Transition Dipole Moment Surfaces Research Articles

ExoMol line lists – XLVII. Rovibronic molecular line list of the calcium monohydroxide radical (CaOH)

ABSTRACT Any future detection of the calcium monohydroxide radical (CaOH) in stellar and exoplanetary atmospheres will rely on accurate molecular opacity data. Here, we present the first comprehensive molecular line list of CaOH covering the $\tilde{A}\, ^2\Pi$–$\tilde{X}\, ^2\Sigma ^+$ rotation-vibration-electronic and $\tilde{X}\, ^2\Sigma ^+$–$\tilde{X}\, ^2\Sigma ^+$ rotation-vibration bands. The newly computed OYT6 line list contains over 24.2 billion transitions between 3.2 million energy levels with rotational excitation up to J = 175.5. It is applicable to temperatures up to T = 3000 K and covers the 0–35 000 cm−1 range (wavelengths λ > 0.29 μm) for rotational, rotation-vibration and the $\tilde{A}\, ^2\Pi$–$\tilde{X}\, ^2\Sigma ^+$ electronic transitions. The strong band around 16 000 cm−1 (λ = 0.63 μm) is likely to be of interest in future astronomical observations, particularly in hot rocky exoplanets where temperatures can become extremely high. The OYT6 line list has been generated using empirically refined $\tilde{X}\, ^2\Sigma ^+$ and $\tilde{A}\, ^2\Pi$ state potential energy surfaces, high-level ab initio transition dipole moment surfaces, and a rigorous treatment of both Renner–Teller and spin-orbit coupling effects, which are necessary for correctly modelling the CaOH spectrum. Post-processing of the CaOH line list has been performed so as to tailor it to high-resolution applications, i.e. by replacing calculated energy levels with more accurate empirically derived values (where available), hence improving the accuracy of the predicted line positions in certain regions. The OYT6 line list is available from the ExoMol data base at www.exomol.com and the CDS astronomical data base.

Theoretical rovibronic spectroscopy of the calcium monohydroxide radical (CaOH).

The rovibronic (rotation-vibration-electronic) spectrum of the calcium monohydroxide radical (CaOH) is of interest to studies of exoplanet atmospheres and ultracold molecules. Here, we theoretically investigate the Ã2Π-X̃2Σ+ band system of CaOH using high-level ab initio theory and variational nuclear motion calculations. New potential energy surfaces (PESs) are constructed for the X̃2Σ+ and Ã2Π electronic states along with Ã-X̃ transition dipole moment surfaces (DMSs). For the ground X̃2Σ+ state, a published high-level ab initio PES is empirically refined to all available experimental rovibrational energy levels up to J = 15.5, reproducing the observed term values with a root-mean-square error of 0.06 cm-1. Large-scale multireference configuration interaction calculations using quintuple-zeta quality basis sets are employed to generate the Ã2Π state PESs and Ã-X̃ DMSs. Variational calculations consider both Renner-Teller and spin-orbit coupling effects, which are essential for a correct description of the spectrum of CaOH. Computed rovibronic energy levels of the Ã2Π state, line list calculations up to J = 125.5, and an analysis of Renner-Teller splittings in the ν2 bending mode of CaOH are discussed.

Account of non-Condon effects in time-independent Raman wavefunction theory: Calculation of the S1← S0 vibronic absorption spectrum of formaldehyde.

The time-independent eigenstate-free Raman wavefunction approach for calculating anharmonic vibronic spectra has been extended for the calculation of Herzberg-Teller contributions on the basis of an n-mode expansion of the transition electric dipole moment surface. This allows for the efficient simulation of Franck-Condon dark vibronic spectra. In addition, vibrational angular momentum terms have been implemented into this formalism, as they are important for an accurate description of vibrational wavefunctions spanning double-well potentials. This approach has been used to compute the FC-forbidden vibronic spectrum of the n → π* transition of formaldehyde based on a potential energy and transition dipole moment surfaces obtained from explicitly correlated multi-reference configuration interaction calculations. An extensive analysis of the resulting vibronic structure is provided, which allows for a detailed assignment and interpretation of the experimental spectrum.

