Rovibrational Calculations Research Articles

Rovibrational calculations without model Hamiltonians: The infrared and microwave spectra of thiopropynal

AbstractRovibrational configuration interaction theory has been used to study the rotational spectrum and low lying rovibrational states of thiopropynal, a molecule, which has recently been detected in an interstellar cloud. Geometrical parameters, fundamental vibrational transitions and spectroscopic constants are also provided. All calculations rely on an ‐mode representation of the multidimensional potential energy surface, which has been obtained from explicitly correlated coupled‐cluster approaches including core correlation effects and an approximate treatment of high‐order coupled‐cluster terms. Comparison with experimental data is provided for several properties and the agreement was found to be excellent in most cases.

The CuTe Molecule: Theoretical investigation of the electronic structure and dipole moments of the ground and lowest excited states with rovibrational calculations

The multireference configuration interaction calculation MRSDCI (with Davidson correction) has been performed to investigate the potential energy curves, the transition electronic energies Te, the spectroscopic constants (Re, ωe and Be), the transition and permanent dipole moments, and the vibrational levels corresponding to the ground and 18 excited electronic states of the molecule CuTe in the representation 2S+1Λ(+/-) (neglecting the spin–orbit effects), whereas the PECs and the spectroscopic constants have been calculated for 27 states in the representation Ω(+/-) [including the spin–orbit (SO) effects]. The ground state equilibrium bond length and the vibrational frequency have also been investigated using the density functional theory (DFT), where different density functionals with different basis sets have been tested. This study represents the first theoretical study of the excited states of the CuTe molecule. Comparison of the present results with the available experimental ones shows an overall satisfying agreement.

Ab Initio Rovibrational Spectroscopy of the Acetylide Anion.

In this work the rovibrational spectrum of the acetylide anion HCC- is investigated using high-level electronic structure methods and variational rovibrational calculations. Using a composite approach the potential energy surface and dipole surface is constructed from explicitly correlated coupled-cluster accounting for corrections due to core-valence correlation, scalar relativistic effects and higher-order excitation effects. Previous approaches for approximating the latter are critically evaluated. Employing the composite potential, accurate spectroscopic parameters determined from variational calculations are presented. In comparison to the few available reference data the present results show excellent agreement with ground state rotational constants within 0.005% of the experimental value. Intensities determined from the variational calculations suggest the bending fundamental transition ν2 around 510 cm-1 to be the best target for detection. The rather weak CD stretching fundamental ν1 in deuterated isotopologues show a second-order resonance with the (0,20,1) state and the consequences are discussed in some detail. The spectroscopic parameters and band intensities provided for a number of vibrational bands in isotopologues of the acetylide anion should facilitate future spectroscopic investigations.

Comprehensive quantum chemical analysis of the (ro)vibrational spectrum of thiirane and its deuterated isotopologue

The (ro)vibrational spectra of thiirane, c-C2H4S, and its fully deuterated isotopologue, c-C2D4S, have been studied by means of vibrational configuration interaction theory, VCI, its incremental variant, iVCI, and subsequent variational rovibrational calculations, RVCI, which rely on multidimensional potential energy surfaces of coupled-cluster quality including up to four-mode coupling terms. Accurate geometrical parameters, fundamental vibrational transitions and first overtones, rovibrational spectra and rotational spectroscopic constants have been determined from these calculations and were compared with experimental results whenever available. A number of tentative misassignments in the vibrational spectra could be resolved and most results for the deuterated thiirane are high-level predictions, which may guide experiments to come. Besides this, a new implementation of infrared intensities within the iVCI framework has been tested for the transitions of the title compounds and are compared with results obtained from standard VCI calculations.

Spectroscopic Characterization of Diazophosphane—A Candidate for Astrophysical Observations

Quite recently, diazophosphane, HP−N≡N, was synthesized for the first time. This was accomplished by a reaction of PH3 with N2 under UV irradiation at 193 nm. As these two molecules have been observed in different astrophysical environments, as for example, in the circumstellar medium and, in particular, in the AGB star envelope IRC+10216, the question arises whether HPN2 can be found as well. So far there is only the aforementioned experimental work, but neither rotational nor rovibrational data are available. Hence, the lack of accurate line lists, etc. to identify diazophosphane is the subject of this work, including a detailed analysis of the rotational, vibrational, and rovibrational properties for this molecule. Our calculations rely on multidimensional potential energy surfaces obtained from explicitly correlated coupled-cluster theory. The (ro)vibrational calculations are based on related configuration interaction theories avoiding the need for any model Hamiltonians. The rotational spectrum is studied between T = 10 and 300 K. In contrast, the partition functions for HPN2 and DPN2 are given and compared for temperatures up to 800 K. In addition, more than 70 vibrational transitions are calculated and analyzed with respect to resonances. All these vibrational states are considered within the subsequent rovibrational calculations. This allows for a detailed investigation of the infrared spectrum up to 2700 cm−1 including rovibrational couplings and hot bands. The results of this study serve as a reference and allow, for the first time, for the identification of diazophosphane, for example, in one of the astrophysical environments mentioned above.

