Quadratic Force Constants Research Articles

Ab initio force fields of alanine dipeptide in C 5 and C 7 conformations

We have followed up our previous ab initio calculations of the force fields and dipole-moment derivatives of glycine dipeptide in C 5 and C 7 conformations with similar studies of the l-alanyl compound [CH 3CONHCH(CH 3)CONHCH 3]. We have done, with the 4–21 Gaussian basis set, calculations of the three lowest-energy optimized conformations with intramolecular hydrogen bonding that were derived by Scarsdale et al.: the C 5, C 7 eq, and C 7 ax structures. The quadratic force constants were scaled, as in our previous work, using the set of scale factors derived by Fogarasi and Balázs for small amides, with slight modifications. The differences in the force constants, harmonic frequencies, dipole derivatives, and infrared intensities among the conformations and within each conformation are discussed and related, where possible, to differences in hydrogen bonding and structure. The results are also compared and integrated with those on Gly dipeptide. The force constants and dipole derivatives show that the C 7 ax hydrogen bond is the strongest, in agreement with the NH·O geometries, even though the SCF energy of this conformer is the highest. The NH stretch and the amide I and II modes are compared with available infrared data on Ala dipeptide in argon matrix, and the comparison supports the empirically based conclusion that C 5 and C 7 conformations are both present in the matrix-isolated sample. The problem of distinguishing between the C 7 eq and C 7 ax forms is also discussed.

The lithium superoxide radical: Symmetry breaking phenomena and potential energy surfaces

The two lowest electronic states of the lithium superoxide radical, LiO 2, have been investigated using ab initio theoretical techniques, including RHF SCF, CISD, Davidson-corrected CISD [CISD + (Q)], UHF SCF, UMP2, UMP3, UMP4(SDTQ), spin-projected UHF and UMP, valence and extravalence CASSCF (CASSCF-v and CASSCF-π), and CISD based on CASSCF natural orbitals (CISD-π). Four basis sets ranging in quality from Li (9s4p/5s2p), O (9s5pld/5s3pld) to Li (10s5pld/6s4pld), O(11s7p2dlf/6s5p2dlf) were employed, these being designated TZP, QZ2P, QZ2P+R, and QZ2P+R+f. The investigation encompassed dissociation energies, relative energies of various conformations, geometrical structures, vibrational frequencies, infrared and Raman intensities, dipole moments, cubic force fields, vibration-rotation interaction constants, and symmetry breaking phenomena. The onset of spatial symmetry breaking in the electronic orbitals of the TZP RHF reference wavefunction for X 2A 2 LiO 2 leads to an irremovable singularity in the quadratic force constant for antisymmetric LiO stretching at the isosceles-triangle (C 2v) geometry d(OO) = 1.3266 Å and r(LiO) = 1.7737 Å. This anomalous lowering of spatial symmetry from C 2v to C s, makes the two oxygen atoms inequivalent, and thus it becomes necessary to avert the symmetry dilemma in the reference wavefunction to provide unequivocal evidence for a C 2v geometrical structure of X 2A 2 LiO 2 which is consistent with the ionic model. This task is achieved with the CASSCF-π and CISD-π wavefunctions, the latter yielding d(OO) = 1.3405 Å, r(LiO) = 1.7937 Å, ω 1(a 1) = 1263 cm −1, ω 2(a 1) = 740 cm −1, and ω 3(b 2) = 519 cm −1 at the C 2v equilibrium geometry. Final proposals of d(OO) = 1.335 Å, r(LiO) = 1.76 Å, and D 0(LiO 2) = 62 kcal/mol are made for X 2A 2 LiO 2, as indicated by appurtenant studies of X 2Π gO 2 −1 and X 2Π LiO. Improved predictions are thereby provided for gas-phase LiO, viz., r e = 1.694 Å ω e = 814 cm −1, ν 0 = 798 cm −1, and D 0(LiO) = 86 kcal/mol. The A 2B 2 state of LiO 2 is also predicted to have a C 2v geometrical structure, d(OO) = 1.3497 Å and r(LiO) = 1.8612 Å being obtained at the TZP CISD level, and a final adiabatic excitation energy of T e = 16.7 kcal/mol is determined. A large differential correlation energy effect is found to be important in obtaining an accurate relative energy for the 2Π, C 2∞ v, LiOO linear structure, which is found to be a shallow minimum 22.2 kcal/mol above the X 2A 2, C 2v state with TZP CISD bond lengths of d(OO) = 1.3149 Å and r(LiO) = 1.6341 Å. Finally, 2Π LiO 2 is connected to the X 2A 2 and A 2B 2 minima via two transition states of 2A″ and 2A′ symmetry, respectively, with interconversion barriers near 1.4 and 1.1 kcal/mol.

