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The analysis and modeling of high-resolution spectra of nonrigid molecules require a specific Hamiltonian and group-theoretical formulation that differs significantly from that of more familiar rigid systems. Within the framework of Hougen–Bunker–Johns (HBJ) theory, this paper is devoted to the construction of a nonrigid Hamiltonian based on a suitable combination of numerical calculations for the nonrigid part in conjunction with the irreducible tensor operator method for the rigid part. For the first time, a variational calculation from ab initio potential energy surfaces is performed using the HBJ kinetic energy operator built from vibrational, large-amplitude motion, and rotational tensor operators expressed in terms of curvilinear and normal coordinates. Group theory for nonrigid molecules plays a central role in the characterization of the overall tunneling splittings and is discussed in the present approach. The construction of the dipole moment operator is also examined. Validation tests consisting of a careful convergence study of the energy levels as well as a comparison of results obtained from independent computer codes are given for the nonrigid molecules CH2, CH3, NH3, and H2O2. This work paves the way for the modeling of high-resolution spectra of larger nonrigid systems. [ABSTRACT FROM AUTHOR]

A simple and intuitive symmetry-based method for deriving the vibration–rotation kinetic energy operator (in polyspherical coordinates) for a general polyatomic molecule using the kinetic energy of a triatomic molecule was considered. Two vectors define the molecule-fixed coordinate system. For example, those vectors can determine positions of two atoms with respect to the third atom. By rotating the coordinate system, it is possible to obtain expressions that relate coefficients determining the kinetic energy in two coordinate systems. Those expressions let us obtain formulas for kinetic energy of general polyatomic molecules from kinetic energy of the triatomic molecules. Vibrational Energy levels of COF2 molecules were calculated from new ab initio potential energy surface. The comparison of the calculated and experimental vibrational energy levels is also reported. [ABSTRACT FROM AUTHOR]

In this work, we report rovibrational energy levels for four isotopologues of methylene (CH2, CHD, CD2, and 13CH2) in their ground triplet electronic state (X~3B1) from variational calculation up to ~10,000 cm−1 and using a new accurate ab initio potential energy surface (PES). Triplet methylene exhibits a large‐amplitude bending vibration and can reach a quasilinear configuration due to its low barrier (~2000 cm−1). To construct the ab initio PES, the Dunning's augmented correlation‐consistent core‐valence orbital basis sets were employed up to the sextuple‐ζ quality [aug‐cc‐pCVXZ, X = T, Q, 5, and 6] combined with the single‐ and double‐excitation unrestricted coupled cluster approach with a perturbative treatment of triple excitations [RHF‐UCCSD(T)]. We have shown that the accuracy of the ab initio energies is further improved by including the corrections due to the scalar relativistic effects, DBOC and high‐order electronic correlations. For the first time, all the available experimental rovibrational transitions were reproduced with errors less than 0.12 cm−1, without any empirical corrections. Unlike more "traditional" nonlinear triatomic molecules, we have shown that even the energies of the ground vibrational state (000) with rather small rotational quantum numbers are strongly affected by the very pronounced rovibrational resonance interactions. Accordingly, the polyad structure of the vibrational levels of CH2 and CD2 was analyzed and discussed. The comparison between the energy levels obtained from the effective Watson A‐reduced Hamiltonian, from the generating‐function approach and from a variational calculation was given. [ABSTRACT FROM AUTHOR]

Variationally computed infrared spectra in the range [0-5000] cm−1 are reported for the deuterated PH2D and PHD2 molecules from accurate potential energy and dipole moment surfaces initially derived for the major isotopologue PH3( C 3 v ). Energy level and line intensity calculations were performed by using a normal-mode model combined with isotopic and symmetry transformations for the H → D substitutions. Theoretical spectra were computed at 296 K up to Jmax = 30 and will be made available through the TheoReTS information system (http://theorets.univ-reims.fr, http://theorets.tsu.ru). For the very first time, ab initio intensity predictions of PH2D/PHD2 are in good qualitative agreement with the literature. This work will be useful for spectral intensity analysis for which accurate spectral intensity data are still missing. [ABSTRACT FROM AUTHOR]