A theoretical study of propynal under interstellar conditions and beyond, covering low-frequency infrared spectra, spectroscopic constants, and hot bands

ABSTRACTFrom an astrochemical point of view, propynal is a complex organic molecule. Moreover, it is a potential candidate for the formation of prebiotic propanal and propenal. Therefore, this molecule is of particular interest for astrochemical investigations. As it has been detected in the interstellar medium, it is of high relevance in this field of research. Although experimental data are available for the vibrational fundamental bands and rotational constants, experimental data for vibrational overtones and combination bands are scarce and fairly old. Additionally, high-level ab initio calculations are also not reported. In this work, we provide accurate quantum chemical calculations as well as a detailed analysis of vibrational and rovibrational properties for this molecule. The low-frequency spectrum up to $350\, \,\,\text{cm}^{-1}$ has been studied for temperatures between 10 and $300\, \text{K}$. For the same temperature range, partition functions are provided. Furthermore, the impact of hot bands up to room temperature has been investigated. A comparison of our results with experimental data is provided for the rotational constants, geometrical parameters, and a rovibrational spectrum. The underlying potential energy surface within these calculations is based on explicitly correlated coupled-cluster theory and includes up to four-mode coupling terms within an n-mode expansion. The vibrational and rovibrational calculations rely on vibrational and rovibrational configuration interaction theories, respectively.

Rovibrational states calculations of the H2O-HCN heterodimer with the multiconfiguration time dependent Hartree method.

Water and hydrogen cyanide are two of the most common species in space and the atmosphere with the ability of binding to form dimers such as H2O-HCN. In the literature, while calculations characterizing various properties of the H2O-HCN cluster (equilibrium distance, vibrational frequencies and rotational constants) have been done in the past, extensive calculations of the rovibrational states of this system using a reliable quantum dynamical approach have yet to be reported. In this work, we intend to mend that by performing the first calculation of the rovibrational states of the H2O-HCN van der Waals complex on a recently developed potential energy surface. We use the block improved relaxation procedure implemented in the Heidelberg MultiConfiguration Time-Dependent Hartree (MCTDH) package to compute the states of the H2O-HCN isomer, from which we extract the transition frequencies and rotational constants of the complex. We further adapt an approach first suggested by Wang and Carrington-and supported here by analysis routines of the Heidelberg MCTDH package-to properly characterize the computed rovibrational states. The subsequent assignment of rovibrational states was done by theoretical analysis and visual inspection of the wavefunctions. Our simulations provide a Zero Point Energy (ZPE) and intermolecular vibrational frequencies in good agreement with past ab initio calculations. The transition frequencies and rotational constants obtained from our simulations match well with the available experimental data. This work has the broad aim to propose the MCTDH approach as a reliable option to compute and characterize rovibrational states of van der Waals complexes such as the current one.

Theoretical studies of the excited electronic states of the molecule ScLi and its ions ScLi± with a feasibility study of laser cooling

For the transition metal lithides ScLi and ScLi±, the adiabatic potential energy and the static and transition dipole moment curves of the low-lying electronic states in the representation 2 s+1Λ(+/−) have been investigated. The spectroscopic constants, the electronic transition energy with respect to the ground state Te, the internuclear distance Re, the harmonic frequency ωe, the rotational constant Be, the permanent dipole moment µe, and the dissociation energies De have been computed for the bound and excited states. Using the canonical function approach, these calculations have been followed by a rovibrational calculation from which the rovibrational constants Ev, Bv, and Dv and the abscissas of the turning points Rmin and Rmax for the investigated bound states are calculated. A feasibility study of laser cooling of ScLi and its ions ScLi± has been done. New 62 electronic states have been investigated in the present work for the first time. No useful cooling scheme was found for those molecules.

