Electric Dipole Moment Function Research Articles

Toward Accurate Ab Initio Ground-State Potential Energy and Electric Dipole Moment Functions of Carbon Monoxide.

Accurate potential energy and electric dipole moment functions of the CO molecule in its ground electronic state X1Σ+ have been obtained using the single-reference coupled-cluster approach, up to the CCSDTQP level of approximation, in conjunction with the augmented core-valence correlation-consistent basis sets, aug-cc-pCVnZ, up to octuple-zeta quality. The scalar relativistic, adiabatic, and nonadiabatic effects were discussed. The ab initio predicted functions were compared with their experimentally derived counterparts.

Three-Parameter Electric Dipole Moment Function for the CO Molecule.

A global electric dipole moment function of the ground electronic state of carbon monoxide is constructed by morphing its best theoretical approximants from the literature to the best available experimental data within the framework of the reduced radial curve approach. The resulting functions coincide with their best many-parameter empirical counterparts so closely that they can be used as highly accurate three-parameter representations. Apparently, given the mathematical nature of the problem addressed, this approach can be applied equally well to all radial molecular functions that have similarly cumbersome shapes as the function probed. This means that the property characteristics of diatomic molecules can, in principle, be described with high precision even when as few as three pertinent experimental data points are accurately known. To date, no such functional approximants are available in the literature.

Reduced Radial Curves of Diatomic Molecules.

The prospect of using the concept of a universal reduced potential energy curve (RPC) for a broader class of radial molecular functions is explored by performing appropriate model calculations for the electric dipole moment functions of the hydrogen halides HF, HCl, and HBr. The reduced radial functions of the model systems, constructed from their best available theoretical approximants, coincide so closely that they can be used as few-parameter universal representations of functions available in the literature. Given the mathematical nature of the problem addressed here, the results are not limited to the functions studied but can be applied equally well to all radial molecular functions that have similar shapes, such as electric quadrupole moment and dipole polarizability functions.

Line lists for the b1Σ+-X3Σ− and a1Δ-X3Σ− transitions of SO

SO is found in many astronomical sources such as the atmospheres of Io and Venus. In order to create more complete line lists, we fit spectroscopic data on SO from the literature using PGOPHER. The fits covered v = 0 to v = 6 for the X3Σ−state, v = 0–5 for the a1Δ state and v = 0–2 for b1Σ+ state. LeRoy's RKR program was used to produce pointwise potential energy curves. High level ab initio calculations, including spin-orbit coupling, were carried out to obtain the electric transition dipole moment functions for the nominally forbidden b1Σ+-X3Σ−and a1Δ-X3Σ−transitions. The RKR potentials and transition dipole moment points were input into LeRoy's LEVEL program to calculate the transition dipole matrix elements for all possible b-X and a-X bands. For the b1Σ+-X3Σ−transition, the electric and magnetic transition dipole matrix elements were scaled using the experimental values obtained by Setzer et al. [J Mol Spectrosc 1999;198:163–174] for the 0–0 band. The transition dipole moment matrix elements were used in PGOPHER to produce our line lists for all possible bands of the b1Σ+-X3Σ−and a1Δ-X3Σ−transitions.

GSRB rotation and rovibration intensities for: The bent HOCl molecule, and for: Quantum monodromy in NCNCS

Considerable work has gone into identifying and delineating the effects of quantum monodromy on molecules. Recently this included consideration of transition intensities of the NCNCS molecule using ab initio electric dipole moment functions in the Generalised SemiRigid Bender (GSRB) model [M. Winnewisser et al. PCCP 16, 17373-17407 (2014)]. In that work a discrepancy between the observed and calculated spectra was discovered. The purpose of the present work is to identify the source of that discrepancy - is it due to the physics of monodromy itself or are other issues involved? To investigate this we use the same theoretical approach for the simpler molecule HOCl. This allows us to identify a programming error affecting the b-type rovibrational transitions. We show that the NCNCS spectrum calculated with the corrected GSRB model does reproduce the experimental spectrum for pure rotational transitions within the ν7 large amplitude bending vibrational states, starting from the ground state and progressing through levels at the monodromy energy and beyond, while also reproducing the a-type υ:1←0rovibrational spectrum. However, the discrepancy with regard to the b-type rovibrational transitions remains. We discuss possible reasons for this discrepancy. In the course of this work we obtain a good GSRB model for the bending vibration-rotation levels of the atmospherically important HOCl molecule and its isotopologues. With ab initio calculations of the electric dipole moment function the GSRB calculates the rotation and bending rovibrational spectrum of HOCl in agreement with other determinations and with experiment. Using the physically constrained GSRB model, errors in tabulated transitions (including in the HITRAN database) were easily identified.

