Potential Function For Internal Rotation Research Articles

Complex character of internal rotation of furfural in the ground S0 and excited S1 electronic states

Abstracts The forms of potential energy surfaces (PESs), in particular, the potential functions of internal rotation, the heights and forms of potential barriers to internal rotation and the energies of torsional levels, can control some important properties of molecules and substances, as well as the pathways and mechanisms of molecular processes. Usually, the determination of the potential function of internal rotation is based on a one-dimensional model due to missing of the experimental data. However, such potential functions are sufficiently accurate only in the cases in which the internal rotation is separated from the other vibrations. Otherwise, the experimental and calculated (quantum chemical) functions can be in serious disagreement. The investigation of PES sections and the comparison of calculated and experimental energies of some vibrational levels proved that internal rotation of furfural in the ground and the first excited singlet electronic states has complex character: two-dimensional (torsion–CHO out-of-plane deformation) and three-dimensional (torsion–CHO out-of-plane deformation–CHald out-of-plane deformation) approximations, respectively.

Theoretical investigation of intramolecular π-type hydrogen bonding and internal rotation of 2-cyclopropen-1-ol, 2-cyclopropen-1-thiol and 2-cyclopropen-1-amine

ABSTRACTTheoretical computations utilising both CCSD and MP2 methods and the cc-pVTZ basis set have been carried out to determine the structures of several conformations as well as the internal rotation potential energy functions for 2-cyclopropen-1-ol, 2-cyclopropen-1-thiol and 2-cyclopropen-1-amine. The energies and wavefunctions for these potential functions have also been computed. Each of these molecules has an energy minimum corresponding to a conformation with intramolecular π-type hydrogen bonding. The π bonding stabilisation is about 2.3 kcal/mole for the alcohol, 2.1 kcal/mole for the thiol, and about 2.5 kcal/mole for the amine. The results for the thiol demonstrate a rare example of intramolecular π-type hydrogen bonding. The calculated O–H, S–H, N–H, and C=C stretching frequencies have also been compared for the conformations with and without the π-type hydrogen bonding. The C=C stretching frequency is substantially lower in all cases for the hydrogen bonded conformers.

Potential functions of internal rotation of the methacryloyl fluoride molecule in the ground (S0) and excited (S1) electronic states

The potential functions of internal rotation V(φ) (PFIR) of methacryloyl fluoride (MAF) in the ground (S0) and excited (S1) electronic states were reconstructed using the TORSIO program from experimental energy levels of the torsional transitions in the s-trans- and s-cis isomers. The energy levels were obtained from the analysis of the vibrational structure in the high-resolution gas-phase UV spectrum. The (S0) and (S1) equilibrium geometries of the s-trans- and s-cis rotational isomers of MAF as well as structural parameters for a set of points along the relaxed geometry scans, which were used to find expansion coefficients of kinematic function F(φ) in the Fourier series, were calculated using extended multiconfiguration quasi-degenerate perturbation theory, XMCQDPT2/SA(2)-CASSCF(6,5)/aug-cc-pVTZ. The ground (S0) state calculations were also done at the MP2 level of theory. In (S0) state, parameters Vn., barriers of internal rotation ΔH‡ and ΔH of MAF isomers were calculated using two theories. The calculated values of Vn, ΔH‡, ΔH in (S0) state are in good agreement with those derived from the vibrationally resolved UV spectrum of MAF in the gas phase. Within the one-dimensional model, the experimentally derived barrier heights that hinder internal rotation in MAF were found to be 2100 ± 50 cm−1 and 4950 ± 250 cm−1 in the (S0) and (S1) states, respectively. The parameters Vn and ΔH‡ in (S1) state are determined for first time.

Internal Rotation of Methylcyclopropane and Related Molecules: Comparison of Experiment and Theory.