Ab initio force fields of glycine dipeptide in C 5 and C 7 conformations

Schäfer and coworkers have previously derived, with the 4–21 Gaussian basis set ab initio optimized geometries for the glycine dipeptide, CH 3CONHCH 2CONHCH 3, in several conformations. Using their geometries for the C 5 and C 7 conformations, respectively with five- and seven-membered intramolecular NH⋯OC hydrogen-bonded rings, we have computed the vibrational force fields and dipole moment derivatives at the 4–21 level. Scale factors for the quadratic force constants were transferred, with two changes, from the set derived by Fogarasi and Balázs from a study of small amides. The differences in the force constants, harmonic frequencies, dipole derivatives, and infrared intensities between the conformations and within each conformation are discussed and related, where possible, to differences in hydrogen bonding and structure. In particular, the NH and CO stretch and bend force constants and dipole derivatives show trends that can be correlated with the C 5 and C 7 hydrogen bonds. The amide modes are compared with some available data on glycine dipeptide in argon matrix, and the comparison supports the empirically-based conclusion that C 5 and C 7 conformations are both present in the matrix-isolated sample.

The spectroscopy and molecular dynamics of the high frequency ν16 intermolecular vibrations in HCN---HF and DCN---DF

Gas phase rovibrational analysis of the high frequency intermolecular hydrogen bonded bending overtone 2ν06 [ν0=1132.4783(2) cm−1] in HCN---HF and its corresponding perdeuterated fundamental ν16 [ν0=409.1660(2) cm−1] are reported. Evaluated rovibrational parameters provide the basis for quantitative modeling of the molecular dynamics associated with this vibration. A quantum mechanical calculation permits determination of the quadratic and quartic force constants K66=537(17) and K6666=4.98(12) cm−1 which in turn are used to estimate the pertinent cubic band stretching interaction constants K466=−149.3(50) cm−1 and account for the unexpected behavior in the rotational constant B16. Second order expansion of the vibrational term energies, give X46=−21.61(2), X67=−7.694(1), X66=−14.84(90), g66=−31.04(90) cm−1, neglecting corrections for Fermi resonance. The common isotopic species equilibrium rotational constant Be is evaluated to be 3681.1(11) MHz.

Reaction paths for the dissociation ã 3A″ CH2CO→X̃ 3B1 CH2 + X̃ 1Σ+ CO

An ab initio investigation of the (CIIs) in-plane bent 3A″ CH2CO→X̃ 3B1 CH2+X̃ 1∑+CO and the (CIs) out-of-plane bent 3A′ CH2CO→X̃ 3B1 CH2+X̃ 1∑+CO dissociation paths has been performed. Geometrical structures, vibrational frequencies, and quadratic force constants have been determined at the DZP SCF and DZP CISD levels of theory for the X̃ 1A1, 3A″, and 3A′ states of ketene and for the 3A″ and 3A′ transition states for dissociation. The DZP CISD structure for à 1A″ ketene is also reported. Final energetic predictions for triplet ketene dissociation have been obtained from large-basis (QZ2P and QZ2P+f) UMP4(SDTQ) calculations at the DZP CISD geometries. The CIIs stationary point for 3A″ ketene dissociation is a true transition state with r(C–C)=2.071 Å at the DZP CISD level of theory. The corresponding CIs stationary point for 3A′ ketene is actually a super transition state for the interconversion of two equivalent 3A″CIIs transition states for dissociation. Final theoretical predictions of Te=19 400 cm−1 and T0=19 150 cm−1 are made for the adiabatic excitation energy of the ã 3A″ state of ketene, and a value of 22.3 kcal/mol is proposed for the 3A″ dissociation energy.

