Transition Moment Surfaces Research Articles

An ab initio study of SbH2 and BiH2: The Renner effect, spin–orbit coupling, local mode vibrations and rovibronic energy level clustering in SbH2

We present the results of ab initio calculations for the lower electronic states of the Group 15 (pnictogen) dihydrides, SbH2 and BiH2. For each of these molecules the two lowest electronic states become degenerate at linearity and are therefore subject to the Renner effect. Spin–orbit coupling is also strong in these two heavy-element containing molecules. For the lowest two electronic states of SbH2, we construct the three dimensional potential energy surfaces and corresponding dipole moment and transition moment surfaces by multi-reference configuration interaction techniques. Including both the Renner effect and spin–orbit coupling, we calculate term values and simulate the rovibrational and rovibronic spectra of SbH2. Excellent agreement is obtained with the results of matrix isolation infrared spectroscopic studies and with gas phase electronic spectroscopic studies in absorption. For the heavier dihydride BiH2 we calculate bending potential curves and the spin–orbit coupling constant for comparison. For SbH2 we further study the local mode vibrational behavior and the formation of rovibronic energy level clusters in high angular momentum states.

Vibronic transition moments and line intensities for H 2O +

Ab initio calculations of the electronic dipole moment components for the A ̃ 2A 1 and X ̃ 2B 1 electronic states and the electronic transition moment for the A ̃ 2A 1 – X ̃ 2B 1 transition of H 2O + have been carried out. Parameterized analytical functions have been fitted through the computed ab initio data points, and the resulting dipole moment and transition moment surfaces have been used, along with potential energy surfaces derived from the ab initio results of Brommer et al. [J. Chem. Phys. 98 (1993) 5222], to simulate H 2O + spectra and to generate an extensive set of vibronic transition moments for the A ̃ – X ̃ and X ̃ – X ̃ band systems of H 2O +. The work is made with the dual purpose of facilitating further assignments of high-resolution spectra [J. Mol. Spectrosc. 219 (2003) 258] and of allowing cometary spectra of H 2O + to be simulated [Ap. J. 574 (2002) L183].

Transition moments and NH2 cometary spectra

We calculate vibronic transition moments for the A−2A1-X−2, electronic band system, and for the vibrational transitions within the à and [Xtilde] states, of the NH2 free radical with the purpose of assisting in the quantitative interpretation of cometary NH2 emission spectra. To do this it is necessary to use molecular wavefunctions, and electric dipole moment and transition moment surfaces. The wavefunctions are obtained using our program system RENNER after we have determined optimized à and [Xtilde] state potential energy surfaces in a fitting to data. We have obtained the electric dipole moment and transition moment surfaces by ab initio calculation.

The Matrix Isolation Spectrum of the CH 2+ Ion

For CH 2 + molecular ions at 5 K we simulate the infrared absorption spectrum, and tabulate all strong absorption lines from 0 to 16 000 cm −1. We use ab initio potential energy, dipole moment, and transition moment surfaces in conjunction with our program system RENNER, which allows for the Renner–Teller effect and spin–orbit coupling in a full-dimensions calculation. This is done for the purpose of guiding our search for the matrix isolation spectrum; our attempts at finding this spectrum are also described.

The Near Ultraviolet Band System of Singlet Methylene

In a classic paper by G. Herzberg and J. W. C. Johns entitled “The Spectrum and Structure of Singlet CH2” (Proc. Roy. Soc. A295, 107–128 (1966)) the analysis of the b̃1B1←ã1A1 red absorption band system of CH2 is discussed in detail for the first time. In addition to that band system the observation of a fragment of a weak near ultraviolet absorption band system is reported. The three observed bands of the system could not be vibrationally assigned or rotationally analyzed but it was pointed out that they probably involve absorption into the second excited singlet state, c̃1A1. We show this supposition to be true here by simulation. In order to simulate the spectrum we have calculated ab initio the c̃–ã and c̃–b̃ transition moment surfaces and used the MORBID and RENNER program systems with previously determined potential energy surfaces for the ã, b̃, and c̃ states in a calculation of the energy levels and wavefunctions. We find that the three bands seen by Herzberg and Johns are part of the c̃←(ã/b̃) system but that all of the bands of the system above about 31 000 cm−1 are missing as a result of c̃ state predissociation. We vibrationally assign the bands but the weakness of the spectrum, and the presence of perturbations, make it impossible for us to analyze the rotational structure fully. Further experimental and theoretical studies are suggested.

Predicted rovibronic spectra of CH 2+ and CD 2+

We present simulations of the A 2 B 1← X 2 A 1 electronic band systems of CH 2 + and CD 2 + in absorption at 200 K. For each isotopomer we calculate the spectrum over the range from 5000 to 18 000 cm −1 for the purpose of assisting the experimental search of the spectrum in a cooled hollow-cathode discharge. We make use of our previously determined ab initio potential energy surfaces, dipole moment and transition moment surfaces in a calculation that includes the Renner–Teller effect and spin–orbit coupling. To complete the picture we also present simulations of the rotation and rotation–vibration spectra of CD 2 +.

