Zero-point Vibrational Effects Research Articles

Theoretical Conformational Analysis of Thiacrown Macrocycles

A gas phase conformational analysis was performed on four sulfur-containing macrocycles (9-thiacrown-3, 12-thiacrown-4, 15-thiacrown-5, and 18-thiacrown-6) using a combination of empirical and ab initio methods. Candidates for low-lying conformers were initially generated from high-temperature molecular dynamics simulations. A more computationally manageable subset of conformations was selected for further study based on their relative energies at successively higher levels of ab initio theory. The highest level of theory included second-order perturbation theory with the aug-cc-pVDZ basis set. The lowest conformation of 9-thiacrown-3 was found to have an exodentate C2 structure with an electronic energy that is 4 kcal/mol below the C3 crystal structure. For 12-thiacrown-4, the lowest energy structure possesses D4 structure in both the gas and crystal phase. In the case of 15-thiacrown-5 the lowest energy conformer possesses an oblong, partially exodentate, gas phase structure with C2 symmetry. The crystal structure has C1 symmetry and lies 3 kcal/mol higher in energy. 18-Thiacrown-6 has an exodentate C2 symmetry, which is estimated with a large uncertainty to be 1 kcal/mol below the folded C2 structure of the crystal. Zero-point vibrational effects shift relative energies by up to 0.3 kcal/mol across an energy span of 5−7 kcal/mol, but the effect on close-lying conformers is less.

A new variational coupled-electron pair approach to the intermolecular interaction calculation in the framework of the valence bond theory: The case of the water dimer system

A general nonorthogonal coupled-electron pair approach based on the intermediate optimization of virtual orbitals is presented. The resulting procedure, similar to the independent electron pair approximation scheme, is developed in the framework of the valence bond (VB) theory, where the effect of the overlap is directly taken into account. Nonorthogonal virtual orbitals optimal for intermolecular correlation effects were determined starting from the self-consistent field for molecular interaction wave function. These were used in the context of a general ab initio variational multistructure VB wave function consisting of double excitations arising from simultaneous single excitations localized on each monomer. The basis set superposition error is excluded in an a priori fashion and geometry relaxation effects are naturally taken into account. As an application example, the equilibrium structure and binding energy of the water dimer system were determined. The equilibrium oxygen–oxygen distance results to be 2.954 Å, in good agreement with the experimental values (2.946 or 2.952 Å) corrected for anharmonicity of the dimer vibrations. The estimated equilibrium interaction energy is −5.02 kcal/mol, thus comparing favorably with the experimental value of −5.44±0.7 kcal/mol. Taking zero-point vibrational effects into account, the calculated binding enthalpy is −3.22 kcal/mol, in accordance with the experimental estimate of −3.59±0.5 kcal/mol, determined from measures of thermal conductivity of the vapor. The importance of employing basis sets that include diffuse polarization functions in correlated calculations on hydrogen-bonded systems is confirmed.

Ab initio MO–VB study of water dimer

The equilibrium structure and binding energy of the water dimer system were determined by employing a general ab initio VB approach. Starting from the SCF–MI wavefunction, non-orthogonal virtual orbitals optimal for intermolecular correlation terms have been determined. BSSE is excluded in an a priori fashion and geometry relaxation effects are naturally taken into account. The equilibrium geometry corresponds to R O–O=3.00 Å, β=134.5° and α=2.5°, in agreement with the experimental values. The donor OH bond results elongated by 0.002 Å. The estimated equilibrium binding energy of the water dimer is −4.69 kcal/mol. Taking zero-point vibrational effects into account, the binding enthalpy is −3.1 kcal/mol, to be compared with the experimental estimate of −3.59±0.5 kcal/mol, determined from measurements of thermal conductivity of the vapour.

Quantum chemical study of hydrogen-bonded CH 2CO…HX and CH 2CCH 2…HX (X = Cl, F) complexes

An ab initio quantum chemical study, largely at the 6–311 + + G ∗ ∗/ MP2 = full level of theory has been carried out on the 1:1 and 2:1 complexes of HX (X = Cl, F) with ketene and are compared with the corresponding isoelectronic complexes of H 2CCCH 2 and HX. Three possible modes of the hydrogen bond between HX and ketene via the dipole-induced dipole (X-H…C, X-H…O) and the weak X-H…π interactions were considered. The binding energy has been calculated after giving careful consideration to basis set superposition effects and zero-point vibrational energy effects. The electron correlation correction to the binding energy has also been computed. Weak X-H…π hydrogen bonds are perhaps possible with nonpolar CC and CC pi-clouds.