A b i n i t i o synthesis of the ozone ultraviolet continuum

Potential energy surfaces for the ground and excited electronic states responsible for the Hartley continuum of ozone are used to obtain quadratic, cubic, and quartic force constants. Vibrational dependence of rotational constants to sixth order is calculated by perturbation theory. The spectroscopic constants enable computation of rovibronic energy levels. Overlap of ground state and excited state perturbed vibrational wave functions yield Franck–Condon factors. Electric dipole allowed rovibronic transitions are generated under the Ir representation. The entire set of results generate the ultraviolet absorption spectrum. It is shown that inclusion of anharmonic terms in the vibrational Hamiltonian has a small effect upon the final spectrum, whereas rotational broadening plays a greater role in achieving agreement with experiment.

Theoretical force fields and vibrational spectra of 4H-pyran-4-one by CNDO/2 and MINDO/3 force methods

The complete harmonic force fields and the in-plane and out-of-plane vibrational fundamentals of 4H-pyran-4-one are determined by CNDO/2 and MINDO/3 semiempirical quantum chemical methods. The quadratic force constants are scaled using 11 scale factors. In the case of MINDO/3 a standard set of scale factors is used, while in the case of CNDO/2 they are refined. The latter, optimized set of scale factors, is very similar to those published for other molecules. The theoretical vibrational spectra calculated from these scaled quantum mechanical (SQM) force fields are in fair agreement with the experimental gas-phase spectra, confirming the applicability of semiempirical force field calculations for vibrational spectra analysis. The choice of the reference geometry is shown to have only a small effect on the scale factors. Dependence of the scale factors on related geometry parameters is predictable, although other factors (e.g., anharmonic vibrations versus harmonic theoretical treatment) also make important contributions to the final values of the scale factors.

Theoretical study of the coordination effect: The CN bond stretch force constants of HCNBF 3 and HCNBCl 3

A theoretical investigation of HCNBF 3 and HCNBCl 3 was undertaken with the aim of understanding the coordination effect of nitriles as the ligand in the CN bond stretching fundamental vibrations. The evaluated CN bond potential parameters given by the MNDO method suggest that the quadratic and cubic force constants are responsible for the characteristic high wavenumber shift of the CN stretching fundamentals and the apparent increase in the harmonic CN stretching force constant derived from the normal coordinate calculations.

Prediction of the nν2 inversional energy levels of the phosphine, arsine, and stibine molecules

Effective inversion potential functions, V eff, of the PH 3, AsH 3, and SbH 3 molecules are constructed using the Frost-Musulin reduced potentials for description of the inversion potential functions and the harmonic approximation in order to account for the role of the (in-plane) vibrational motions. Consequently, the functions V eff involve eight free parameters [the equilibrium bond length, r X-H e ( X=P, As, Sb), the inversion barrier B, and six quadratic valence force constants, f ij ]. To determine V eff, we fix r X-H e and f ij at values taken from the literature and fit B to the experimental ν 2 band origins using a simple version of the nonrigid invertor Hamiltonian. The resulting potential functions are used with the same rotation-vibration theory to predict energies of the nν 2 inversional levels of the XH 3, XH 2D, XHD 2, XD 3, XH 2Mu, XHMu 2, and XMu 3 molecules, where Mu is muonium. In addition, inversion splittings of these levels are estimated by means of a simple WKB procedure.

Infrared spectrum of the fundamental vibration–rotation band of OD−

The fundamental v=1←0 vibration–rotation band of OD− has been observed using the tunable infrared radiation from a difference frequency laser system and the velocity modulation technique for detection. The band origin is determined to be 2625.332(3) cm−1. The rotational constant B and the centrifugal distortion constant D have been determined for both the ground state and the first excited state. A remarkable similarity between molecular constants of OD− and OD has been noticed and utilized to estimate equilibrium vibration–rotation constants. These vibration–rotation constants were used to estimate the equilibrium bond length and the quadratic, cubic, and quartic force constants.