Determination of spectroscopic constants from rovibrational configuration interaction calculations

Rotational constants and centrifugal distortion constants of a molecule are the essence of its rotational or rovibrational spectrum (e.g., from microwave, millimeter wave, and infrared experiments). These parameters condense the spectroscopic characteristics of a molecule and, thus, are a valuable resource in terms of presenting and communicating spectroscopic observations. While spectroscopic parameters are obtained from experimental spectra by fitting an effective rovibrational Hamiltonian to transition frequencies, the ab initio calculation of these parameters is usually done within vibrational perturbation theory. In the present work, we investigate an approach related to the experimental fitting procedure, but relying solely on ab initio data obtained from variational calculations, i.e., we perform a nonlinear least squares fit of Watson's A- and S-reduced rotation-vibration Hamiltonian to rovibrational state energies (resp. transition frequencies) from rotational-vibrational configuration interaction calculations. We include up to sextic centrifugal distortion constants. By relying on an educated guess of spectroscopic parameters from vibrational configuration interaction and vibrational perturbation theory, the fitting procedure is very efficient. We observe excellent agreement with experimentally derived parameters.

Molecular frames for a symmetry-adapted rotational basis set

In molecular ro-vibrational calculations, it is desirable to build a symmetry-adapted basis set where both the rotational and vibrational functions are each separately symmetrised. Enabling rotational symmetrisation requires the use of body-fixed frames whose rotations under molecular symmetry operations are constant. The familiar Eckart and Sayvetz frames are examples of such frames, as are bisector frames for certain molecules. In this work, we introduce alternative frames for CH3Cl-type molecules and C2H6 that can be used for rotational symmetrisation. These are defined by the vibrational coordinates without the need for a reference geometry. We also provide one method to find such frames. Finally, we state a straightforward transformation of the s-vectors when changing frames which facilitates the evaluation of kinetic energy operators in these non-standard frames.

A comprehensive study of the radiative properties of NO—a first step toward a complete air opacity

In this paper we propose a methodology to calculate the radiative properties of the diatomic molecular constituents of air, and utilize the present approach to model the radiative properties of nitrogen monoxide, NO. We also investigate the important physics involved in calculating accurate radiative quantities for air, such as the Planck and Rosseland mean opacities, and emission and absorption coefficients, as well as the couplings accounted for in rovibrational calculations. Complete active space self-consistent field multi-reference configuration interaction (CAS-MRCI) calculations were performed in order to model the NO X 2Π, a 4Π, b 4Σ−, 12Σ+, 22Σ+, 32Σ+, G 2Σ−, B′2Δ, (C, B) 22Π, (H′, L) 32Π, and 12Φ adiabatic states, and calculate the respective molecular data. The γ X 2Π − A 2Σ+, ɛ X 2Π − D 2Σ+, β′ X 2Π − B′2Δ, ‘11 000 Å’ A 2Σ+ − D 2Σ+, ‘infrared’ X 2Π − X 2Π and X 2Π − (C, B) 22Π (δ and β) band systems are investigated in monochromatic spectra calculations, as well as the Ogawa a 4Π − b 4Σ− band and several other band systems. Several conclusions are drawn, such as the importance of including the Ogawa band, which has not been included in previous air radiative models or comprehensive line-list calculations, as well as the importance of performing coupled rovibrational line-list calculations in order to accurately calculate the Rosseland means. We also found that the additional band systems modeled here contribute significantly to the total Planck and Rosseland means.

Quantum chemical rovibrational analysis of aminoborane and its isotopologues.

Aminoborane, H2 NBH2 and its isotopologues, H2 N10 BH2 , D2 NBD2 , and D2 N10 BD2 , have been studied by high-level ab initio methods. All calculations rely on multidimensional potential energy surfaces and dipole moment surfaces including high-order mode coupling terms, which have been obtained from electronic structure calculations at the level of explicitly correlated coupled-cluster theory, CCSD(T)-F12, or the distinguishable cluster approximation, DCSD. Subsequent vibrational structure calculations based on second-order vibrational perturbation theory, VPT2, and vibrational configuration interaction theory, VCI, were used to determine rotational constants, centrifugal distortion constants, vibrationally averaged geometrical parameters and (an)harmonic vibrational frequencies. The impact of core-correlation effects is discussed in detail. Rovibrational VCI calculations were used to simulate the gas phase spectra of these species and an in-depth analysis of the ν7 band of aminoborane is provided. Color-coding is used to reveal the identity of the individual progressions of the rovibrational transitions for this particular mode.

Theoretical investigation of the electronic structure of the ground and lowest excited states with dipole moment and rovibrational calculations of the CuSe molecule

The potential energy curves of 24 doublet and quartet electronic states in the representation 2S+1Λ(+/−) of the molecule CuSe have been investigated via ab initio CASSCF and MRSDCI calculations. The corresponding electronic energy Te, the harmonic frequency ωe, the internuclear distance Re, the rotational constant Be, the permanent dipole moments and the vibrational levels have been calculated. The ground state has also been investigated by CCSD(T) and different density functional DFT methods using different basis sets. The present work represents the first theoretical study of the electronic structure of the excited states of CuSe.