Quantum Chemistry Study of Conformational Energies and Rotational Energy Barriers in n-Alkanes

The gauche energy, the t-g barrier, and the cis barrier in n-butane and n-hexane have been investigated using high-level ab initio electronic structure calculations. CCSD(T)/cc-pVTZ//MP2/6-311G(2df,p) calculations yield a gauche energy in n-butane of 0.59 kcal/mol, which after correction for zero-point and thermal vibrational effects is within 0.05 kcal/mol of the values obtained from recent experiments. Calculations at the same level yield t-g and cis barrier energies in n-butane of 3.31 and 5.48 kcal/mol, respectively, supporting the traditional view that the cis barrier in n-butane is much higher than the t-g barrier. We found that torsional potential functions previously parametrized to reproduce the measured low-lying torsional vibrational transitions in the trans and gauche conformers of n-butane and which yield only a small energy difference between the barriers can be modified to reproduce both the spectroscopic data and the large quantum chemistry energy difference between barriers. For the central bond in n-hexane, the gauche energy is about 0.07 kcal/mol lower than the gauche energy in n-butane at the same level of theory. The chain length effect is greater on the barriers, with the t-g and cis barriers being about 0.5 and 0.3 kcal/mol lower, respectively, for the central bond in n-hexane compared to n-butane at the same level of theory.

Hexamethylenetetramine: extinction and thermal vibrations from neutron diffraction at six temperatures.

Neutron diffraction data have been collected for hexamethylenetetramine (HMT) at 15, 50, 80, 120, 160 and 200K using a single crystal (mass 8.1 mg). The structure refinement at each temperature included two extinction parameters and third-order thermal parameters for the H nuclei. Extinction effects are very severe with extinction factors as small as 0.2Fkin2 for three reflections (800, 110 and 440). Application of the Sabine extinction theory indicates that the crystal domain size decreases from 115 microns at 200 K to 85 microns at 15 K. The half-width in the mosaic spread (7" of arc) is almost independent of temperature. An extinction model without phase correlations between mosaic blocks gives a slightly better fit to the diffraction data. The nuclear mean square thermal displacements have been analysed assuming no coupling between the external (rigid body) and internal vibrations. This gives mean square displacements for rigid-body vibration in which zero-point vibrational effects are apparent. The methylene H nuclei have internal vibrations approximately independent of temperature. At 200 K, the H nuclear vibrations have a small anharmonic component, but at temperatures below 160 K this becomes insignificant in terms of the experimental error.

The molecular electric quadrupole tensor of ethene from the rotational Zeeman effect of CH2=CD2

The Zeeman effect of several rotational transitions of [1,1-2H2]ethene has been observed in the millimetre wave range using field strengths close to 2·65 T and cell temperatures near - 170 °C. The rotational g values and susceptibility anisotropies fitted to the field splittings were transferred to those of CH2=CH2 leading to gaa = - 0·3954(9), gbb = - 0·1159(3), gcc = 0·0453(2), 2ζ aa - ζ bb - ζ cc = 0·759(21) × 10- 29 erg G- 2, and 2ζ bb - ζ cc - ζ aa = 1·926(45) 10- 29 erg G- 2. These data are combined to yield Qaa = 1·48(10), Qbb = 1·67(19), Qcc = - 3·16(19) for the principal axis electric quadrupole tensor components (all in 10- 26 esu) of ethene. The errors are standard deviations, and do not include contributions possibly arising from zero-point vibrational effects.

Calculation of deuterium isotope effects in proton transfer reactions

Abstract Various levels of theory are tested for the purpose of computing the rate constant for proton transfer reactions. Standard transition state theory is applied to a series of molecules with a progressively more bent intramolecular hydrogen bond. The systems all display similar deuterium isotope effects (DIEs); the larger DIE at low temperature is attributed to zero-point vibrational effects. However, when tunneling is incorporated via a microcanonical approach, a dramatically enhanced effect is observed for the most distorted H-bond. The energy barrier for proton transfer between carbon atoms involved in triple bonds is smaller than for carbons with lesser multiplicity. The DIE displays a sensitivity to temperature that is least for the carbon atoms with the greatest multiplicity of bonding. The tunneling obtained by following the minimum energy reaction path along the potential energy surface is similar to that when the potential is approximated by an Eckart barrier. However, significant discrepancies are observed at temperatures below about 250 K.