The internal rotation about the single bond connecting a cyclopropyl ring to a CH3, SiH3, GeH3, NH2, SH, or OH group was investigated. Both CCSD/cc-pVTZ and MP2/cc-pVTZ ab initio calculations were performed to predict the structures of these molecules and their internal rotation potential energy functions in terms of angles of rotation. The barriers to internal rotation for the CH3, SiH3, and GeH3 molecules from the calculations agree well with the experimental ones, within -11% to +1% for CCSD/cc-pVTZ and -4% to +9% for MP2/cc-pVTZ. Comparisons between theory and experiment were also performed for propylene oxide and propylene sulfide, and the agreements were very good. Theoretical calculations were performed to compute the internal rotation potential energy function for cyclopropanol, and these were used to guide the determination of a potential function based on experimental data. This molecule has two equivalent synclinal (gauche) conformers with an estimated barrier of 759 cm(-1) (9.1 kJ/mol) between them. The minima are at internal rotation angles of the OH group of 109° and 251°. The theoretical potential functions for cyclopropanethiol and cyclopropylamine were also calculated, and these agree reasonably well with previous experimental studies.

Potential function of the internal rotation of a methacrolein molecule in the ground (S 0) electronic state

The structural parameters of s-trans- and s-cis-isomers of a methacrolein molecule in the ground (S0) electronic state are determined by means of MP2 method with the cc-pVTZ basis set. Kinematic factor F(φ) is expanded in a Fourier series. The potential function of internal rotation (PFIR) of methacrolein in this state is built using experimental frequencies of transitions of the torsional vibration of both isomers, obtained from an analysis of the vibrational structure of the high-resolution UV spectrum with allowance for the geometry and difference between the energy (ΔH) of the isomers. It is shown that the Vn parameters of the potential function of internal rotation of the molecule, built using the frequencies of the transition of the torsional vibrations of s-trans- and s-cis-isomers of the methacrolein molecule, determined from vibrational structure of the high-resolution UV spectrum and the FTIR spectrum, are close.

Observation of Evidence for the π*-σ* Hyperconjugation in the S1 State of o-, m-, and p-Fluorotoluenes by Double-Resonance Infrared Spectroscopy.

Drastic changes of the methyl internal rotation potential energy functions upon the electronic excitation have been reported for o- and m-fluorotolunes [ Okuyama , K. , Mikami , N. , and Ito , M. J. Phys. Chem. 1985 , 89 , 5617 - 5625 ], and their physical origin has been attributed to the π*-σ* hyperconjugation. To observe direct evidence of the π*-σ* hyperconjugation, double-resonance infrared spectroscopy was carried out in the CH stretching vibrational region in both the S0 and S1 states of jet-cooled o-, m-, and p-fluorotoluenes. In the spectra of both o- and m-fluorotoluenes, some of the methyl CH bands were red-shifted upon the electronic excitation while the residual CH bands stayed in the same frequency region. The normal-mode analysis demonstrated that the shift behavior correlates to the relative conformation between the methyl CH bond and the phenyl ring plane. This conformation-dependent methyl CH bond weakening clearly supports the presence of the π*-σ* hyperconjugation in o- and m-fluorotoluenes. The similar red-shift of the methyl CH bands upon the electronic excitation was seen also in p-fluorotoluene though the magnitude of the shift was much smaller. The mechanism of its internal rotation potential energy behavior, however, can be different from those of the o- and m-isomers.

Internal rotation potential functions of an acryloyl fluoride molecule in the ground (S 0) and excited (S 1) electronic states

Structural parameters of trans- and cis-isomers of an acryloyl fluoride molecule in the ground (S0) and excited (S1) electronic states are determined. The F(φ) function is expanded into the Fourier series. The internal rotation potential functions (IRPFs) of acryloyl fluoride in both electronic states are derived. To this end, torsional vibrational transition frequencies of both isomers of this molecule were used, which were obtained from the analysis of the vibrational structure Щf a high resolution UV spectrum of acryloyl fluoride vapor with regard to the geometry and energy difference (ΔH) of the isomers. The IRPF parameters Vn of this molecule in the (S0) state, which were derived based on the transition frequencies of torsional vibrations from the vibrational structure of the high resolution UV spectrum and the IR Fourier spectrum coincided.

