Equilibrium Rotational Constants Research Articles

Accurate structures and rotational constants of bicyclic monoterpenes at DFT cost by means of the bond-corrected Pisa composite scheme (BPCS).

The structural, conformational, and spectroscopic properties in the gas phase of 20 bicyclic monoterpenes and monoterpenoids have been analyzed by a new accurate, reduced-cost computational strategy. In detail, the revDSD-PBEP86 double-hybrid functional in conjunction with the D3BJ empirical dispersion corrections and a suitable triple-zeta basis set provides accurate geometrical parameters, whence equilibrium rotational constants, which are further improved by proper account of core-valence correlation. Average deviations within 0.1% between computed and experimental rotational constants are reached when taking into account the vibrational corrections obtained by the B3LYP functional in conjunction with a double-zeta basis set in the framework of second-order vibrational perturbation theory. In addition to their intrinsic interest, the studied terpenes further extend the panel of systems for which the proposed strategy has provided accurate results at density functional theory cost. Therefore, a very accurate yet robust and user-friendly tool is now available for systematic investigations of the role of stereo-electronic effects on the properties of large systems of current technological and/or biological interest by experimentally oriented researchers.

Electronic structure, spectroscopy and photophysics of rubidium mono-sulphide

We investigated the nineteen first electronic states of the RbS diatomic using post Hartree-Fock configuration interaction methods at the internally contracted multi-reference configuration interaction (MRCI+(Q)) level. We thus mapped their respective potential energy curves with and without considering spin-orbit effects. After nuclear motion treatments, we derived their equilibrium distances, rotational and vibrational constants, and dissociation and electronic excitation energies. Moreover, an evaluation of the dipole moments of RbS was conducted, which in turn were used to evaluate the radiative lifetimes of the vibrational levels of RbS (X2П and A2Σ+) states. Computations show that spin-orbit interactions are important and cannot be omitted. Afterwards, and utilizing the sum rule approximation and the Franck–Condon factors, we computed both the bound-bound contributions and the bound-free terms. Our findings suggest that RbS exhibits intriguing characteristics suitable for laser cooling experiments. In sum, this work contributes to the understanding in-depth of the spectroscopy of RbS and predicts its use as a promising molecular system for laser cooling applications.

High Accuracy Ab Initio Potential Energy Curves and Dipole Moment Functions for the X1Σ+ and a3Π Spin States of the CF+ Diatomic Molecule.

Potential energy curves and dipole moment functions constructed using high-accuracy ab initio methods allow for an in-depth examination of the electronic structure of diatomic molecules. Ab initio computations serve as a valuable complement to experimental data, offering insights into the nature of short-lived molecules such as those encountered within the interstellar medium (ISM). While laboratory experiments provide critical groundwork, the ISM's conditions often permit longer lifetimes for lower stability molecules, enabling unique observations. The CF+ diatomic molecule is one such molecule that has been observed spectroscopically in the ISM. Previous experimental and theoretical work have examined different spectroscopic aspects of the CF+ molecule, but the development of newer, more complete potential energy curves and dipole moment functions allows for even greater insight. We constructed both potential energy curves and dipole moment functions for the ground X1Σ+ and first excited a3Π states of CF+ for both the 12C and 13C isotopologues. The potential energy curves were constructed using coupled cluster with single, double, and perturbative triple excitations (CCSD(T)) at the complete basis set limit with corrections from full triple, quadruple, quintuple, and hextuple excitations within a finite-basis coupled cluster wave function as well as corrections from full configuration interaction and relativistic effects. Rovibrational wave functions were calculated using a vibrational Hamiltonian matrix, which moves beyond the harmonic oscillator approximation. The equilibrium bond length, vibrational constant, and rotational constant were reproduced to within 0.00013 Å, 0.28 cm-1, and 0.00045 cm-1, respectively, of experimental values. Experimental transition energies from rovibrational spectra were reproduced with an error of no larger than 0.63 cm-1. The triplet excited state (a3Π) was found to have a longer equilibrium bond length at 1.21069 Å, a vibrational constant of 1611.29 cm-1, and a rotational constant of 1.56376 cm-1. Rovibrational line lists for the 12C and 13C isotopologues for both the X1Σ+ and the excited a3Π states were generated.