In this work, we report calculated vibrational energy levels of the methane molecule up to 10 300 cm−1. Two potential energy surfaces constructed in quite different coordinate systems with different analytical representations are employed in order to evaluate the uncertainty of vibrational predictions. To calculate methane energy levels, we used two independent techniques of the variational method. One method uses an exact kinetic energy operator in internal curvilinear coordinates. Another one uses an expansion of Eckart-Watson nuclear motion Hamiltonian in rectilinear normal coordinates. In the Icosad range (up to five vibrational quanta bands–below 7800 cm−1), the RMS standard deviations between calculated and observed energy levels were 0.22 cm−1 and 0.41 cm−1 for these two quite different approaches. For experimentally well-known 3v3 sub-levels, the calculation accuracy is estimated to be ∼1 cm−1. In the Triacontad range (7660-9188 cm−1), the average error of the calculation is about 0.5 cm−1. The accuracy and convergence issues for higher energy ranges are discussed. [ABSTRACT FROM AUTHOR]

Full 9-dimensional ab initio potential energy surfaces for the methane molecule are constructed using extended electronic structure coupled-cluster calculations with various series of basis sets following increasing X cardinal numbers: cc-pVXZ (X = 3, 4, 5, 6), aug-cc-ACVXZ (X = 3, 4, 5), and cc-pCVXZ-F12 (X = 3, 4). High-order dynamic electron correlations including triple and quadrupole excitations as well as relativistic and diagonal Born-Oppenheimer breakdown corrections were accounted for. Analytical potential functions are parametrized as non-polynomial expansions in internal coordinates in irreducible tensor representation. Vibrational energy levels are reported using global variational nuclear motion calculations with exact kinetic energy operator and a full account of the tetrahedral symmetry of CH4. Our best ab initio surface including above-mentioned contributions provides the rms (obs.-calc.) errors of less than 0.11 cm-1 for vibrational band centers below 4700 cm-1, and ~0.3 cm-1 for all 229 assigned experimentally determined vibrational levels up to the Icosad range <7900 cm-1 without empirically adjusted parameters. These results improve the accuracy of ab initio methane vibrational predictions by more than an order of magnitude with respect to previous works. This is an unprecedented accuracy of first-principles calculations of a five-atomic molecule for such a large data set. New ab initio potential results in significantly better band center predictions even in comparison with best available empirically corrected potential energy surfaces. The issues related to the basis set extrapolation and an additivity of various corrections at this level of accuracy are discussed. [ABSTRACT FROM AUTHOR]

A simultaneous use of the full molecular symmetry and of an exact kinetic energy operator (KEO) is of key importance for accurate predictions of vibrational levels at a high energy range from a potential energy surface (PES). An efficient method that permits a fast convergence of variational calculations would allow iterative optimization of the PES parameters using experimental data. In this work, we propose such a method applied to tetrahedral AB4 molecules for which a use of high symmetry is crucial for vibrational calculations. A symmetry-adapted contracted angular basis set for six redundant angles is introduced. Simple formulas using this basis set for explicit calculation of the angular matrix elements of KEO and PES are reported. The symmetric form (six redundant angles) of vibrational KEO without the sin(q)-2 type singularity is derived. The efficient recursive algorithm based on the tensorial formalism is used for the calculation of vibrational matrix elements. A good basis set convergence for the calculations of vibrational levels of the CH4 molecule is demonstrated. [ABSTRACT FROM AUTHOR]

A rovibrational model based on the normal-mode complete nuclear Hamiltonian is applied to methane using our recent potential energy surface [A. V. Nikitin, M. Rey, and Vl. G. Tyuterev, Chem. Phys. Lett. 501, 179 (2011)]. The kinetic energy operator and the potential energy function are expanded in power series to which a new truncation-reduction technique is applied. The vibration-rotation Hamiltonian is transformed systematically to a full symmetrized form using irreducible tensor operators. Each term of the Hamiltonian expansion can be thus cast in the tensor form whatever the order of the development. This allows to take full advantage of the symmetry properties for doubly and triply degenerate vibrations and vibration-rotation states. We apply this model to variational computations of energy levels for 12CH4, 13CH4, and 12CD4. [ABSTRACT FROM AUTHOR]

Vibrational energy levels of the PH3, PH2D, and PHD2 molecules were calculated from the new extended potential energy surface (PES) determined in this work. The coupled-cluster approach with the perturbative inclusion of the connected triple excitations CCSD(T) and correlation consistent polarized valence basis set cc-pV5Z was employed in the ab initio calculations of electronic ground state energies. The contribution of relativistic effects to the overall electronic energy surface was computed using quasirelativistic mass-velocity-Darwin approach. These ab initio points were fitted by a parametrized function with one parameter empirically adjusted. The grid of 11 697 geometrical nuclear configurations covers a large domain of the six dimensional internal coordinate space and was designed to provide vibration energy levels of phosphine molecule up to 7000 cm-1 above the zero point vibration energy with reasonable accuracy. The analytical representation of the PES was determined through the expansion in symmetry adapted products of nonlinear internal coordinates for various orders of analytical expansions up to the tenth order. The dependence of calculated vibration energy levels on the analytical representation of PES and on the coordinate choice was studied. Calculated vibration levels are in very good agreement with observations: The root mean squares deviation between theoretically calculated and observed band centers is 1.4 cm-1 for PH3, 0.4 cm-1 for PH2D, and 0.6 cm-1 for PHD2. [ABSTRACT FROM AUTHOR]