On the Impact of Singularities in the Two-State Adiabatic to Diabatic State Transformation: A Global Treatment.

Diabatizations based on molecular properties can remove the singularity in the derivative coupling at a conical intersection in the diabatic representation. Yet, they can also create new singularities in the derivative couplings because of the defining equations of the adiabatic to diabatic state transformation. In the iconic two-state case, these singularities occur at points termed diabolical singular points and form a seam of dimension Nint-2, where Nint is the number of internal degrees of freedom. This seam is of the same dimension as the conical intersection seam, but is distinct. Here, the global topography of the diabolical singularity seam of 1,21A states of ammonia is reported using a Boys localization (BL) dipole-based diabatization and juxtaposed with a previously reported global representation of the coupled electronic state potential energy surfaces. The principal finding is that the seam of BL diabatization-induced singularities passes very close to the key saddle point on the 21A potential energy surface which connects the 21A equilibrium structure with the NH2(X̃,Ã) + H channel. The construction and detailed study of the reported diabolical singularity seam is made possible by a recently constructed analytic representation of the dipole and transition dipole moment surfaces.

The lowest lying excited electronic states for HFCO including a potential energy surface for S 1 in sum-of-products form

The vertical excitation energies to the S and T states for HFCO were determined using multi-reference (CASSCF, CASPT2, CASPT2-F12, MRCI, and MRCI-F12) and the single reference EOM-CCSD methods. The geometries, relative energies, and harmonic frequencies for the stationary points (minimum and transition state to inversion) on both the S and T potential energy surfaces (PESs) were characterised. A six-dimensional PES for the S state was constructed, in sum-of-products form using a neural network with exponential neurons, based on EOM-CCSD/aug-cc-pVTZ ab initio energies. Using the PES, the fundamental vibrational frequencies were computed using block-improved relaxation in MCTDH, and they agreed well with previous experiments (RMSE cm). A corresponding transition dipole moment surface (TDMS) was also fit to sum-of-products form. With the present PES and TDMS, along with the previous S surface, UV-vis absorption, stimulated emission pumping spectra, or optimal control of quantum dynamics via S can be explored.

Ro-vibronic transition intensities for triatomic molecules from the exact kinetic energy operator; electronic spectrum for the C̃ 1B2 ← X̃ 1A1 transition in SO2.

A procedure for calculating ro-vibronic transition intensities for triatomic molecules within the Born-Oppenheimer approximation is reported. Ro-vibrational energy levels and wavefunctions are obtained with the DVR3D suite, which solves the nuclear motion problem with an exact kinetic energy operator. Absolute transition intensities are calculated both with the Franck-Condon approximation and with a full transition dipole moment surface. The theoretical scheme is tested on C̃ 1B2 ← X̃ 1A1 ro-vibronic transitions of SO2. Ab initio potential energy and dipole moment surfaces are generated for this purpose. The calculated ro-vibronic transition intensities and cross sections are compared with the available experimental and theoretical data.

Potential energy and dipole moment surfaces of the triplet states of the O2(X3Σg-) - O2(X3Σg-,a1Δg,b1Σg+) complex.

We compute four-dimensional diabatic potential energy surfaces and transition dipole moment surfaces of O2-O2, relevant for the theoretical description of collision-induced absorption in the forbidden X3Σg- → a1Δg and X3Σg- → b1Σg+ bands at 7883 cm-1 and 13 122 cm-1, respectively. We compute potentials at the multi-reference configuration interaction (MRCI) level and dipole surfaces at the MRCI and complete active space self-consistent field (CASSCF) levels of theory. Potentials and dipole surfaces are transformed to a diabatic basis using a recent multiple-property-based diabatization algorithm. We discuss the angular expansion of these surfaces, derive the symmetry constraints on the expansion coefficients, and present working equations for determining the expansion coefficients by numerical integration over the angles. We also present an interpolation scheme with exponential extrapolation to both short and large separations, which is used for representing the O2-O2 distance dependence of the angular expansion coefficients. For the triplet ground state of the complex, the potential energy surface is in reasonable agreement with previous calculations, whereas global excited state potentials are reported here for the first time. The transition dipole moment surfaces are strongly dependent on the level of theory at which they are calculated, as is also shown here by benchmark calculations at high symmetry geometries. Therefore, ab initio calculations of the collision-induced absorption spectra cannot become quantitatively predictive unless more accurate transition dipole surfaces can be computed. This is left as an open question for method development in electronic structure theory. The calculated potential energy and transition dipole moment surfaces are employed in quantum dynamical calculations of collision-induced absorption spectra reported in Paper II [T. Karman et al., J. Chem. Phys. 147, 084307 (2017)].