CCSD(T) Rotational Constants for Highly Challenging C5H2 Isomers-A Comparison between Theory and Experiment.

We evaluate the accuracy of CCSD(T) and density functional theory (DFT) methods for the calculation of equilibrium rotational constants (Ae, Be, and Ce) for four experimentally detected low-lying C5H2 isomers (ethynylcyclopropenylidene (2), pentatetraenylidene (3), ethynylpropadienylidene (5), and 2-cyclopropen-1-ylidenethenylidene (8)). The calculated rotational constants are compared to semi-experimental rotational constants obtained by converting the vibrationally averaged experimental rotational constants (A0, B0, and C0) to equilibrium values by subtracting the vibrational contributions (calculated at the B3LYP/jun-cc-pVTZ level of the theory). The considered isomers are closed-shell carbenes, with cumulene, acetylene, or strained cyclopropene moieties, and are therefore highly challenging from an electronic structure point of view. We consider both frozen-core and all-electron CCSD(T) calculations, as well as a range of DFT methods. We find that calculating the equilibrium rotational constants of these C5H2 isomers is a difficult task, even at the CCSD(T) level. For example, at the all-electron CCSD(T)/cc-pwCVTZ level of the theory, we obtain percentage errors ≤0.4% (Ce of isomer 3, Be and Ce of isomer 5, and Be of isomer 8) and 0.9-1.5% (Be and Ce of isomer 2, Ae of isomer 5, and Ce of isomer 8), whereas for the Ae rotational constant of isomers 2 and 8 and Be rotational constant of isomer 3, high percentage errors above 3% are obtained. These results highlight the challenges associated with calculating accurate rotational constants for isomers with highly challenging electronic structures, which is further complicated by the need to convert vibrationally averaged experimental rotational constants to equilibrium values. We use our best CCSD(T) rotational constants (namely, ae-CCSD(T)/cc-pwCVTZ for isomers 2 and 5, and ae-CCSD(T)/cc-pCVQZ for isomers 3 and 8) to evaluate the performance of DFT methods across the rungs of Jacob's Ladder. We find that the considered pure functionals (BLYP-D3BJ, PBE-D3BJ, and TPSS-D3BJ) perform significantly better than the global and range-separated hybrid functionals. The double-hybrid DSD-PBEP86-D3BJ method shows the best overall performance, with percentage errors below 0.5% in nearly all cases.

Accuracy Meets Feasibility for the Structures and Rotational Constants of the Molecular Bricks of Life: A Joint Venture of DFT and Wave-Function Methods.

A fully unsupervised computational protocol is proposed with the aim of obtaining reliable structural properties for molecular bricks of life in the gas phase. The results of the new composite scheme approach spectroscopic accuracy at a moderate cost without any empirical parameter in addition to those of the underlying electronic structure method. The whole workflow is fully automated and provides optimized geometries and equilibrium rotational constants. Direct comparison with experimental ground state rotational constants can be performed thanks to the effective computation of vibrational corrections in the framework of second-order vibrational perturbation theory. The results for all the nucleic acid bases and several flexible molecules of biological or medicinal interest show that the accuracy of the new tool is close to that delivered by state-of-the-art composite wave function methods for small semirigid molecules.

Rotational spectra of singly substituted rare isotopologues of two conformers of 3,3,3-trifluoropropanol

The conformational distribution and the associated conformational conversion paths of 3,3,3-trifluoropropanol (TFP) were explored experimentally and theoretically using jet-cooled chirped pulse and cavity Fourier transform microwave spectroscopy in tandem with quantum chemical calculations. Rotational spectra of two TFP conformers, as well as their singly substituted 13C, 18O, and OD isotopologues, were measured and analyzed. The semi-experimental equilibrium rotational constants of the two conformers were also extracted for all isotopologues using the anharmonic calculations and used to obtain the semi-experimental equilibrium geometries.