Dicyanomethane : microwave spectrum, quadrupole coupling and structure

The microwave spectra of seven isotopic species of CH2(CN)2 have been studied in the ground vibrational state. The zero-point average structure has been determined to be: r(C—C)= 1.459(2)A, r(CN)= 1.160(2)A and r(C—H)= 1.109(2)A with ∠ CCN = 180 – 1.4(3)°, ∠ CCC/2 = 56.3(2)° and ∠ HCH/2 = 53.5(2)°. A near-equilibrium structure has also been estimated using an rρm method tested by a similar calculation for formaldehyde. Microwave Fourier-transform spectroscopy has been used to investigate the main species and single-nitrogen-15 species under high resolution. For CH2(CN)C15N accurate 14N quadrupole coupling constants have been determined as χaa=–2.364(9) MHz, χbb= 0.313(6) MHz and χcc= 2.051(6) MHz. These results have been combined with those previously obtained for the main species to show that the quadrupole tensor is almost symmetrical about the CN bond direction. There is some disagreement between the constants for the two isotopic molecules close to experimental error, possibly indicating zero-point vibrational effects on the coupling tensor. The quadrupole tensor is of especial interest in CH2(CN)2 in view of the bent CCN moieties.

The second stable conformer of 1,3-butadiene. Geometry optimizations with configuration interaction and coupled cluster methods

The structures of s-cis and gauche butadiene have been determined using methods that include the effects of dynamical electron correlation. Optimized geometries, energies and harmonic vibrational frequencies are presented and discussed at the various levels of theory employed. The information yielded by the highest theoretical level used leads to a prediction that the gauche conformer is a minimum on the potential energy surface, lying 0.8 kcal/mol below the s-cis conformer which is predicted to be a transition state. This barrier to planarity is reduced to 0.5 kcal/mol with inclusion of zero-point vibrational energy effects. It is postulated that the gauche structure is favoured since the reduction in steric interactions in this conformation overcomes any loss of conjugation relative to the planar structure. Isoprene and dimethyl-butadiene have also been shown to display these effects in a more pronounced manner.

The stabilities of the hydrogen fluoride trimer and tetramer

A b initio calculations have been carried out to determine the dissociation pathways for the hydrogen fluoride trimer and tetramer that are accessible with single photon excitation of an HF stretching vibration. This requires evaluation of the stabilities of the small HF clusters. Electron correlation effects are found to contribute 1.0 kcal to the stability of the trimer, compared to 0.5 kcal for the dimer. The equilibrium stabilities with respect to dissociation into monomers are 4.6 kcal for the dimer, 14 kcal for the trimer, and 25 kcal for the tetramer. With zero-point vibrational effects, single photon vibrational excitation is sufficient for dissociation of the trimer into three monomers. The orientational structural parameters of the trimer and tetramer, like those of the dimer are found to be well explained by dipole and quadrupole moment interactions.

A priori predictions of the rotational constants for protonated formaldehyde and protonated methanol

Protonated formaldehyde and protonated methanol are candidate interstellar molecules and models for classes of protonated oxygen compounds. Ab initio molecular orbital theory has been used to compute rotational constants to guide spectroscopic searches both in the laboratory and in space. The ab initio results are empirically corrected to account for systematic deficiencies in the theory and zero-point vibrational effects; they are expected to be accurate to ≈ ±2%. For H 2COH + the resultant constants are (in GHz) A = 194.3, B = 34.28, and C = 29.14; for H 3COH 2 + A = 103.7, B = 21.18, and C= 20.30.

Effect of zero-point lattice vibrations on the scattered particle flux

Abstract It is demonstrated that taking account of even only the zero-point lattice vibrations results in disappearance of the singularities in the shadow edge behind the scattering centre.