Signature of Congregated Effects of Mechanical and Electrical Anharmonicities, Fermi Resonances, and Dampings on the IR Spectra of Hydrogen Bonded Systems: Quantum Dynamic Study.

Theoretical IR spectral density of the high-frequency stretching mode of hydrogen bond (H-bond) systems is reported using a three-dimensional approach. The model, studied within the framework of linear response theory, involves the mechanical anharmonicity of the high-frequency stretching mode by contemplating its potential as an asymmetric double well potential, the mechanical anharmonicity of the H-bond Bridge by contemplating its potential as a Morse potential, Fermi resonances which occur between the high frequency stretching mode and the overtones of the bending modes, the electrical anharmonicity translated by the nonlinearity to second order in the electric dipole moment function of the fast mode, the second order modulation of the angular frequency and the equilibrium position of the fast mode on the slow mode coordinate, and direct and indirect relaxation mechanism. Moreover, the repulsive potential interposing in the fast mode potential is chosen in Gaussian form to account for the asymmetry of the fast mode potential and thereby elucidate the nature of the H-bond. The anharmonic coupling between the fast and slow frequency modes is handled within the strong anharmonic coupling theory. The direct relaxation of the fast mode and the indirect relaxation of the H-bond Bridge are consolidated using previous results [Rekik et al. Chem. Phys. 2008, 352, 65-76]. The infrared spectral density is calculated using the Fourier transform of the autocorrelation function of the transition dipole moment operator of the fast mode. The evolution of the infrared absorption is demonstrated, indicating that mixing of all these effects results in a broadening and complicated distribution of the spectral density. The result of this work underscores the necessity of simultaneously combining the maximum effects in H-bonded complexes for effectively modeling and interpreting their corresponding IR spectra.

High-level theoretical rovibrational spectroscopy of HCS+ isotopologues

In this work the rovibrational spectrum of the HCS+ molecular cation is revisited through high-level electronic structure and variational rovibrational calculations. A local potential energy function is built from explicitly correlated coupled-cluster results, incorporating corrections for core-valence, scalar relativistic and higher-order excitation effects. The computed spectroscopic parameters, based on variational calculations with Watson’s isomorphic Hamiltonian for linear molecules lead to a nearly perfect agreement with experimentally reported values (Rosenbaum et al., 1989). Furthermore, the documented Fermi resonance within the (0,00,1)/(0,20,0) and (1,00,1)/(1,20,0) pairs of states is clarified. Based on a newly developed electric dipole moment function transition dipole moments of fundamental transitions are predicted for the most important isotopologues.

High-level theoretical rovibrational spectroscopy beyond fc-CCSD(T): The C3 molecule

An accurate local (near-equilibrium) potential energy surface (PES) is reported for the C3 molecule in its electronic ground state (X̃(1)Σg (+)). Special care has been taken in the convergence of the potential relative to high-order correlation effects, core-valence correlation, basis set size, and scalar relativity. Based on the aforementioned PES, several rovibrational states of all (12)C and (13)C substituted isotopologues have been investigated, and spectroscopic parameters based on term energies up to J = 30 have been calculated. Available experimental vibrational term energies are reproduced to better than 1 cm(-1) and rotational constants show relative errors of not more than 0.01%. The equilibrium bond length has been determined in a mixed experimental/theoretical approach to be 1.294 07(10) Å in excellent agreement with the ab initio composite value of 1.293 97 Å. Theoretical band intensities based on a newly developed electric dipole moment function also suggest that the infrared active (1, 1(1), 0)←(0, 0(0), 0) combination band might be observable by high-resolution spectroscopy.

Ab initio spectroscopic characterization of borane, BH, in its X1Σ+ electronic state.

The accurate potential energy and electric dipole moment functions of borane, BH, in its X1Σ+ electronic state have been determined from ab initio calculations using the multireference averaged coupled-pair functional method in conjunction with the correlation-consistent core-valence basis sets up to septuple-zeta quality. The higher-order electron correlation, scalar relativistic, adiabatic, and nonadiabatic effects were discussed. Vibration-rotation energy levels of the (11)BH, (11)BD, (10)BH, and (10)BD isotopologues were predicted to near "spectroscopic" accuracy. For the main isotopologue (11)BH, the adiabatic dissociation energy D0 and the effective equilibrium internuclear distance r(e) were predicted to be 28,469 ± 10 cm(-1) and 1.23214 ± 0.0001 Å, respectively.

Electric dipole moment function and line intensities for the ground state of carbon monxide**Project supported by the National Natural Science Foundation of China (Grant Nos. 11374217 and 11474207).