The molecular structure, spectroscopic properties and partition functions of C3H2S isomers: An ab initio study

The anharmonic force fields, spectroscopic constants and partition functions of three isomers of C3H2S have been studied employing B3LYP, B3PW91, M06-2X, MP2 or CCSD(T) methods with 6-311++G (2d,2p) or 6-311++G (3df,2pd) basis sets. The equilibrium geometries, energies, rotational constants, harmonic and fundamental frequencies, centrifugal distortion constants and partition functions of three isomers of C3H2S are calculated and compared with the existing data. The MP2/6-311++G (3df,2pd) results well reproduce the previous theoretical or experimental results, so we predict other spectroscopic properties of C3H2S based on the MP2/6-311++G (3df,2pd) theoretical level. The relationship between structure and spectroscopic properties for three isomers of C3H2S is also analyzed in detail. We hope that the obtained spectroscopic constants and partition functions of C3H2S isomers can provide strong support for further research of spectroscopic properties.

Extending the Applicability of the Semi-experimental Approach by Means of "Template Molecule" and "Linear Regression" Models on Top of DFT Computations.

The accurate determination of equilibrium structures for isolated molecules plays a central role in the evaluation and interpretation of stereoelectronic, thermodynamic, and spectroscopic properties. For small semi-rigid systems, state-of-the-art quantum-chemical computations can rival the most sophisticated experimental results. For larger molecules, cheaper yet accurate approaches need to be defined. The double-hybrid rev-DSD-PBEP86 functional already delivers remarkable results that can be further improved by means of a “Lego brick” model. This is based on the idea that a molecular system can be seen as formed by different fragments (the “Lego bricks”), whose accurate semi-experimental (SE) equilibrium geometries are available. The template molecule (TM) approach can be used to account for the modifications occurring when going from the isolated fragment to the molecular system under investigation, with the linear regression (LR) model employed to correct the linkage between the different fragments. The resulting TM-SE_LR approach has been tested with respect to available SE equilibrium structures and rotational constants. Indeed, the latter parameters straightforwardly depend on the equilibrium geometry of the system under consideration. The main outcome of our study is the reliability, robustness, and accuracy of this novel approach. The molecular systems considered for benchmarking the TM-SE_LR scheme are those formally issued from addition/elimination reactions of nucleophilic unsaturated radicals (e.g., CN, C2H, and phenyl) to alkenes, imines, and aldehydes, whose rotational spectra have been investigated, but accurate structural determinations are not yet available.

Structural and Energetic Properties of Amino Acids and Peptides Benchmarked by Accurate Theoretical and Experimental Data.

Structural, energetic, and spectroscopic data derived in this work aim at the setup of an "experimentally validated" database for amino acids and polypeptides conformers. First, the "cheap" composite scheme (ChS, CCSD(T)/(CBS+CV)MP2) is tested for evaluation of conformational energies of all eight stable conformers of glycine, by comparing to the more accurate CCSD(T)/CBS+CV computations (Phys. Chem. Chem. Phys. 2013, 15, 10094-10111 and J Mol. Model. 2020, 26, 129). The recently proposed jun-ChS (J. Chem. Theory and Comput. 2020, 16, 988-1006), employing the jun-cc-pVnZ basis set family for CCSD(T) computations and CBS extrapolation, yields conformational energies accurate to 0.2 kJ·mol-1, at reduced computational cost with respect to aug-ChS employing aug-cc-pVnZ basis sets. The jun-ChS composite scheme is further applied to derive conformational energies for three dipeptide analogues Ac-Gly-NH2, Ac-Ala-NH2, and Gly-Gly. Finally, dipeptide conformational energies and semiexperimental equilibrium rotational constants along with the CCSD(T)/(CBS+CV)MP2 structural parameters (J. Phys. Chem. Lett. 2014, 5, 534-540) stand as the reference for benchmarking of selected density functional methodologies. The double-hybrid functionals B2-PLYP-D3(BJ) and DSD-PBEP86, perform best for structural and energetic characterization of all dipeptide analogues. From hybrid functionals CAM-B3LYP-D3(BJ) and ωB97X-D3(BJ) represent promising methods applicable for larger peptide-based systems for which computations with double-hybrid functionals are not feasible.