Variational rovibrational calculations for tetra atomic linear molecules using Watson’s isomorphic Hamiltonian: II. The B11244 story retold

A new six-dimensional near-equilibrium potential energy function for propynylidynium (l-C3H+) is developed based on a high-level composite ab initio method. The importance of higher-order correlation contributions to the composite potential is clearly demonstrated. Variational rovibrational calculations were performed using the new C8v4 program based on Watson’s isomorphic Hamiltonian and a basis of symmetrized harmonic oscillator/rigid rotor product wave functions. The results of these calculations employing the new composite potential as well as a previously constructed quartic force field rectify long-standing discrepancies between theory and experiment. Effective Hamiltonian fits yield a ground state rotational parameter within 5 MHz of the experimental result and a quartic centrifugal distortion constant in virtual agreement with experiment. Spectroscopic parameters for low-lying excited vibrational states are presented which should provide a starting point in forthcoming experimental studies on l-C3H+. A close relationship can be established by comparing the properties of l-C3H+ with floppy C3 from which follows that l-C3H+ behaves in many respects like a “protonated”, albeit more rigid, C3.

Variational rovibrational calculations for tetra atomic linear molecules using Watson’s isomorphic Hamiltonian, I: The C8v4 approach

The implementation of an algorithm for the variational determination of rovibrational state energies and wave functions for linear tetra atomic molecules is presented. The approach, termed C8v4, is based on Watson’s isomorphic Hamiltonian formulated in normal coordinates. Products of harmonic oscillator and rigid-rotor functions are used to expand the rovibrational wave function. Intricacies related to the coupling of the bending–rotation basis and the vibrational angular momentum in linear molecules require a careful study of symmetry properties to set up a symmetry adapted basis set. Kinetic energy matrix elements can be evaluated in a fast mixed numerical/analytical fashion. The main computational bottlenecks are the integration of the potential energy matrix and the diagonalization of the Hamiltonian. These can be overcome by exploiting the block structure of the Hamiltonian which is discussed in some detail. Test calculations on acetylene (HCCH) and boranimine (HBNH) are presented and the C8v4 results reproduce previous variational calculations based on a Hamiltonian formulated in internal coordinates.

Accurate equilibrium structures of linear triatomic molecules from a combined theoretical–experimental method: The protonated nitrogen molecule, HN[formula omitted

This article examines several strategies which can be used to derive molecular equilibrium structure from experimental data and extends our previously suggested method to HN2+. Full-dimensional rovibrational calculations are carried out for eight isotopologues of HN2+ using two ab initio potential energy representations. Rovibrational energies computed for rotational angular momenta J as high as 15 in both parities are used to derive theoretical vibration–rotation corrections to ground-state rotation constants B0. These results are combined with the available experimentally derived B0 values to determine the r0, rα, and re structures of the ion. Higher-order corrections beyond the vibration–rotation α constants are found to be essential for the structure determination. Our analysis is supported by graphical representations, illustrating the anticorrelation of the structural parameters. The r0 structure is rationalized in terms of a structure projected onto the principal a axis and examined for the isoelectronic series of linear triatomic molecules HCO+, HCN, HN2+, HNC, and HOC+.

Structural investigation for the low-lying electronic states with rovibrational calculations of the alkaline-earth fluoride cations XF+ (X = Be, Mg, Ca)

Due to the lack of theoretical data about the electronic structure on the molecular cations BeF+, MgF+ and CaF+, an accurate ab initio calculations have been investigated for these molecules using the multi-reference configuration interaction plus Davidson correction (MRCI + Q) method. The potential energy curves (PECs) of the low-lying electronic states in the representation 2s+1Ʌ(+/-) of the three alkaline-earth fluoride cations have been computed. The spectroscopic constants Te, Re, ωe, Be, αe, the dipole moment µe, and the dissociation energy De have been calculated for the bound states. Moreover, the transition dipole moment curves (TDMCs) of the (X)1Σ+-(1)1Π, (X)1Σ+-(2)1Σ+ and (1)1Π-(2)1Σ+ transitions have been analyzed. A rovibrational study has been done to investigate the vibrational levels of the bound states and the vibrational constants Ev, Bv, Dv, Rmin and Rmax are calculated. These theoretical results are quite interesting for further experimental works, especially, in the advancement of creation of cold alkaline-earth monofluoride cations in the low-lying vibrational states.

