same molecule.     

Concerted and stepwise reaction mechanisms for the addition of ozone to acetylene: a computational study

The mechanism of the reaction between acetylene and ozone to form a primary ozonide (POZ) in the gas phase has been studied theoretically. The concerted pathway, HCCH + O3 --> POZ, proceeds via a biradicaloid transition state TS0. The stepwise pathway is a three-step reaction, HCCH + O3 --> M1 --> M2 --> POZ, involving two biradical TSs and two biradical intermediates M1 and M2. The segment of the global potential energy surface (PES) for the concerted pathway is characterized as a R-PES, which is obtained from the restricted (R) density functional theory and Hartree-Fock-based methods. The RDFT and RHF solutions of TS0 and O3 are unstable toward spin-symmetry breaking. The wave function instability for TS0 and O3 results in a discontinuity between the R-PES and the region of the global PES encompassing the biradical TSs and the intermediates of the stepwise pathway, which are characterized with unrestricted (U) methods. The global PES is characterized separately as an U(R)-PES using a combination of the R and U methods. Several different values of barriers for the concerted pathway and the energy of concert (Ec) can be estimated due to complications arising from the discontinuity between the R- and the U(R)-PES and the existence of two different RDFT and UDFT O3 equilibrium geometries. RCCSD(T)//RDFT predicts a barrier of 8.2 kcal/mol. U(R)CCSD(T)/U(R)DFT predicts a barrier of 13.8 kcal/mol for the concerted and 15.3 kcal/mol for the stepwise pathway. Comparison between the R-PES barrier to the concerted pathway and the U(R)-PES barrier to the stepwise pathway suggests the former to be the only significant mechanism. Consideration of the energy difference between TS1, the TS for the first step of the stepwise mechanism, and TS0 within the global PES leads to a significantly smaller Ec. Geometry optimization with CASSCF and energy point calculations with MRMP2 are employed to characterize TS0 and TS1. MRMP2//CASSCF predicts the energy level of TS1 to be higher than that of TS0 by 2 kcal/mol. Analysis of experimental and computational data based on the low estimate of Ec shows that the possibility of the stepwise pathway being a secondary channel at elevated temperatures cannot be ruled out.     

Intermolecular potential energy surface and rovibrational spectra of the He-N2O complex from ab initio calculations

We report an ab initio intermolecular potential energy surface calculation on the He-N(2)O complex with N(2)O at its ground state using a supermolecular approach. The calculation was performed at the coupled-cluster [CCSD(T)] level, with the full counterpoise correction for the basis set superposition error and a large basis set including midpoint bond functions. The CCSD(T) potential is found to have two minima corresponding to the T-shaped and linear He-ONN structures. The T-shaped minimum is the global minimum. The two-dimensional discrete variable representation method was employed to calculate the rovibrational energy levels for (4)He-N(2)O and (3)He-N(2)O with N(2)O at its ground and nu(3) excited states. The results indicate that the CCSD(T) potential supports five and four vibrational bound states for the (4)He-N(2)O and (3)He-N(2)O, respectively. Moreover, the calculations on the line intensities of the rotational transitions in the nu(3) region of N(2)O for the ground vibrational state shows that the (3)He-N(2)O spectrum is dominated by a-type transitions (DeltaK(a)=0), while the (4)He-N(2)O spectrum is contributed by both the a-type and b-type (DeltaK(a)=+/-1) transitions. The calculated transition frequencies and the intensities are in good agreement with the observed results.