The molecular structure and spectroscopic properties of C3H2O and its isomers: An ab initio study

The spectroscopic parameters and anharmonic force fields of three isomers (c-H2C3O, HCCCHO and CH2CCO) of C3H2O have been calculated by Density Functional Theory (B3LYP, CAM-B3LYP, wB97XD) and second-order Møller-Plesset perturbation theory (MP2) combining with 6–311++G (3df, 3pd) and aug-cc-pVTZ basis sets. The equilibrium geometries, energies, rotational constants, harmonic and fundamental frequencies, and centrifugal distortion constants of three isomers of C3H2O are calculated and compared with the existed results. The anharmonic constants, vibration–rotation interaction constants, Coriolis coupling constants and force constants of three isomers of C3H2O are firstly predicted. The ingredients of complex vibration modes, and infrared spectral characteristics of three isomers as well as the relationship between structure and spectroscopic properties are detailedly discussed.

Precise equilibrium structure determination of thiophene (c-C4H4S) by rotational spectroscopy-Structure of a five-membered heterocycle containing a third-row atom.

The rotational spectrum of thiophene (c-C4H4S) has been collected between 8 and 360GHz. Samples of varying deuterium-enrichment were synthesized to yield all possible deuterium-substituted isotopologues of thiophene. A total of 26 isotopologues have been measured and least-squares fit using A- and S-reduced distorted-rotor Hamiltonians in the Ir representation. The resultant rotational constants (A0, B0, and C0) from each reduction were converted to determinable constants (A″, B″, and C″) to remove the impact of centrifugal distortion. The computed vibrational and electron mass corrections [CCSD(T)/cc-pCVTZ] were applied to the determinable constants to obtain semi-experimental equilibrium rotational constants (Ae, Be, and Ce) for 24 isotopologues. A precise semi-experimental equilibrium (re SE) structure has been achieved from a least-squares fit of the equilibrium moments of inertia. The combination of the expanded isotopologue rotational data with high-level computational work establishes a precise re SE structure for this sulfur-containing heterocycle. The CCSD(T)/cc-pCV5Z structure has been obtained and corrected for the extrapolation to the complete basis set, electron correlation beyond CCSD(T), relativistic effects, and the diagonal Born-Oppenheimer correction. The precise re SE structure is compared to the resulting "best theoretical estimate" structure. Several of the best theoretical re structural parameters fall within the narrow statistical limits (2σ) of the re SE results. The possible origin of the discrepancies for the computed parameters that fall outside the statistical uncertainties is discussed.

Photochemistry from low-lying states of HOSO.

Using configuration interaction ab initio methods, the evolution of the lowest electronic states of singlet and triplet spin multiplicities of HOSO+ along the stretching and bending coordinates of is investigated. Equilibrium geometries, rotational constants, and harmonic vibrational frequencies of the lowest electronic states are calculated, i.e., X1A', 11A″, 13A', and 13A″. The global minimum of the 11A″ state is located below the first dissociation limit and its calculated lifetime is predicted to be 0.40 µs, making it suitable for detection by laser-induced fluorescence. According to the potential energy surfaces, HOSO+ should produce SO2 + and H after ultraviolet photon absorption to the 21A' state. This work opens the door to investigate the branching ratio and the production rates of SO2 +, SO+, and OH from HOSO+. These insights can help understand the SO2 cycle in the earth's atmosphere and its effect on cooling our planet.

Rotational spectra of 2,3,6-trifluoropyridine: Effect of fluorination on ring geometry

The ground state rotational spectrum of 2,3,6-trifluoropyridine has been investigated in the 2.0–20.0 GHz region by pulsed jet Fourier transform microwave spectroscopy. The experimental rotational constants are A=3134.4479(2) MHz, B=1346.79372(7) MHz, and C=941.99495(6) MHz. The transitions are so intense that rotational transitions of all mono-13C and 15N isotopologues are measured in natural abundance. The semi-experimental equilibrium rotational constants of the 7 isotopologues were derived by taking account of the anharmonic vibrational corrections, which allowed a semi-experimental determination of the equilibrium structure of 2,3,6-trifluoropyridine.

Rich Collection of n-Propylamine and Isopropylamine Conformers: Rotational Fingerprints and State-of-the-Art Quantum Chemical Investigation.