Hadron resonances as rovibrational states * *Supported by the Brazilian funding agencies CNPq – Conselho Nacional de Desenvolvimento Científico e Tecnológico and CAPES – Coordenação de Aperfeiçoamento de Pessoal de Nível Superior

A rovibrational model, including anharmonic, centrifugal, and Coriolis corrections, is used to calculate π, K,N, and Ʃ orbital and radial resonances. The four orbital excitations of the π meson correspond to the b(1235), π2(1670), b 3(2030), and π4(2250) resonances. Its first four radial excitations correspond to the π(1300), π(1800), π(2070), and π(2360) resonances. The orbital excitations of the K meson are interpreted as the K 1(1270), K 2(1770), K 3(2320), and K 4(2500) resonances; its radial excitations correspond to the K(1460) and K(1830) resonances. The N orbital excitations are identified with the N(1520), N(1680), N(2190), N(2220), and N(2600) resonances. The first four radial excitations of the N family correspond to the N(1440), N(1880), N(2100), and N(2300) resonances. The orbital excitations of the Ʃ baryon are associated with the Ʃ(1670), Ʃ(1915), Ʃ(2100), and Ʃ(2250) resonances, whereas its radial excitations are identified with the Ʃ(1660), Ʃ(1770), and Ʃ(1880) resonances. The proposed rovibrational model calculations show a good agreement with the corresponding experimental values and allow for the prediction of hadron resonances, thereby proving to be useful for the interpretation of excited hadron spectra.

Artificial Symmetries for Calculating Vibrational Energies of Linear Molecules

Linear molecules usually represent a special case in rotational-vibrational calculations due to a singularity of the kinetic energy operator that arises from the rotation about the a (the principal axis of least moment of inertia, becoming the molecular axis at the linear equilibrium geometry) being undefined. Assuming the standard ro-vibrational basis functions, in the 3N−6 approach, of the form ∣ν1,ν2,ν3ℓ3;J,k,m⟩, tackling the unique difficulties of linear molecules involves constraining the vibrational and rotational functions with k=ℓ3, which are the projections, in units of ℏ, of the corresponding angular momenta onto the molecular axis. These basis functions are assigned to irreducible representations (irreps) of the C2v(M) molecular symmetry group. This, in turn, necessitates purpose-built codes that specifically deal with linear molecules. In the present work, we describe an alternative scheme and introduce an (artificial) group that ensures that the condition ℓ3=k is automatically applied solely through symmetry group algebra. The advantage of such an approach is that the application of symmetry group algebra in ro-vibrational calculations is ubiquitous, and so this method can be used to enable ro-vibrational calculations of linear molecules in polyatomic codes with fairly minimal modifications. To this end, we construct a—formally infinite—artificial molecular symmetry group D∞h(AEM), which consists of one-dimensional (non-degenerate) irreducible representations and use it to classify vibrational and rotational basis functions according to ℓ and k. This extension to non-rigorous, artificial symmetry groups is based on cyclic groups of prime-order. Opposite to the usual scenario, where the form of symmetry adapted basis sets is dictated by the symmetry group the molecule belongs to, here the symmetry group D∞h(AEM) is built to satisfy properties for the convenience of the basis set construction and matrix elements calculations. We believe that the idea of purpose-built artificial symmetry groups can be useful in other applications.

High-Level Rovibrational Calculations on Ketenimine.

From an astrochemical point of view ketenimine (CH2CNH) is a complex organic molecule (COM) and therefore likely to be a building block for biologically relevant molecules. Since it has been detected in the star-forming region Sagittarius B2(N), it is of high relevance in this field. Although experimental data are available for certain bands, for some energy ranges such as above 1200 cm−1 reliable data virtually do not exist. In addition, high-level ab initio calculations are neither reported for ketenimine nor for one of its deuterated isotopologues. In this paper, we provide for the first time data from accurate quantum chemical calculations and a thorough analysis of the full rovibrational spectrum. Based on high-level potential energy surfaces obtained from explicitly correlated coupled-cluster calculations including up to 4-mode coupling terms, the (ro)vibrational spectrum of ketenimine has been studied in detail by variational calculations relying on rovibrational configuration interaction (RVCI) theory. Strong Fermi resonances were found for all isotopologues. Rovibrational infrared intensities have been obtained from dipole moment surfaces determined from the distinguishable cluster approximation. A comparison of the spectra of the CH2CNH molecule with experimental data validates our results, but also reveals new insight about the system, which shows very strong Coriolis coupling effects.