• Ab initio potential energy surface was reported. • Vibrational levels of acetylene were calculated. • Accurate prediction of the J dependence of (e–f) splitting was calculated. • 13C2H2 and C2D2 vibrational energy levels were calculated. Ro-vibrational energy levels of acetylene are reported using variational nuclear motion calculations from new ab initio and empirically optimized full six-dimensional potential energy surfaces in the ground electronic state of the acetylene molecule. The calculations account for the triple, quadruple and quintuple excitations as well as relativistic and diagonal Born-Oppenheimer corrections. Variational nuclear motion calculations were performed using the exact kinetic energy operator in orthogonal coordinates. The convergence of energy levels calculations versus the size of the vibrational basis set functions was verified. Our best ab initio potential energy surface that includes the above-mentioned contributions provides the RMS (obs.-calc.) errors of 0.95 cm−1 for five fundamental energy levels. The largest contribution to the RMS error is caused primarily by a significant deviation of the ν 4 fundamental frequency. Experimental values of 120 vibrational band origins were used to empirically adjust few lower-order parameters of the potential energy surface. The average error drops down to 0.45 cm−1 or 0.25 cm−1 for empirically optimized potential energy function with two or seven adjusted parameters corresponding to quadratic force field terms and one third order term. The splitting of (e – f) rovibrational doublets and their J dependence were calculated with high accuracy due to the full account of Coriolis interactions. Computed (e – f) splittings allow one to check the correctness of the assignment of empirical energy levels. The estimation of the accuracy for the calculated vibrational levels in an extended range up to 9500 cm−1 shows that the set of ab initio vibrational levels can be used for future assignments of empirically not observed ro-vibrational energy levels. The comparison of the calculated and experimental ro-vibrational energy levels of the C 2 D 2 and 13C 2 H 2 isotopologues is also reported. [ABSTRACT FROM AUTHOR]

Nine-dimensional potential energy surface (PES) and dipole moment surface (DMS) of the germane molecule are constructed using extended ab initio CCSD(T) calculations at 19 882 points. PES analytical representation is determined as an expansion in nonlinear symmetry adapted products of orthogonal and internal coordinates involving 340 parameters up to eighth order. Minor empirical refinement of the equilibrium geometry and of four quadratic parameters of the PES computed at the CCSD(T)/aug-cc-pVQZ-DK level of the theory yielded the accuracy below 1 cm-1 for all experimentally known vibrational band centers of five stable isotopologues of 70GeH4, 72GeH4, 73GeH4, 74GeH4, and 76GeH4 up to 8300 cm-1. The optimized equilibrium bond re = 1.517 594 Å is very close to best ab initio values. Rotational energies up to J = 15 are calculated using potential expansion in normal coordinate tensors with maximum errors of 0.004 and 0.0006 cm-1 for 74GeH4 and 76 GeH4. The DMS analytical representation is determined through an expansion in symmetry-adapted products of internal nonlinear coordinates involving 967 parameters up to the sixth order. Vibration--rotation line intensities of five stable germane isotopologues were calculated from purely ab initio DMS using nuclear motion variational calculations with a full account of the tetrahedral symmetry of the molecules. For the first time a good overall agreement of main absorption features with experimental rotationally resolved Pacific Northwest National Laboratory spectra was achieved in the entire range of 700-5300 cm-1. It was found that very accurate description of state-dependent isotopic shifts is mandatory to correctly describe complex patterns of observed spectra at natural isotopic abundance resulting from the superposition of five stable isotopologues. The data obtained in this work will be made available through the TheoReTS information system. [ABSTRACT FROM AUTHOR]