The conformational isomerism of isopropylamine and n-propylamine has been investigated by means of an integrated strategy combining high-level quantum-chemical calculations and high-resolution rotational spectroscopy. The equilibrium structures (and thus equilibrium rotational constants) as well as relative energies of all conformers have been computed using the so-called “cheap” composite scheme, which combines the coupled-cluster methodology with second-order Møller–Plesset perturbation theory for extrapolation to the complete basis set. Methods rooted in the density functional theory have been instead employed for computing spectroscopic parameters and for accounting for vibrational effects. Guided by quantum-chemical predictions, the rotational spectra of isopropylamine and n-propylamine have been investigated between 2 and 400 GHz with Fourier transform microwave and frequency-modulation millimeter/submillimeter spectrometers. Spectral assignments confirmed the presence of several conformers with comparable stability and pointed out possible Coriolis resonance effects between some of them.

Spectroscopic constants and anharmonic force fields of F2SO: An ab inito study

The equilibrium geometry, spectroscopic constants and anharmonic force field of F2SO (X∼1A′) have been reported employing B3LYP, B3P86, B3PW91 and MP2 methods combining with Dunning’s correlation-consistent cc-pVQZ, cc-pV5Z, aug-cc-pVQZ and aug-cc-pV5Z basis sets. The calculated equilibrium geometry, equilibrium rotational constants and fundamental vibrational frequencies of F2SO well reproduce the previous theoretical or experimental values. The calculated equilibrium geometry verifies that F2SO has pyramidal structure and Cs symmetry instead of C1 symmetry. The ground-state rotational constants, harmonic vibrational frequencies, anharmonic constants, quartic and sextic centrifugal distortion constants, cubic and quartic force constants, vibration-rotation interaction constants, and Coriolis coupling constants of F2SO are also predicted. The calculated results show that B3P86 and MP2 methods are superior to B3LYP and B3PW91 methods for the spectroscopic constants of F2SO, we hope that our predictions can provide the useful data for the experiment study of the corresponding spectroscopic constants of F2SO.

Accurate equilibrium structures of methyl methacrylate and methacrylic acid by microwave spectroscopy and dispersion corrected calculations.

The rotational constants of s-trans and s-cis methyl methacrylate and methacrylic acid are determined from microwave spectra. All singly substituted heavy-atom isotopologs of the four species are measured in natural abundance. The experimental rotational constants are combined with anharmonic vibrational corrections using the Coulomb-attenuating method, Becke, three-parameter, Lee-Yang-Parr density functional with Grimme's D3 dispersion corrections and the Becke-Johnson damping function, yielding precise semi-experimental equilibrium rotational constants. These constants are used to determine semi-experimental equilibrium structures with sub-picometer accuracy, suitable for benchmarking purposes.

Electronic and vibrational spectroscopy of the low-lying states of potassium mono-sulphide KS, and comparison in the series of MS (M = Li, Na, K, Rb, Cs)

ABSTRACTPotential energy curves (PECs) of the lowest electronic states of the potassium mono-sulphide KS have been determined with highly correlated ab initio calculations, using internally contracted multi reference interaction configuration methods including Davidson correction (MRCI + Q) with and without considering spin-orbit effects. For the three low-lying bound states, we report a set of spectroscopic parameters including equilibrium distances, dissociation energies, vibrational and rotational constants. The effects of spin-orbit-induced changes on these parameters are also discussed. An analysis of the properties of the three bound states, X2Π, 12Σ+ and 22Π, illustrates the common characteristics of the whole series of compounds in the MS family (M = Li, Na, K, Rb, Cs). Indeed, the shapes of the PECs of these bound states are strongly affected by the interactions between the two ionic states, 2Σ+ and 2Π, correlating at large internuclear separations (RMS) to the first ionic dissociation limit [M+ + S−] and the electronic states correlating to the three/four lowest dissociation limits. The spectroscopy of these low-lying electronic states and the lifetime of their vibrational levels are thus affected by the spin-orbit interactions which are mainly related to the S atom and consequently common to all alkali-metal mono-sulphides.