Do enantiomers of benzenesulfonic acid exist? Electron diffraction and quantum chemical study of molecular structure of benzenesulfonic acid

Molecular structure of benzenesulfonic acid was studied by gas-phase electron diffraction and quantum chemical (B3LYP/cc-pVTZ, МР2/cc-pVDZ, МР2/cc-pVTZ) methods. On the base of mass spectrometric analysis it was found that saturated vapor at Т=396(9)K is represented by only molecular species, monomeric benzenesulfonic acid. Theoretical calculations showed that the molecule has two mirror conformers of C1 symmetry which can invert to each other via transition state of Cs symmetry by rotation of OH-group around SO(H) bond. Both computational methods, B3LYP and MP2, resulted in the same structure of enantiomers; the MP2/cc-pVDZ calculations denoted a over-barrier transition between enantiomers at the temperature of electron diffraction experiment, while B3LYP and MP2 calculations with cc-pVTZ basis set estimated the barrier height to be comparable with the thermal energy value. Two geometric models of C1 and Cs symmetry were examined in gas electron diffraction structural analysis. It was established that the structure of C1 symmetry (Rf=3.3%) demonstrated the best fit with GED data in comparison with Cs structure (Rf=3.8%).In conformer of C1 symmetry an ordinary bond SO(Н) is located almost orthogonal to benzene ring plane, and an OH bond practically eclipses one of SO bonds of SO3H fragment. The following internuclear distances (Å) in benzenesulfonic acid were determined: rh1(CH)av=1.116(6), rh1(CC)ср=1.402(4), rh1(CS)=1.770(5), rh1(SO)av=1.438(4), rh1(SO)=1.623(4), rh1(OH)=0.870(17).Calculations of internal rotation potential functions and NBO-analysis of electron density distribution in a conformer and transition states between enantiomers were performed to establish the reasons of stability of the found asymmetric structure of the studied molecule. The structure of free molecule of benzenesulfonic acid was compared with that of molecular form in crystal.

Effect of free valence on the characteristics of internal rotation in n-alkyl radicals

A study of internal rotation in the radicals n-CnH2n+1C·H2, (2 ≤ n ≤ 7) was carried out for the case of rotation around the bonds not including the radical center. 21 potential functions of internal rotation V(φ) were calculated. The coefficients in V(φ) were shown to depend only on the immediate environment at the bond of rotation. Characteristics of internal rotation in n-alkyl radicals were compared with related parameters of the corresponding alkane molecules. The generalized function Vav(φ) with the coefficients defined only by the position of the bond of rotation in the hydrocarbon chain and possessing the transposition property were proposed. The functions Vav(φ) were recommended for the simulation of the structure and properties of large molecules containing hydrocarbon fragments. This work continues a systematic study on the characteristics of the internal rotation in the n-alkane molecules and the groups containing free valence in n-alkyl radicals.

An analysis of the vibrational structure of high-resolution UV spectra and long-wave IR Fourier transform spectra in studies of internal rotation in molecules

The methods for analyzing the vibrational structure of high-resolution UV spectra and long-wave IR Fourier transform spectra in studies of internal rotation in α,β-unsaturated carbonyl compounds R4R3C=CR2-COR1 (R1 = F, Cl; R2 = R3 = R4 = H, CH3) are compared. These methods were found to give different experimental values for systems of torsional vibration energy levels up to high quantum numbers, torsional frequencies (0–1 transitions), and anharmonicity coefficients x 11 for trans and cis isomers of the same molecules in the ground electronic state (S 0). It was shown that the experimental technique for analyzing the vibrational structure of UV spectra excludes the hydrolysis of compounds under study. Taking into account Fermi resonance and numerous Deslandres tables constructed for trans and cis isomers provides reliable determination of values necessary for the construction of internal rotation potential functions, because they are multiply repeated in various Deslandres tables. An analysis of the vibrational structure of UV spectra gives more reliable V n internal rotation potential function parameters. The V n parameter values were substantiated by quantum-mechanical calculations performed by other authors.