Refined potential-energy surfaces for the 2A" and à 2A' electronic states of the HO2 molecule

In a previous paper (G. Osmann et al. J. Mol. Spectrosc. 197, 262 (1999)) we calculated ab initio the potential-energy surfaces of the ground [Formula: see text]2A" and excited Ã2A' electronic states of the HO2 molecule; these two states correlate with a 2Π state at linearity and participate in a Renner effect interaction. In that paper, we also calculated the electric- and magnetic-dipole moment and transition-moment surfaces, and the spin-orbit coupling constant; we then simulated the à ® [Formula: see text] emission band system including both electric-dipole and magnetic-dipole transitions. We now calculate more points on the surfaces to cover a wider range of bending geometries, and then refine the surfaces by fitting to rovibronic term values for both electronic states simultaneously. In the fitting we include levels having J values up to 9/2 and term values up to about 8000 cm–1. In our calculation of the energy levels we allow for the Renner effect and spin-orbit coupling by using our variational computer program RENNER. A good fitting to the data is obtained and as a result we obtain an accurate representation of these two potential surfaces over an energy range of more than 1 eV. We tabulate the vibronic energies up to 1 eV for both HO2 and DO2. We can explain the origin of a perturbation observed in the F1 spin component levels of the Ã(0, 0, 0) vibronic state for J values around 51/2; this is caused by a spin-orbit interaction satisfying Δ N = ± 1 with the F2 spin component levels of the [Formula: see text](1,1,2) vibronic state. Using the new rovibronic energies and wave functions, with our ab initio electric dipole moment and transition moment surfaces, we calculate Stark coefficients and compare them with experiment for some ground vibronic state levels. PACS Nos.: 31.20D, 31.50, 33.10, 33.20E, 35.20D, 35.20J

A theoretical calculation of the absorption spectrum of CH 2+

The ground X̃ 2 A 1 electronic state of CH 2 + is quasilinear with a small barrier to linearity, and at linearity the state becomes degenerate with the à 2 B 1 electronic state forming a 2Π u state. Because of the nonzero electronic angular momentum the rovibrational basis states belonging to the two electronic states strongly interact due to both the Renner effect and spin-orbit coupling. In a previous paper (P. Jensen, M. Brumm, W. P. Kraemer, and P. R. Bunker, J. Mol. Spectrosc. 172 (1995) 194) we calculated the rovibronic energies of the states using ab initio potential energy surfaces that we generated. In the present paper we use the electronic wavefunctions of the previous ab initio calculation to determine the dipole moment and transition moment surfaces, and we develop the theory that allows us to use these to calculate intensities. As a result we now calculate both the positions and intensities of the lines in the absorption spectrum of CH 2 +, and its deuterated isotopomers, making full allowance for the effects of the Renner interaction and of spin-orbit coupling. We predict the appearance of the absorption spectrum over the whole wavenumber range from 0 cm −1 to beyond 15 000 cm −1; this involves only the X̃ and à electronic states. We hope that these results allow experimentalists to search successfully for the features that we predict, and thereby to achieve a better spectroscopic characterization of this important molecular ion.

Dissociation of NH3 to NH2+H

Potential energy, dipole moment, and electronic transition moment surfaces for the lowest dissociative pathways of the singlet X̃ and à states of NH3 yielding NH2 (X̃ 2B1,à 2A1) +H(2S) products have been calculated using complete active space MCSCF ab initio wave functions. The à state dissociation proceeds via a minimum barrier at the following planar geometry: αHNH =113°, rNH =1.042 Å (in the NH2 fragment), and RNH =1.323 Å (in the dissociation coordinate). The barrier height is calculated to be 3226 cm−1 with an expected accuracy of about 300 cm−1. The barrier height increases with increasing out-of-plane angle. Close to the barrier there are strong variations of the shapes of the dipole moment and transition moment surfaces. The minimum energy path through the X̃–à conical intersection follows planar geometries. Along this pathway the angle αHNH decreases, but the distance rNH in the NH2 fragment hardly changes. The crossing distance RcNH of the X̃ and à states in planar structures depends strongly on αHNH and varies from about 1.68 Å (60°) to infinity (180°). The photodissociation process NH3(Ã) →NH2(X̃ 2B1) +H(2S) is discussed on the basis of the calculated potential energy surfaces.

Theoretical A 1A″2–X 1A1 absorption and emission spectrum of ammonia

Potential energy, electric dipole moment, and electronic transition moment surfaces have been calculated for the A and X states of NH3 from CASSCF and CEPA electronic wave functions. Anharmonic vibrational term values, Franck–Condon factors, and A–X radiative transition probabilities for the symmetric stretching and bending modes of NH3 and ND3 have been evaluated. The theoretical absorption spectra at room and low temperatures agree well with experimental data. The symmetric stretching mode in the A state has only small intensities in the A–X absorption spectrum. Emission rates from various initial vibronic levels of the A state are given. The ab initio electric dipole moment surfaces for the ground state of NH3 have been used to compute transition moments, which are in good agreement with experimental data.

Atoms-in-molecules calculation of dipole moments of the lowest Σ and Π states of LiH

AIM calculations of dipole and transition moment functions are reported for the lowest Σ and Π states of LiH using a relatively small basis. The functions obtained agree quite satisfactorily with the best ab initio calculations. The results seem to indicate that the AIM approach might become useful in producing missing input data to the DIM calculations of dipole and transition moment surfaces for molecular collision systems interacting with a laser field.