Study of correlation effects on stretching force constants of the H 3N⋯LiF lithium-bonded and H 3N⋯HF hydrogen-bonded complexes

All quadratic, cubic and quartic force constants associated with high and low vibrational modes of the H 3N⋯HF hydrogen-bonded and H 3N⋯LiF lithium-bonded complexes have been calculated employing the Møller—Plesset perturbation theory to the second order (MP2) with the 4-31G** basis set.

ChemInform Abstract: The Average Structure and Force Constants of Gaseous Trichlorofluoromethane Determined by Electron Diffraction and Spectroscopy

Abstract The molecular structure and mean amplitudes of CC1 3 F have been determined by gas electron diffraction. General quadratic force constants have been derived from vibrational frequencies, Coriolis coupling constents, a centrifugal distortion constant and mean amplitudes. The zero-point average structure obtained by a joint analysis of electron diffraction and microwave spectroscopic data has been compared with structures given by molecular mechanics and ab initio calculations.

A b i n i t i o studies of the low-lying electronic states of ketene

Features of the potential energy surfaces of the X̃ 1A1, 3A2(3A″), 1A2(1A″), 3A1(3A′), 1B1, and 2 1As1 low-lying electronic states of ketene have been investigated using self-consistent-field (SCF) and configuration interaction singles and doubles (CISD) methods with double zeta plus polarization (DZP) and DZP+Rydberg (DZP+R) basis sets. The DZP+R CISD vertical excitation energies are in excellent agreement with observed transition energies and suggest assignments for the X̃ 1A1→1B1 and X̃ 1A1→2 1A1 transitions in the electronic spectrum of ketene. Stationary points have been located at the DZP SCF level of theory for the first four states listed above, and SCF quadratic force constants and harmonic vibrational frequencies have been computed analytically at these stationary points. The X̃ 1A1 geometry and vibrational frequencies compare favorably with experimental values, the agreement being typical of DZP SCF results. Due to curve crossings and conical intersections of potential surfaces, the four lowest theoretical excited state surfaces have only two valid (double) minima, corresponding to 3A″ and 1A″ electronic states. At the DZP SCF geometries, Davidson-corrected CISD adiabatic excitation energies of 16 700 and 19 000 cm−1 have been obtained for the 3A″ and 1A″ states, supporting the previous experimental T0 upper bounds of Laufer and Keller. Finally, the X̃ 1A1 state is predicted to lie only 5500–7000 cm−1 below the 1A″ state at the 1A″ optimum geometry and appears to have a significant effect on the 1A″ out-of-plane frequencies.

Ab initio quadratic, cubic and quartic force constants for the calculation of spectroscopic constants

Ab initio third and fourth SCF energy derivatives have been evaluated and employed in the calculation of a series of observable spectroscopic constants for the water and ammonia molecules and their deuterated species. The third derivatives were evaluated analytically while the fourth derivatives were calculated by central differences of analytic third derivatives. The anharmonic constants χ rs (and g u′ for ammonia). Darling-Dennison constants K 1133 (and K 1333 for ammonia), the vibration-rotation constants α r B ( B = A, B, C), and the l-doubling constants q t for ammonia are reported. The agreement between the ab initio calculated constants and the experimentally obtained constants indicates that these SCF calculated constants are of sufficient quality to be of real use to the experimental community.

The average structure and force constants of gaseous trichlorofluoromethane determined by electron diffraction and spectroscopy

The molecular structure and mean amplitudes of CC1 3F have been determined by gas electron diffraction. General quadratic force constants have been derived from vibrational frequencies, Coriolis coupling constents, a centrifugal distortion constant and mean amplitudes. The zero-point average structure obtained by a joint analysis of electron diffraction and microwave spectroscopic data has been compared with structures given by molecular mechanics and ab initio calculations.