The geometry of the nitroguanyl fragment in the simplest nitroguanidine derivatives in the absence of intermolecular interactions: The gas electron diffraction data on 1,1,3,3-tetramethyl-2-nitroguanidine

The structures and force fields of the equilibrium forms of 2-nitroguanidine (1), 1,1,3,3-tetramethyl-2-nitroguanidine (2), and nitroguanyl azide (3) were determined in the MP2(full)/6-311G(3df, 2p) approximation; wagging-inversion motions of the N amine atoms were studied. The internal rotation potential function of the NO2 group was calculated for 1. Similar functions for 1 and 2 were also obtained in the MP2(full)/6-311G(d, p) approximation. Direct one-dimensional problems for a nonrigid model were solved by the variational method, and the distribution of torsional levels was obtained. In the region of potential minimum, rotation in both molecules had the character of large-amplitude motions. For the first time, electron diffractions data were obtained at 100°C for molecule 2 without noticeable traces of substance decomposition. A structural re analysis was performed using the model of large-amplitude motions for characteristic NO2 group torsional vibrations. Vibrational corrections to internuclear distances and mean amplitudes were calculated taking into account nonlinear kinematic effects using the force fields obtained in this work. The geometry of molecule 2 calculated in the MP2(full)/6-311G(3df, 2p) approximation well corresponds to the gas electron diffraction data. The parameters of molecule 2 in the crystalline phase, however, differ substantially from the parameters of the free molecule. This corresponds with the suggestion of the influence of intermolecular H-bonds involving the imine nitrogen atom and nitro groups oxygen atoms.

Vibronic spectra, ab initio calculations, and structures of conformationally non-rigid molecules of oxalyl halides in the ground and lowest excited electronic states. Part V: Oxalyl chloridefluoride (COCl–COF)

The structure and conformational dynamics of the COCl–COF molecule in the ground and lowest excited electronic states were investigated theoretically by the CASPT2/cc-pVTZ method. The equilibrium geometric parameters, harmonic vibrational frequencies, potential functions of internal rotation, and adiabatic transition energies were obtained. According to the results of calculations, the molecule in the ground electronic state exist as the trans and gauche (dOCCO ~30–40°) conformers with a low potential barrier to gauche–gauche transition therefore it is impossible to exclude existence of the cis conformer (instead of gauche) with a very broad and flat potential minimum. For all the investigated excited electronic states of oxalyl chloridefluoride molecule calculations predicted the trans and cis conformers. The strong coupling of internal rotation around the C–C bond and non-planar vibrations of carbonyl fragments was found for the excited electronic states. The results of calculation were utilized for reanalysis of experimental \( \tilde{A}^{1} A^{\prime \prime} \leftarrow \tilde{X}^{1} A^{\prime} \) and \( \tilde{a}^{3} A^{\prime \prime} \leftarrow \tilde{X}^{1} A^{\prime} \) vibronic spectra reported in Kidd and King (J Mol Spectrosc 50:209–219 (1974), and ibid. 48:592–599 (1973)). The vibrational assignment that does not contradict the vibrational spectroscopy data and results of calculations was obtained.

ChemInform Abstract: Conformational Studies by Liquid Crystal NMR and ab initio Calculations: Methyl Nicotinate and Methyl Isonicotinate.

Abstract Conformational properties of methyl nicotinate and methyl isonicotinate have been studied by liquid crystal 1 H-NMR spectroscopy combined with ab initio calculations. The solvent used is a mixture of 80 mol.% of EBBA and 20 mol.% of MBBA.Ab initio calculations have been performed with 4-21G and MINI-4 basis sets to estimate molecular structures and the potential functions for internal rotation. Some structural parameters and the energy difference between rotational isomers have been refined by using observed dipolar coupling constants. The correlation between internal rotation and reorientational molecular motion has been taken into account according to the theory of Emsley, Luckhurst and Stockley. The parameters of the mean external potential are found to take similar values for methyl nicotinate and methyl isonicotinate. The energy difference of the two stable conformers of methyl nicotinate is in agreement with the analysis neglecting the correlation between the two motions.