Line-shape theory of the X3Σg-→a1Δg,b1Σg+ transitions in O2-O2 collision-induced absorption.

We derive the theory of collision-induced absorption for electronic transitions in the approximation of an isotropic interaction potential. We apply this theory to the spin-forbidden X3Σg-→a1Δg and X3Σg-→b1Σg+ transitions in O2-O2, which are relevant for calibration in atmospheric studies. We consider two mechanisms for breaking the spin symmetry, either by the intermolecular exchange interaction between paramagnetic collision partners or by the intramolecular spin-orbit coupling. The calculations for the exchange-based mechanism employ the diabatic potential energy surfaces and transition dipole moment surfaces reported in Paper I [T. Karman et al., J. Chem. Phys. 147, 084306 (2017)]. We show that the line shape of the theoretical absorption spectra is insensitive to the large uncertainty in the electronic transition dipole moment surfaces. We also perform calculations using a simple model of the alternative mechanism involving intramolecular spin-orbit coupling, which leads to absorption intensities which are well below the experimental results. The relative intensity of this spin-orbit-based mechanism may impact the relative contribution to the absorption by collisions with diamagnetic collision partners, such as the atmospherically relevant N2 molecule. We furthermore show that both the line shape and temperature dependence are signatures of the underlying transition mechanism.

Full-dimensional quantum molecular dynamics calculations of the rovibrationally mediated X 1A′ → 2 1A′′ transition of nitrous oxide

A full dimensional time-dependent quantum wavepacket approach is used to study the photodissociation dynamics of nitrous oxide for the X 1A′ → 2 1A′′ bound–bound transition based on new highly accurate potential energy and transition dipole moment surfaces. The computed 2 1A′′ absorption spectra at room temperature are characterized by sharp vibrational structures that contribute slightly to the diffuse vibrational structures around the maximum peak at 180 nm of the first ultraviolet absorption band (from the contribution of 2 1A′, 1 1A′′, and 2 1A′′ states) of N2O. Transitions from different initial rovibrational states reveal that the sharp structures arise mainly from N2O bending vibrations, whereas, at higher temperatures, the N2O and NNO stretching vibrations are responsible for enhancing the intensity of the structures. At absorption wavelengths 166 nm and 179 nm, vibrational quantum state distributions of N2 product fragments decrease monotonically with increasing vibrational quantum number v = 0, 1, 2. At 166 nm, rotational quantum state distributions of N2 at fixed v = 0 and v = 1 display multimodal profiles with maximum peaks at j = 77 and j = 75, respectively, whereas, the distributions at the 179 nm absorption wavelength display bimodal profiles with maximum peaks at j = 73 and j = 71, respectively. Accordingly, the presence of rotationally hot N2 from previous experimental and theoretical works in the first band strongly implies a significant influence of the 2 1A′′ state in determining the final dissociation pathway of N2 + O. © 2016 Wiley Periodicals, Inc.

Luminescence of the (O2(a(1)Δ(g)))2 collisional complex in the temperature range of 90-315 K: Experiment and theory.