Accurate basis set convergence of first-principles predictions of rotationally resolved spectra at high energy range is a common challenging issue for variational methods. In this paper, a detailed convergence study for the methane spectra is presented both for vibrational and rotational degrees of freedom as well as for intensities. For this purpose, we use our previously reported nine-dimensional potential energy and dipole moment surfaces of the methane molecule [Nikitin et al. Chem Phys Lett 2011;501:179–86; 2013;565:5–11]. Vibration–rotation calculations were carried out using variational normal mode approach with a full account of the T d symmetry. The aim was to obtain accurate theoretical methane line lists for the wavenumber range beyond currently available spectra analyses. The focus of this paper is the complicated icosad range (6280–7900 cm −1 ) containing 20 bands and 134 sub-bands where over 90% of experimental lines still remain unassigned. We provide variational line lists converged to a “spectroscopic precision” for icosad transitions for T =80 K and T =296 K. The first one contains 70 300 lines and the second one 286 170 lines with the intensity cut-off 10 − 29 cm − 1 / ( molecule cm − 2 ) with J max =18. An average error in line positions of theoretical predictions up to J =15 is estimated as 0.2–0.5 cm −1 from the comparisons with currently analyzed bands. Ab initio line strength calculations give the integrated intensity 4.37 × 10 − 20 cm − 1 / ( molecule cm − 2 ) at T =80 K for the sum of all icosad bands. This is to be compared to the integrated intensity 4.36 × 10 − 20 cm − 1 / ( molecule cm − 2 ) of the experimental icosad line list recorded in Grenoble University [Campargue et al., J Mol Spectrosc 2013;291:16–22] using very sensitive laser techniques. The shapes of absorption bands are also in a good qualitative agreement with experimental spectra. [ABSTRACT FROM AUTHOR]

Abstract: A new potential energy surface of methyl fluoride is constructed using extended ab initio CCSD(T) calculations with the cc-pVQZ basis at 5100 nuclear configurations. Its analytical representation is determined through an expansion in symmetry adapted products of orthogonal coordinates involving 600 parameters up to 6th order. A good convergence for variational calculations of vibrational levels of the CH3F molecule was obtained with a RMS(obs.-calc.) deviation of less than 4cm−1 for fundamental band centers. The equilibrium geometry of the ab initio PES was empirically optimized using experimental J =1 energy levels for four isotopologues 12CH3F, 13CH3F, 12CD3F, and 13CD3F. The resulting variational calculations with the full normal mode Hamiltonian in the irreducible tensor representation gave a RMS(obs.-calc) deviation of 0.00036cm−1 for rotational energies up to J =5 for the major isotopologue. This represents a considerable improvement with respect to available global predictions of vibration and rotational levels of methyl fluoride. [Copyright &y& Elsevier]

This paper illustrates a method for the construction of a symmetry-adapted contracted angular basis set for AB3 molecules. Simple formulas that use this basis set for calculations of the angular matrix elements of the kinetic energy (KE) operator and angular matrix elements of potential energy surface (PES) are reported. The efficient recursive algorithm based on the tensorial formalism is used for the calculation of vibrational matrix elements. The symmetric form of vibration KE operators without the sin(q)-2 type singularity is applied. A good basis set convergence for the calculations of vibrational levels of the PH3 molecule is demonstrated. [ABSTRACT FROM AUTHOR]

Abstract: A new potential energy surface of methane is constructed using extended ab initio CCSD(T) calculations at 19882 points. Its analytical representation is determined through an expansion in symmetry adapted products of orthogonal coordinates involving 276 parameters up to 8th order with the equilibrium bond re =1.08601±0.00004Å and four quadratic parameters scaled to experimental fundamental vibration frequencies. Variational calculations give RMS (obs.-calc.) deviations of 0.085 and 0.25cm−1 for vibration levels of the pentad and octad. Rotational energies up to J =10 are calculated using potential expansion in normal coordinate tensors with maximum errors of 0.0007 and 0.0003cm−1 for 12CH4 and 13CH4. [ABSTRACT FROM AUTHOR]

A theoretical approach to study ro-vibrational molecular states from a full nuclear Hamiltonian expressed in terms of normal-mode irreducible tensor operators is presented for the first time. Each term of the Hamiltonian expansion can thus be cast in the tensor form in a systematic way using the formalism of ladder operators. Pyramidal XY3 molecules appear to be good candidates to validate this approach which allows taking advantage of the symmetry properties when doubly degenerate vibrational modes are considered. Examples of applications will be given for PH3 where variational calculations have been carried out from our recent potential energy surface [Nikitin et al., J. Chem. Phys. 130, 244312 (2009)]. [ABSTRACT FROM AUTHOR]

Abstract: The absorption spectra of the 12CH4 and 13CH4 molecules have been recorded and assigned in the 5560–6200cm−1 region. The effects of isotopic substitution for 12C by 13C on the methane vibrational energy levels have been calculated from an ab initio potential energy surface and compared with experiment. Comparison of the results obtained for two isotopic species allows us to confirm the vibrational assignment for the strongest bands of 12CH4 in this region. Good agreement of ab initio calculations with observed energy levels has been demonstrated. A list of the assigned 13CH4 lines valuable in atmospheric applications is reported. [Copyright &y& Elsevier]