Study of internal rotation of radical center in n-alkyl radicals

A quantum-mechanical study of internal rotation around C-C· bond in n-alkyl radicals from C2H5 to C7H15 was carried out using B3LYP/6-311++G(3df, 3pd) approach. The values of barriers and local minima were found. Analysis of the distribution of electron density was carried out. By application of the methods of mathematical statistics different types of representation of the potential functions of internal rotation were analyzed and the optimal approximation was revealed. Contributions to the thermodynamic properties of the considered radicals were calculated. The generalized function of internal rotation was suggested for the radicals of the type CnH2n+1, n > 4.

Quantum chemical analysis of vibrational spectra of methylphenylcarbamate

UDC 539.19 We present results of ab initio and DFT calculations of the structure, potential function of internal rotation of the methyl group, and vibrational frequencies and intensities in IR and Raman spectra of methylphenylcar- bamate. The calculations were carried out in different basis sets in the HF, MP2, and DFT/B3LYP approxi- mations with partial force field scaling. The influence of the phenyl substituent on structural and spectral characteristics of the urethane group has been analyzed. Calculated characteristics of vibrational spectra show satisfactory agreement with experimental values. Herein we present results of quantum-chemical ab initio and DFT calculations of the structure and IR and Raman vibrational spectra of MPC taking into account its internal rotation. We used our previous studies (3) to deter- mine the optimal ratio of approximations and bases for which calculations could adequately reproduce experimental structural and spectral-energy characteristics of methylcarbamate (MC) in a reasonable time. These approximations were used to calculate the corresponding parameters of MPC. Experimental. Structural, energy, and spectral characteristics of MPC were calculated using the US version (4) of the applied quantum-chemical set GAMESS (5) and the PC set GAMESS/Firefly (6). Results were plotted using the MacMolPlt program (7). Calculations were performed with the standard bases 6-31G, 6-311G, 6-311++G(2d, p), and cc-pVDZ (8) with the Hartree-Fock approximation and partial consideration of electron correlation using the methods MP2 (9) and DFT with the B3LYP hybrid functional (10). Discussion. Structure. Based on calculations of the MC structure (3), we selected the approximations B3LYP/6-311++G(2d, p) and B3LYP/cc-pVDZ to calculate the geometric parameters of MPC because ab initio calcu- lations using these approximations reproduce with high accuracy the experimental structural parameters of MC (3). The geometry from the B3LYP/6-311++G(2d, p) approximation was optimized assuming that the equilibrium structure of MPC has Cs symmetry. The geometry from the B3LYP/cc-pVDZ approximation was optimized for two molecular symmetries, Cs and C1. The calculated vibrational spectrum for the geometry optimized for Cs symmetry showed an imaginary frequency (for methyl torsion). Therefore, the final geometry was optimized for the structure with C1 sym- metry. Symmetry lowering produced insignificant (in the range 1-3 o ) deviations of the urethane atoms from the plane of the phenyl ring and also rotation of the methyl by ≈5 o relative to the symmetric position.

The internal rotation potential functions of the methacryloyl chloride molecule in the ground and excited electronic states

The systems of torsional vibration levels of the trans and cis methacryloyl chloride isomers in the ground (S0) and excited (S1) electronic states obtained by analyzing the vibrational structure of the gas-phase UV spectrum were used to reproduce the internal rotation potential functions of the molecule in both electronic states. The kinematic F factor in the S0 and S1 electronic states was calculated taking into account the relaxation of geometric parameters depending on the internal rotation angle. The internal rotation potential function parameters in the S0 state are substantially different from the parameters obtained using the torsional levels of the IR Fourier transform spectrum; at the same time, they are substantiated by quantum-mechanical calculations.