Electronic and Vibrational Spectroscopy of CsS

Using multi configurational ab initio methodologies, we compute the potential energy curves (PECs) of the lowest electronic states of the diatomic CsS. These computations are performed using internally contracted multireference interaction configuration including Davidson correction (MRCI+Q) with and without considering spin-orbit effects. The shapes of the PECs are governed by the interactions between the two ionic states, 2Σ+ and 2Π, correlating at large internuclear separations ( RCsS) to the first ionic dissociation limit and the other electronic states correlating to the three lowest neutral dissociation limits. Computations show the importance of considering a large amount of electron correlation for the accurate description of the PECs and spectroscopy of this molecular system. As expected, these PECs are also strongly affected by the spin-orbit interaction. For the bound states, we report a set of spectroscopic parameters including equilibrium distances, dissociation energies, and vibrational and rotational constants. The effects of spin-orbit-induced changes on these parameters are also discussed. Moreover, we show that the 22Π state presents a "bowl" potential with a rather flat region extending to large RCsS distances. After being promoted to this state, wavepackets should undergo strong oscillations, similar to those observed by Zewail and co-workers for the NaI molecule. These should provide information on the shape of the PEC for the 22Π state and also on the couplings between this and the neighboring states.

Density functional theory of InCn+(n=110) clusters

Small indium-doped carbon clusters InCn+(n=110) are systematically studied by the density functional theory at the B3 LYP/LANL2 DZ level. The computed properties include equilibrium geometries, electronic energies, vibrational frequencies, dipole moments and rotational constants for individual species. The calculation results show that the open-chain linear isomers with the indium atom bound to the end of the carbon chain are the most stable geometry in all cases. There must exist a cyclic or fan structure in the metastable or the third stable structure of cluster. The bigger the size of the cluster, the more obvious the stability of the structure is. The electronic ground state is found to be alternately a triplet for even n and a singlet for odd n with the only exception of InC+. It is generally observed that the spin contamination is not serious for all electronic ground states because the s2 values are uniform and in general deviate slightly from the pure spin values, and the B3 LYP wave functions are nearly spin-pure. It is also found that in the lowest-energy linear structure, the InC bond is longer (from 2.319 to 2.850 ) than the corresponding CC bonds in a range from 1.268 to 1.360 . The CC distances can be assimilated to moderately strong double bonds underlying a clear bonding in the corresponding structures. In addition, we observe a clear alternation in CC distances. The CoddCeven distances are shorter than the CevenCodd ones which mainly results from the charge distribution and spin density. According to the calculation and analysis of the incremental binding energy and the second difference we can deduce an even-odd alternation in the cluster stability for the linear InCn+, with their n-odd members being more stable than the adjacent even-numbered ones. This parity effect also appears in the adiabatic ionization potential curves. The analysis of magnetic properties shows the even-odd alternation with n-even clusters presenting higher values of magnetic moment than n-odd ones. The study of the polarizability indicates that the average values of both the polarization tensors and the anisotropic invariants increase with the size of cluster increasing.

Experimental values of the rotational and vibrational constants of deuterated silyl fluoride

ABSTRACTAccurate experimental values of the αA and αB rotation–vibration interaction, and ωi, xij and gij vibrational constants have been extracted from the most recent high-resolution Fourier transform infrared and millimetre-wave measurements in the spectra of the prolate symmetric top SiD3F, between 400 and 2000 cm−1. From the experimental values of the ground state rotational and rovibrational interaction parameters, accurate equilibrium rotational constants have been derived: Ae = 1.432326 (12) cm−1 and Be = 0.4112012 (45) cm−1 for silyl fluoride. The effective ground state structure has also been determined from the observed moments of inertia of SiD3F: r0(Si-D) = 1.4755 (29) Å; r0(Si-F) = 1.5931 (26) Å; θ0(DSiD) = 110.47 (32)° and θ0(DSiF) = 108.45 (56)°. A merge of equilibrium moments of 28SiH3F and 28SiD3F yielded an experimental equilibrium structure of silyl fluoride. This geometry has been found in good agreement with semi-experimental median values, as well as with the recent semi-experimental ab initio equilibrium structure obtained using all data available of the various isotopic species of silyl fluoride.