An accurate electric dipole moment function (EDMF) is obtained for the carbon monoxide (CO) molecule (X1Σ+) by fitting the experimental rovibrational transitional moments. Additionally, an accurate ab initio EDMF is found using the highly accurate, multi-reference averaged coupled-pair functional (ACPF) approach with the basis set, aug-cc-pV6Z, and a finite-field with ±0.005 a.u. (The unit a.u. is the abbreviation of atomic unit). This ab initio EDMF is very consistent with the fitted ones. The vibrational transition matrix moments and the Herman–Wallis factors, calculated with the Rydberg–Klein–Rees (RKR) potential and the fitted and ab initio EDMFs, are compared with experimental measurements. The consistency of these line intensities with the high-resolution transmission (HITRAN) molecular database demonstrates the improved accuracy of the fitted and ab initio EDMFs derived in this work.

Studies on the electric dipole moment function and line parameters for high overtone bands of NO

An accurate electric dipole moment function (EDMF) has been obtained by fitting the best available data including the pure rotational band 0–0 for individual ro-vibrational transitions for nitric oxide. Line intensities calculated using the fitted EDMF agree better with the measurements than the current HITRAN database. Moreover, the accurate ab initio potential energy curve (PEC) and EDMF were found using the multi-reference averaged quadratic coupled-cluster (AQCC) approach with the basis set aug-cc-pV6Z (aV6Z). The good agreement of the vibrational transition moments, computed using the Rydberg–Klein–Rees (RKR) potential and the fitted EDMFs, with experiments shows the present fitted EDMF could be more accurate than other fitted ones at the valid range. Our ab initio vibrational transition moments agree better with experimental data than the ones calculated using the previous theoretical PEC and EDMF, especially at the high overtones. We expect that the present study will be helpful for the transitions including high υ and high overtone bands of NO.

Studies on electric dipole moment function and line parameters for high overtone bands of NO

An accurate electric dipole moment function (EDMF) has been obtained by fitting the best available data including the pure rotational band 0–0 for individual ro-vibrational transitions for nitric oxide (NO). Line intensities calculated using the fitted EDMF agree very well with the measurements. Moreover, an accurate ab initio EDMF was also found using the highly accurate MRCI approach with the basis set aug-cc-pV6Z using a finite field. The ab initio EDMF is more consistent with the fitted ones than found in previous theoretical results of Langhoff et al. The good agreement of the vibrational transition moments, computed using the Rydberg–Klein–Rees (RKR) potential and fitted EDMFs, with experiments shows our fitted EDMF could be more accurate than other fitted ones at the valid range. Our ab initio vibrational transition moments agree well not only with experimental data but also with our fitted results for experimentally unobserved bands. By combining RKR potential and the ab initio EDMF, we further predict the Einstein coefficients, which can help measure in the transitions including high υ and high overtone bands of NO.

The accurate transition dipole moment and line intensities of NO(X2П) based on averaged quadratic coupled-cluster calculations

For NO(X2П), the vibrational dipole moments calculated using previous accurate ab initio electric dipole moment functions (EDMFs) are not consistent with experiments, especially for high-overtone bands 3–0, 4–0, 21–17, 5–0, 6–0, and 7–0. Moreover, the band intensities of the current HITRAN database agree only roughly with recent experimental results for high-overtone bands 3–0, 4–0, and 5–0. Thus, further theoretical calculation is necessary. We adopt the highly accurate multi-reference averaged quadratic coupled-cluster (MR-AQCC) approach and four different basis sets to investigate the potential-energy curves (PECs) and EDMFs of NO(X2П). The PECs and EDMFs obtained using the aug-cc-pV6Z basis set agree well with Rydberg–Klein–Rees (RKR) potential and experimental EDMFs. They are used to deduce the vibrational dipole moments and Herman–Wallis factors, which are further be utilized to evaluate line intensities and band intensities. Both the calculated transition dipole moments and the calculated band intensities are in remarkably better agreement with the experimental results for high-overtone bands. The Herman–Wallis factors of band 7–0 are also fairly consistent between experiment and our result. We expect that these reliable and accurate theoretical results will be helpful in producing accurate theoretical predictions concerning the spectroscopic characteristics and the analysis of some experimentally measured properties of NO(X2П).

Calculation of vibrational matrix elements of the CO2 molecule in the formalism of polynomials of the quantum numbers

The vibrational energies and the matrix elements of the electric dipole moment function and the rotation function are calculated for an arbitrary linear polyatomic molecule in the first order of perturbation theory using the formalism of polynomials of quantum numbers. The formulas obtained are tested for the example of the CO2 molecule. The experimental data available at present are briefly analyzed. It is shown that the calculated matrix elements are in good agreement with the corresponding experimental data even in the first order of the theory.