A quantum-chemical study of the structure and conformational dynamics of the acrolein molecule in the ground electronic state

The geometric parameters (including vibrationally averaged parameters), energy differences (ΔE) between the s-cis and s-trans conformers, and barrier to internal rotation (Vt) were calculated for the acrolein molecule CH2=CHCHO by various quantum-chemical methods (MP2, DFT, CASSCF, QCISD, CCSD(T), and MR-AQCC). The MP2 and B3LYP methods were used to calculate internal rotation potential functions and vibrational frequencies; the calculations were performed in various anharmonic approximations. To refine the ΔE and Vt values, two-dimensional (using a basis set of atomic orbitals) VFPA extrapolation procedure was applied, which allowed the results to be estimated in the FCI/CBS approximation taking into account nonadiabaticity, core correlation effects, and changes in the difference between zero point energies.

An ab initio quantum-chemical study of C6H5SO2CH3 and C6H5SO2CF3 in the MP2(full)/6-31+G* approximation with NBO analysis of wave functions

Potential functions of internal rotation around $$C_{sp^2 } - S$$ bonds in C6H5SO2Ch3 (I) and C6H5SO2CF3 (II) were obtained by ab initio MP2(full)/6-31+G* calculations. The revealed stationary points were identified by solving vibration problems. In the energetically favorable conformations of I and II, the $$C_{sp^2 } - S - C_{sp^3 } $$ plane is perpendicular to the benzene ring plane. The barriers to rotation around the $$C_{sp^2 } - S$$ bonds in I and II are 20.81 and 28.23 kJ mol−1, respectively. The parameters of the molecular geometry were estimated. The wave functions were analyzed using the NBO formalism, and the distribution of natural charges over atoms was considered.

Potential functions of internal rotation in n-alkanes and its contribution to thermodynamic properties

The potential functions of braked internal rotation V(ϕ) in n-alkanes (ethane, propane, butane, n-pentane, n-hexane, n-heptane) were calculated by ab initio and DFT methods with the 6-311++G(3df,3pd) basis set. The functions were approximated as a series of six cosines. The dependences of V(ϕ) on the length of the hydrocarbon chain in n-alkanes were analyzed. The heights of the trans-cis and trans-gauche barriers and the differences between the energies of the trans and gauche conformers were calculated and compared with the experimental data. From the calculated geometric parameters and V(ϕ), the contributions of the braked internal rotation to the enthalpy, entropy, heat capacity, and Gibbs free energy at 298 K were determined. The contributions of internal rotations are transferable within the framework of additive approaches. The generalized function Vav(ϕ) for n-alkanes and averaged contributions of internal rotation of the C-C bonds and CH3- and -CH2- tops to the thermodynamic properties were suggested.

Structure and conformation of (trifluoromethyl)thiobenzene, C 6H 5SCF 3: Gas electron diffraction and quantum chemical calculations

The geometric structure and conformation of (trifluoromethyl)thiobenzene, C 6H 5SCF 3, has been determined by two independent gas electron diffraction (GED) studies at the Universities of Moscow and Ivanovo and by quantum chemical calculations. Both experimental studies result in perpendicular orientation of the S CF 3 bond relative to the benzene plane. This result is confirmed by several quantum chemical calculations (HF/6-31G(d), B3LYP/cc-pVTZ, MP2/6-31G(d), MP2/6-311+G(d,p) and MP2/cc-pVTZ) which predict single-minimum potential functions for internal rotation around the C(sp 2) S bond. A double-minimum potential function predicted by the B3LYP/6-31G(d) calculation is not compatible with the experiment. B3LYP and MP2 calculations with large basis sets (6-311+G(d,p) and cc-pVTZ) predict barriers to internal rotation around the C(sp 2) S bond between 2.4 and 2.6 kcal/mol. The geometric parameters of both experimental studies agree with each other within the experimental uncertainties, except for the C F bond distance. The effect of fluorination of the methyl group in thioanisole, C 6H 5SCH 3, i.e., conformational change from planar orientation of the S CH 3 bond to perpendicular orientation of the S CF 3 bond, is rationalized on the basis of a natural bond orbital (NBO) analysis. The predominant effect is loss of conjugation between the p-shaped sulfur lone pair and the π system of the ring upon fluorination.