The potential energy surface of the methane molecule in the ground electronic state is ab initio constructed. The CCSD(T) method with the cc-pVQZ basis set is used to calculate the potential energy at 18982 points. The obtained set of points makes it possible to determine the force field up to the tenth order. The modified Gray-Robiette coordinates were used for the construction of the analytical form of the surface. Vibrational energy levels for 12CH4 were calculated up to 6200 cm−1. Calculations performed are compared with experiment and other calculations. [ABSTRACT FROM AUTHOR]

• Ab initio potential energy surface was calculated. • Vibrational levels of formaldehyde were calculated up to 7000 cm−1. • RMS error for 15 known energy levels was 0.25cm−1. • COD2 vibrational energy levels were calculated. Vibrational energy levels of H 2 CO are reported using variational nuclear motion calculations from new ab initio and empirically optimized full 6-dimensional ab initio potential energy surfaces in the ground electronic state of the formaldehyde molecule. Ab initio calculations were carried out using extended electronic structure coupled-cluster calculations accounting for dynamic electron correlations including triple and quadruple excitations as well as relativistic and diagonal Born-Oppenheimer corrections. Variational nuclear motion calculations are compared in different sets of coordinates with exact kinetic energy operator and in normal coordinates with Watson-Eckart kinetic energy operator. Our best ab initio potential energy surface including the above mentioned contributions provides the RMS (obs.-calc.) errors of 0.25 cm−1 for fifteen vibrational band origins without empirically adjusted parameters. The average error drops down to 0.08 cm−1 for an empirically optimized potential energy function with six adjusted parameters corresponding to quadratic force field terms. The estimation of the accuracy for the calculated vibrational levels in an extended range up to 4500 cm−1 shows that the set of ab initio vibrational levels could be more consistent than experimental levels obtained from earlier studies of low resolution spectra. The comparison of the calculated and experimental vibrational energy levels of the D 2 CO isotopologue is also reported. [ABSTRACT FROM AUTHOR]

A 13 C-enriched spectrum of methane ( 13 CH 4 ) was recorded at Doppler-limited resolution (0.0044 cm −1 ) at 80 K covering the entire Tetradecad region in the 4970–6200 cm −1 . In this paper we present the spectral analysis of the lower part of the 13 CH 4 Tetradecad in the 4970–5470 cm −1 region. Starting with a non-empirical effective Hamiltonian derived by high-order Contact Transformations (CT) from the ab initio potential energy surface (PES), the effective Hamiltonian parameters have been determined for this region by extending the previous DAS (Differential Absorption Spectroscopy) spectral analysis for the upper part of the Tetradecad in the 5853–6200 cm −1 region. In total, 1387 rovibrational transitions were assigned belonging to five cold bands of the Tetradecad up to J max  = 11. Their positions were fitted with an rms deviation of 1.6 × 10 −3 cm −1 . Measured line intensities for 737 transitions were modeled using the effective dipole transition moments approach with an rms deviation of about 10%. Finally, the observed transitions were incorporated to fit simultaneously the 13 CH 4 Hamiltonian parameters for the {Ground state / Dyad / Pentad / Octad / Tetradecad} system and the dipole moment parameters for the {Ground state - Tetradecad} system. [ABSTRACT FROM AUTHOR]

[Display omitted] • 16 ab initio PESs of S 2 O were constructed and validated. • The corrections beyond the CCSD(T) level of the theory were included and analyzed. • The coupled cluster energies were extrapolated to the full configuration interaction limit. • For the first time, the agreement within 0.5 cm−1 was achieved for all band origins which were experimentally studied by high-resolution. • The validity of the advanced ab initio methods for molecules with a relatively large number of electrons was demonstrated. • For the first time, band origins of 32S 2 16O, 32S34S16O, 34S32S16O, 32S33S16O, 33S32S16O, and 32S 2 18O were predicted up to 5000 cm−1. In this work, a series of potential energy surfaces (PESs) of S 2 O was constructed in order to get the most accurate ab initio band origins of this massive molecule. The convergence of the coupled cluster energies with respect to both basis set size [aug-cc-pCVXZ, X = T, Q, 5, and 6] and the order of the excitation [CC(n), n = 2, 3, and 4] was analyzed. For the first time, the band origins of 32S 2 16(18)O were variationally calculated with the error of 0.5 cm−1 using the ab initio PES. The vibrational energies of the most abundant six isotopologues of S 2 O were predicted. [ABSTRACT FROM AUTHOR]