Population redistribution in optically trapped polar molecules

We investigate the rovibrational population redistribution of polar molecules in the electronic ground state induced by spontaneous emission and blackbody radiation. As a model system we use optically trapped LiCs molecules formed by photoassociation in an ultracold two-species gas. The population dynamics of vibrational and rotational states is modeled using an ab initio electric dipole moment function and experimental potential energy curves. Comparison with the evolution of the v″ = 3 electronic ground state yields good qualitative agreement. The analysis provides important input to assess applications of ultracold LiCs molecules in quantum simulation and ultracold chemistry.

Accurate Potential Energy Surface and Calculated Spectroscopic Properties for CdH2 Isotopomers

Ab initio calculations employing the coupled cluster method CCSD(T), in conjunction with a small-core pseudopotential for the cadmium atom, have been employed to construct a near-equilibrium potential energy function (PEF) and an electric dipole moment function (EDMF) for CdH(2). The significance of the spin-orbit interaction was checked and found to be of minor importance. Making use of two pieces of experimental information for the most abundant isotopomer (114)CdH(2), we obtained a refined PEF, which, within variational calculations of rovibrational states and wave functions, reproduces all available experimental data (S. Yu, A.Shayesteh, and P. F. Bernath, J. Chem. Phys. 2005, 122, 194301) very well. In addition, numerous predictions are made. In particular, the nu(2) band origins for (114)CdH(2) and (114)CdD(2) are predicted at 605.9 and 436.9 cm(-1), respectively, and the state perturbing the e parity levels of the (0,0(0),1) state of (114)CdH(2) at J = 12-17 is identified as the (0,3(3),0) state. Assignments for further perturbations found in the emission spectra are given as well.

Calculation of rovibronic intensities for triatomic molecules in double-Renner-degenerate electronic states: Application to the X̃ A2″ and à A2′ electronic states of HO2

An algorithm and a computer program implementing it are presented for calculation of the rovibronic intensities for a triatomic molecule in a "double-Renner-degenerate" electronic state. The program has been applied to investigate, by theoretical simulation, the absorption spectrum of HO(2) in the X (2)A(") and A (2)A(') electronic states. The spectrum simulations are based on potential energy functions, electric dipole moment functions, and electric dipole transition moment functions constructed from ab initio values calculated at the core-valence MR-SDCI+Q/[cc-pVQZ (H), aug-cc-pCVQZ (O)] level of theory.

Electric dipole rovibrational transitions in the HD molecule

The rovibrational electric dipole transitions in the ground electronic state of the HD molecule are studied. A simple, yet rigorous formula is derived for the transition rates in terms of the electric dipole moment function $D(R)$, which is calculated in a wide range of $R$. Our numerical results for transition rates are in moderate agreement with experiments and previous calculations, but are at least an order of magnitude more accurate.

Erratum: “Theoretical transition probabilities for the OH Meinel system” [J. Chem. Phys. 126, 114314 (2007)

about 2.5% or 1.4 ms. Furthermore, we found a phase difference in the basis sets used to implement the rotational Hamiltonian of Eq. 2 and the lambda-doubling Hamiltonian of Eqs. 8–10. Finally, we found an inconsistency in the implementation of the spin-orbit Hamiltonian. The equations in the paper are consistent. In the new calculations we also replace the re = 1.8342a0 value by a more recent value 3 of re = 1.8324a0. The new calculations affect the numbers in Tables IV and V, which are reproduced here in Tables I and II. Our electric dipole moment function yields slightly higher values for the expectation values of the dipole moment than experimentally observed. Therefore, in Table II, we also include a lifetime based on our dipole moment function scaled with a factor of 0.9966. This is the average ratio between the experimentally observed v =0,1,2 dipole moment and our ab initio values. Finally, we make available a new EPAPS document 4 based on the corrected calculations. The line strengths are computed using the partition function QT = 296 = 80.362 from the HITRAN database. The changes reported here do not significantly alter our conclusions.

Radiative transition probabilities in the [formula omitted] state of [formula omitted

Using ab initio calculated potential energy and electric dipole moment functions, absolute radiative transition probabilities between the rovibronic Renner–Teller states of the electronic ground state X 2 Π g of CO 2 + have been evaluated. The rovibronic eigenstates were obtained (up to 6500 cm - 1 and J ⩽ 13 2 ) from variational calculations including the Renner–Teller and spin–orbit angular momentum couplings. The absolute intensities for the rovibrational states of the neutral CO 2 electronic ground state, calculated by a similar approach, are found to be in excellent agreement with experimental data. For CO 2 + the presented results are expected to have similar accuracy. It is found that the overtone intensities of the antisymmetric stretching mode of CO 2 + are of similar magnitude as the fundamental transitions, in contrast with CO 2 . The theoretically generated IR-emission spectrum is compared with the limb spectrum of the Mars atmosphere, measured by the Thermal Emission Spectrometer on Mars Global Surveyor.