Anomalies in the temperature dependence of the yield stress of metals at low temperatures

Yield stress "anomalies" have been studied in polycrystalline nickel at low temperatures. Both quantum effects and structural changes below 0.1–0.2 of the Debye temperature contribute to low-temperature anomalies in the temperature dependence of the yield stress. The anomalies appear to be basically a consequence of the effect of zero-point vibrations on the rates of transition in the localized process of activation. An attempt is made to explain the anomalies by introducing a "strain-enhancement" effect, i.e., f(T), semiempirically in the logrithmic creep equation [Formula: see text] where Teff = T0 + AT2 (T0 and A are constants), which allows for quantum effects below a certain temperature.

Upper and lower bounds of quartic centrifugal distortion constants

Expressions are obtained for the maximum and minimum possible values of the equilibrium centrifugal distortion constants τ αβγδ for a molecule with given structure and vibrational frequencies. The method of calculation, based on Lagrangian multipliers, is also applied to the empirical centrifugal constants (such as D J , D JK , D K , or Δ J , Δ JK , Δ K , δ J , δ K ) employed in fitting the rotational structure of spectra. These formulas make it possible to test whether a set of observed centrifugal constants is consistent with the rotational constants and vibrational frequencies. When inconsistencies arise, they are probably due to zero-point vibrational effects. By means of a second method employing inequalities, simpler formulas are derived for wider bounds. These are useful in calculating approximate values of the constants, as a preliminary to deciding which terms to include in the rotational Hamiltonian of any particular molecule.

Anharmonic phonon spectrum and heat capacities of solid neon

A pseudoanharmonic central-force rigid-atom model has been used to study the phonon spectrum, dispersion curves and heat capacities of solidified neon. The model uses a Buckingham-type exponential potential function, the parameters of which are derived from crystal data. The effect of zero-point vibrations has been taken into account by an iteration method and the contributions of cubic and quartic terms of the potential-energy expansion are included at 0 °K, through Helmholtz free energy. The effect of zero-point anharmonicity over frequency spectrum, dispersion of phonons and heat capacities is seen to be appreciable. The (ϑ, T) curve has a shape similar to other theoretical ones. The agreement between computed and observed specific heats is good. The inherent defects of the model have also been pointed out.

Effect of Anharmonic Vibrations on the Bond Lengths of Polyatomic Molecules. I. Model of Force Field and Application to Water

The detailed information on molecular force fields required for precise determinations of molecular structure is only rarely available for polyatomic molecules. A model of the force field is therefore proposed from which the cubic potential constants may be estimated from commonly available data. The potential energy is represented by a modified, anharmonic Urey-Bradley field in which the stretching and nonbonded potentials are assumed to have the Lippincott and Buckingham forms, respectively, and in which stretch-stretch interactions are included. The model is applied to H2O and D2O, for which exceptionally complete spectroscopic data are available for comparison, and is found to give cubic constants in satisfactory agreement with experiment. The cubic constants thus estimated are used to evaluate the effect of zero-point vibrations on the internuclear distances and rotational constants of water by a first-order perturbation treatment. The resultant mean distances and mean amplitudes are in good agreement with those of Reitan's second-order treatment using the experimental cubic constants, and the rotation-vibration constants α agree satisfactorily with Benedict's experimental values.

Scattering of Slow Neutrons from Propane Gas

Measurements of the partial differential neutron scattering cross sections for room-temperature propane gas are reported. These measurements were made at incident energies of 0.0101, 0.0254, 0.0736, and 0.102 ev at seven scattering angles between 16.3\ifmmode^\circ\else\textdegree\fi{} and 84.7\ifmmode^\circ\else\textdegree\fi{} using the Materials Testing Reactor phased chopper velocity selector. The data are converted to the scattering-law presentation and compared with three theoretical calculations: (a) The ideal gas, using an effective mass obtained from an average of the mass tensors for the three types of H atoms in propane, gives poor agreement. (b) The Krieger-Nelkin approximation, which includes the effect of zero-point vibrations, gives limited agreement for energy transfer less than $0.5{k}_{B}T$ at intermediate momentum transfers. At large momentum transfers where vibrational effects become important it underestimates the cross section. (c) A modification of the Krieger-Nelkin theory that includes the effects of single-quantum transitions from the three lowest vibrational states gives better agreement. The discrepancies still present at large momentum and energy transfers are attributed to an uncertainty in the methyl-group barrier height for the three lowest energy modes, to the harmonic oscillator approximation for these modes, and to the approximate molecular orientation averaging used in the calculation.