Intramolecular vibrational energy redistribution in CHCl3: A theoretical analysis

The mechanism of intramolecular vibrational energy redistribution (IVR) in the vibrationally excited chloroform (CHCl3) has been studied theoretically. An analytic form of potential energy function was constructed with the aid of quadratic and cubic force constants calculated by ab initio MO method. Classical trajectory methods were applied to simulate the IVR process from the high CH stretch overtone states and the results were analyzed in terms of the moments of energy in each vibrational mode. The overtone absorption line shapes were also calculated. The results obtained are summarized as follows: (1) The IVR process is characterized by the two different time scales. The energy transfer from the CH stretch to the CH bend occurs rapidly, while it takes a longer time to complete the energy flow into the low frequency CCl vibrations. (2) There is a discontinuous transition of the mechanism of IVR between v=3 and 5. Above v=5, the energy in the CCl vibrations increases monotonically and the distribution in each mode can be represented by a simple exponential form, while the amount of energy transferred into the CCl modes is negligibly small for v=1–3.

Force field in the hydroxylamine molecule from ab intio MO calculation

Sixty-nine anharmonic force constants of hydroxylamine were calculated by an ab initio Hartree-Fock SCF MO method with the 4-31G* basis set. The calculated fundamental frequencies which include the anharmonic effects are still larger than the observed frequencies by = 6%. This is because of the overestimation of the quadratic force constants rather than inaccurate anharmonic constants. The characteristics of geometries and force constants are compared for three amines, methylamine. hydrazine, and hydroxylamine, and they are interpreted by a model of the orbital interactions of the fragment radicals which constitute each molecule.

Rotational spectra of mono-18O-substituted ozones in the ν2 excited vibrational state

Abstract Millimeter wave rotational spectra of the mono-18O-substituted ozones, 16O18O16O, 18O16O16O, were studied for the ν2 excited vibrational state at selected frequencies between 59 and 367 GHz. The spectra were fitted using both Watson A and S reductions to parameter sets which were complete through the sextic terms and included two octic terms. The parameters were compared with those of the respective ground states fitted in the same way. The changes in the inertial defects with vibrational state agree very well with those calculated from the quadratic force constants of the normal species.

Force fields of allylamine conformers as studied by an ab initio calculation and infrared spectroscopy

The quadratic force constants of the five possible conformers of allylamine were calculated by an ab initio MC method. The infrared spectra of this molecule in the gas phase were remeasured and analyzed on the basis of the calculated vibrational frequencies. A potential energy surface with respect to the skeletal torsions was also calculated. The relative abundances of the S +G +, ST, CT, CG, and S +G − conformers, predicted to be 44:32:16:7:1 at room temperature, are consistent with the experimental data.

Theoretical study of H2O–HF and H2O–HCl: Comparison with experiment

The H bonds in H2O–HF and H2O–HCl are studied and compared using ab initio molecular orbital methods and the results compared to experimental data. Basis sets used are: (i) triple valence 6-311G** and (ii) double ζ with two sets of polarization functions. Electron correlation, included via second- and third-order Mo/ller–Plesset perturbation theory, is found to have profound effects on both systems, particularly H2O–HCl. Both H bonds are strengthened substantially with a concomitant reduction in length. H-bond energies and geometries calculated at correlated levels are in excellent accord with available experimental information. In both systems, all levels of theory indicate the equilibrium geometry contains a pyramidal arrangement about the oxygen atom. However, the difference in energy between this structure and a C2v planar arrangement is found to be small enough that consideration of probability amplitudes in the ground vibrational level leads to nearly equal likelihood of observing either geometry. Agreement between experimental vibrational frequencies in H2O–HF and those calculated at correlated levels and involving quadratic, cubic, and quartic force constants is quite good. An explanation is offered for the increase in HX bond length which occurs at SCF and correlated levels upon H-bond formation based upon nearly linear relationships between this length on one hand and subunit dipole moment and polarizability on the other. The dispersion energy is found to be a very sensitive, almost exactly linear function of the increase of H–X bond length. This energy contributes substantially to the weakening of the HX bond upon complexation.