Experimental and theoretical studies of collision induced emission of singlet oxygen molecules O2(a(1)Δg) in the visible range have been performed. The rate constants, half-widths, and position of peaks for the emission bands of the (O2(a(1)Δg))2 collisional complex centered around 634 nm (2) and 703 nm (3) have been measured in the temperature range of 90-315 K using a flow-tube apparatus that utilized a gas-liquid chemical singlet oxygen generator. The absolute values of the spontaneous emission rate constants k2 and k3 are found to be similar, with the k3/k2 ratio monotonically decreasing from 1.1 at 300 K to 0.96 at 90 K. k2 slowly decreases with decreasing temperature but a sharp increase in its values is measured below 100 K. The experimental results were rationalized in terms of ab initio calculations of the ground and excited potential energy and transition dipole moment surfaces of singlet electronic states of the (O2)2 dimole, which were utilized to compute rate constants k2 and k3 within a statistical model. The best theoretical results reproduced experimental rate constants with the accuracy of under 40% and correctly described the observed temperature dependence. The main contribution to emission process (2), which does not involve vibrational excitation of O2 molecules at the ground electronic level, comes from the spin- and symmetry-allowed 1(1)Ag←(1)B3u transition in the rectangular H configuration of the dimole. Alternatively, emission process (3), in which one of the monomers becomes vibrationally excited in the ground electronic state, is found to be predominantly due to the vibronically allowed 1(1)Ag←2(1)Ag transition induced by the asymmetric O-O stretch vibration in the collisional complex. The strong vibronic coupling between nearly degenerate excited singlet states of the dimole makes the intensities of vibronically and symmetry-allowed transitions comparable and hence the rate constants k2 and k3 close to one another.

Multireference calculations of potential energy and transition dipole moment surfaces for first and second UV absorption bands of N2O

A great deal of theoretical work has been carried out to investigate the properties of the six lowest singlet electronic states of N 2 O molecule: the ground state X 1A′; the excited states 11A′′, 21A′, 21A′′, 31A′ and 31A′′. Multireference configuration interaction (MRCI) approach has been used to compute the full-dimensional potential energy surfaces of the six lowest states employing aug-cc-pVQZ minus g orbital basis set. It was found that such of highly accurate potential yields excellent results of bond dissociation and vertical excitation energies in comparison with the experimental values. Several important symmetry and nonsymmetry related conical intersections in linear and bent geometries have been discussed. Of particular interest is the location of conical intersections between the 21A′(1Δ) and 31A′(1Π) states, and between the 11A′′(1Σ-) and 31A′′(1Π) states in linear geometry, as well as conical intersection between the X 1A′ and 21A′ states in bent geometry. The corresponding transition dipole moment surfaces have also been computed, connecting the ground electronic state to the lowest five excited states. Detailed discussion on the vector properties of the dipole transition has been presented specifically in the vicinity of the conical intersections.

Simulation of [formula omitted] laser excitation spectrum of CH3O and CD3O

A theoretical calculation of the laser-induced fluorescence excitation spectrum from X∼2E→A∼2A1 is carried out for CH3O and CD3O using a transition dipole moment surface expanded up to second order. The vibronic form of these operators is obtained using symmetry arguments. The A∼2A1 vibrational levels are calculated using Van Vleck perturbation theory, and the latter is used to adjust harmonic constants of the potential to match experimental fundamentals. The CH3O fit force field is tested on CD3O. For both molecules the transition energies are well reproduced, but there are systematic differences between experimental and theoretical intensities. The origins of these differences are discussed.

Absorption Cross Section of Ozone Isotopologues Calculated with the Multiconfiguration Time-Dependent Hartree (MCTDH) Method: I. The Hartley and Huggins Bands

The absorption cross sections of 18 isotopologues of the ozone molecule have been calculated in the range of the Hartley-Huggins bands (27000-55000 cm(-1)). All 18 possible ozone isotopologues made with (16)O, (17)O, and (18)O have been considered, with emphasis on those of geophysics interest like (16)O(3) (17)O(16)O(2), (16)O(17)O(16)O, (18)O(16)O(2), and (16)O(18)O(16)O. We have used the MCTDH algorithm to propagate wavepackets. As an initial wavepacket, we took the vibrational ground state multiplied by the transition dipole moment surface. The cross sections have been obtained from the autocorrelation function of this wavepacket. Only two potential energy surfaces (PESs) and the corresponding transition dipole moment are involved in the calculation. The dissociating R state has been omitted. The calculations have been performed only for J = 0. The comparison with the experimental absorption cross sections of (16)O(3) and (18)O(3) has been performed after an empirical smoothing which mimics the rotational envelop. The isotopologue dependence of the cross sections of 18 isotopologues can be split into two energy ranges, (a) from 27000 to 32000 cm(-1), the Huggins band, which is highly structured, and (b) from 32000 to 55000 cm(-1), the main part of the cross section which has a bell shape, the Hartley band. This bell-shaped envelop has been characterized by a new analytic model depending on only four parameters, amplitude, center, width, and asymmetry. The isotopologue dependence of these parameters reveals the tiny differences between the absorption cross sections of the various isotopologues. In contrast to the smooth shape of the Hartley band, the Huggins band exhibits pronounced vibrational structures and therefore shows large isotopologue differences which may induce a significant isotopologue dependence of the ozone photodissociation rates under actinic flux.

Isotopomer Fractionation in the UV Photolysis of N2O: 3. 3D Ab Initio Surfaces and Anharmonic Effects

The wavelength-dependent isotopic fractionation of N(2)O is calculated, extending our previous work, Parts 1 and 2, in several aspects: (1) the fully three-dimensional ab initio electronic potential and transition dipole moment surfaces of S. Nanbu and M. S. Johnson (J. Chem. Phys. A 2004, 108, 8905) are used to calculate the absorption cross sections, instead of a 2D surface and (2) the vibrational frequencies and wave functions with anharmonicity correction are used for the ground electronic state. The results for the absorption spectrum and for the isotopic fractionation of the different isotopomers are discussed. One difference between experiments measuring the absorption coefficient (von Hessberg et al. Atmos. Chem. Phys. 2004, 4, 1237) and the others that measure instead the photodissociation is also discussed. Experiments on the quantum yield for wavelengths longer than 200 nm (>50 000 cm(-1)) would be helpful in treating the observed difference.

The HOOH UV spectrum: Importance of the transition dipole moment and torsional motion from semiclassical calculations on an ab initio potential energy surface

The absorption cross section of HOOH, a starting point for larger ROOH, was calculated using the "Wigner method." Calculations use the Wigner transform of ground state wave functions and classical approximations for excited state wave functions. Potential energy and transition dipole moment surfaces were calculated using the equation-of-motion coupled-cluster singles and doubles method over an extended Franck-Condon region. The first two O-O stretches and the first five HOOH torsional levels are included. This study also addresses two fundamental questions about ROOH photodissociation. The long wavelength A(1)A:B(1)B excited state preference has been measured from dynamics experiments, but a Franck-Condon overlap explanation has not been directly verified. A moderate barrier to HOOH torsional motion and excited state dynamics affect the temperature dependence in the UV spectrum. Based on these initial findings for HOOH, photodissociation of large ROOH cannot be eliminated as an important factor for ozone and particulate matter production seen in both ambient and laboratory studies.

Conformational Effects on Excitonic Interactions in a Prototypical H-Bonded Bichromophore: Bis(2-hydroxyphenyl)methane

Laser-induced fluorescence, single-vibronic level fluorescence (SVLF), UV hole burning, and fluorescence dip infrared (FDIR) spectroscopy have been carried out on bis-(2-hydroxyphenyl)methane in order to characterize the ground-state and first excited-state vibronic spectroscopy of this model flexible bichromophore. These studies identified the presence of two conformational isomers. The FDIR spectra in the OH-stretch region determine that conformer A is an OH...O H-bonded conformer, while conformer B is a doubly OH...pi H-bonded conformer with C(2) symmetry. High-resolution ultraviolet spectra ( approximately 50 MHz resolution) of a series of vibronic bands of both conformers confirm and refine these assignments. The transition dipole moment (TDM) direction in conformer A is consistent with electronic excitation that is primarily localized on the donor phenol ring. A tentative assignment of the S(2) origin is made to a set of transitions approximately 400 cm(-1) above S(1). In conformer B, the TDM direction firmly establishes C(2) symmetry for the conformer in its S(1) state and establishes the electronic excitation as delocalized over the two rings, as the lower member of an excitonic pair. The S(2) state has not been clearly identified in the spectrum. Based on CIS calculations, the S(2) state is postulated to be several times weaker than S(1), making it difficult to identify, especially in the midst of overlap from vibronic bands due to conformer A. SVLF spectra show highly unusual vibronic intensity patterns, particularly in conformer B, which cannot be understood by simple harmonic Franck-Condon models, even in the presence of Duschinsky mixing. We postulate that these model flexible bichromophores have TDMs that are extraordinarily sensitive to the distance and orientation of the two aromatic rings, highlighting the need to map out the TDM surface and its dependence on the (up to) five torsional and bending coordinates in order to understand the observations.

Ab Initio Potential Energy Surfaces for the Ground (X̃1A′) and Excited (Ã1A′′) Electronic States of HGeBr and the Absorption and Emission Spectra of HGeBr/DGeBr

We report global potential energy surfaces for both the ground (X(1)A') and the excited (A(1)A'') electronic states of HGeBr as well as the transition dipole moment surface between them using an internally contracted multireference configuration interaction method with the Davidson correction and an augmented correlation-consistent polarized valence quadruple-zeta basis set. Vibrational energy levels of HGeBr and DGeBr are calculated on both the ground and the excited electronic states and found in good agreement with the available experimental band origins. In addition, the A(1)A''-X(1)A' absorption and emission spectra of the two isotopomers were obtained, and an excellent agreement with the available experimental spectra was found.

The predicted spectrum of FeOH in its Renner-degenerate [formula omitted] and [formula omitted] electronic states

FeOH is an iron-containing molecule that is a candidate for detection in interstellar space. It has not yet been spectroscopically characterized and we simulate the microwave and infrared spectra to assist in its discovery. At linearity the ground electronic state of FeOH is an orbitally degenerate 6Δ Renner state which, at bent configurations, splits into the electronic ground state X ∼ 6 A i ′ and the excited state A ∼ 6 A i ″ . We have calculated the three-dimensional potential energy surfaces of the X ∼ and A ∼ states (which are close in energy over the range of geometries studied) at the MR-SDCI + Q + E rel/[Roos ANO (Fe), aug-cc-pVQZ (O, H)] level of theory together with associated electric dipole moment and transition dipole moment surfaces at the corresponding MR-SDCI/[Roos ANO (Fe), aug-cc-pVQZ (O, H)] level of theory. The equilibrium structure of the X ∼ state is bent with r e(Fe–O) = 1.806 Å, r e(O–H) = 0.952 Å, and ∠ e(Fe–O–H) = 134.2°. The barrier to linearity is 273 (266) cm −1 in the X ∼ ( A ∼ ) state so that FeOH is quasilinear in the X ∼ and A ∼ states. The second excited electronic state ( B ∼ 6 A ′ correlating with 6Π at linearity) is located about 3740 cm −1 above the X ∼ and A ∼ states. We have carried out variational RENNER calculations, using our potential energy and dipole moment surfaces, in order to determine rovibronic term values and to simulate the microwave and infrared spectra that arise from transitions within and between these electronic states.

Ab initio potential energy surfaces for both the ground (X̃ A1′) and excited (Ã A1″) electronic states of HGeCl and the absorption and emission spectra of HGeCl/DGeCl

Potential energy surfaces for the ground (X (1)A(')) and excited (A (1)A(")) electronic states of HGeCl and the transition dipole moment surface were obtained using an internally contracted multireference configuration interaction method with the Davidson correction and an augmented correlation-consistent polarized valence quadruple zeta basis set. Calculated vibrational energy levels of HGeCl and DGeCl on both the ground and excited electronic states are in excellent agreement with available experimental data. In addition, the absorption and emission spectra of both HGeCl and DGeCl were obtained using an efficient single Lanczos propagation method and the agreement with experimental spectra is also excellent.

Ab initio study of the first excited state A2Σ+ and of the transition A2Σ+←X2Π of CNO

The potential energy surface of the A2Σ+ electronic state of CNO is calculated using the cc-pVQZ/MRCI+Q method. The rovibrational levels are determined variationally up to 18 000 cm−1 above the electronic ground state zero energy point and are used with the transition dipole moment surfaces, obtained with the cc-pVQZ/CASSCF method, in order to model the rovibrational absorption A2Σ+←X2Π spectrum at 5 K which is compared with the measurement of Bondybey et al. [V.E. Bondybey, J.H. English, C.W. Mathews, R.J. Contolini, Chem. Phys. Lett. 82 (1981) 208].