Zero-point Energy Differences Research Articles

An ab initio study of the structures, barriers for internal rotation, vibrational frequencies, and thermodynamic functions of the hydrochlorofluorocarbon CH3CF2Cl and the corresponding radical CH2CF2Cl

Ab initio molecular orbital calculations were performed using the GAUSSIAN 90 system of programs at the HF/6-31G* level of theory, on the hydrochlorofluorocarbon (HCFC) 1-chloro-1,1-difluoroethane and the 1-chloro-1,1-difluoroethyl radical. Equilibrium geometries, barriers for internal rotation, and harmonic vibrational frequencies were thus calculated. A single conformational minimum in the potential energy surface was located for both the radical and the parent molecule. The radical center in CH2CF2Cl was found to be nonplanar. Transition structures for internal rotation about the C—C bond were located for both the molecule and the radical using analytical methods. The rotation barriers, evaluated at the fourth-order Møller–Plesset perturbation theory ((U)MP4/6-311G**/6-31G*). were calculated after inclusion of zero-point vibrational energy differences to be 1.11 and 4.12 kcal/mol for the radical and the parent molecule, respectively. Computed thermodynamic properties including heat capacity, entropy, enthalpy, and free energy functions are reported as a function of temperature. Using an experimentally measured heat of formation of CH3CF2Cl at 298 K, the heat of formation of CH2CF2Cl was calculated to be −74.3 ± 1.7 kcal/mol. Tabulations of ΔH0f,T, ΔG0f,T, and log10Kf,T over the temperature range of 0–1500 K are also reported for both species.

Theoretical study of deuterated ethane radical cations

Equilibrium and transition-state geometries, torsional barriers, and relative abundances at 4.2 and 77 K of different rotational isomers of deuterated ethane cations have been calculated, using ab initio MP2/6-31G ** and MP4(SDTQ)/6-31G ** theories. The relative abundances of rotationally related isomers, predicted from Boltzmann statistics based on differences in zero-point vibrational energies (ZPE), are in good agreement with low-temperature matrix isolation ESR data. The rotational barrier in the singly deuterated cation is calculated to be 0.11 kcal/mol higher than in the undeuterated ion, in reasonable agreement with the experimentally estimated difference of 70.25 kcal/mol

Isotope effects on the stability of the nitrogen—acetylene van der Waals dimer

Harmonic vibrational frequencies for various isotopomers of the nitrogen—acetylene van der Waals dimer are calculated at the SCF and MP2 ab initio levels of theory, using large basis sets. The relative stabilities of the dimers N 2…HCCD and N 2…DCCH are determined from differences in the zero-point energies. It is found that the D-bonded species are energetically favoured over the H-bonded species by 8.9 cm −1 with our largest basis set at MP2. We also computed a zero-point energy difference of about 0.6 cm −1 favouring N 2…H 13CCH over N 2…HC 13CH and 14N 15N…HCCH over 15N 14N…HCCH. These calculations are consistent with most, although not all, recent experimental observations of Legon, Wallwork and Fowler

低温でのクラスター形成による同位体分離

The isotope enrichment by the formation of neutral and ionic clusters is discussed. In the free jet expansion, the heavier isotopes are enriched in the neutral clusters and the lighter isotopes are preferentially eliminated from the neutral clusters. In the free jet seeded with ions, the enrichment of heavier isotopes in the ionic clusters is greatly enhanced compared to that in the neutral clusters. This is mainly due to the large zero-point energy difference in the bond energies between the neutral and ionic clusters. The enrichment factor for ionic clusters decreases with the growth of cluster size and converges to that for the neutral ones. The deuteron-held heavy hydrogen clusters D3+(D2)n are found to be thermochemically more stable than the proton-held hydrogen clusters H3+(H2)n with n=2~9. This is due to the tighter bond formation with n≤6 and to the more favorable entropy effect with n=7~9 for the clusters D3+(D2)n.

The van der Waals potential-energy surfaces and the structures of ArClF and ArCl2

The potential-energy surfaces of the ArClF and ArCl2 complexes are determined by the Hartree-Fock (HF) and Mo/ller–Plesset calculations (up to MP4) in an efficient basis set of 6-31+G(2df ) for the intermolecular energy. The interaction energies are calculated by the supermolecular approach with the full counterpoise corrections for the basis-set superposition error. Three local potential minima are found for ArClF corresponding to the linear Ar–Cl–F and Ar–F–Cl and the asymmetric T-shaped structures. For these the well depths and the distances are D(Ar–Cl–F)=233.5 (MP2) or 219.7 cm−1 (MP4), RArCl=3.38 Å; D(Ar–F–Cl)=119.2 (MP2) or 127.2 cm−1 (MP4), RArF=3.3 Å; and D(T-shaped)=130.4 (MP2) or 132.6 cm−1 (MP4), RArCl=3.83 Å. The results are in accord with the linear ArClF structure as the most-stable structure determined by experiment with the estimate of De=228 cm−1 at RArCl=3.33 Å. For the ArCl2 complex, minima are found corresponding to the linear and the T-shaped structures. At the MP2 level the well depths and distances are D(linear)=220.1 cm−1, RArCl=3.5 Å; D(T-shaped)=183.6 cm−1, RArCl=3.9 Å. Only a small change results at the MP4 level D(linear)=195.3 cm−1, D(T-shaped)=165.2 cm−1. The results for the T-shaped ArCl2 are in good agreement with the experimental results of De=185±1 cm−1 and RArCl=3.8±0.1 Å. Estimates for the effects of differences in zero-point energy show the two structures may be of similar stablity.

Theoretical investigation of asymmetric methyl rotor dynamics in partially deuterated acetophenones

A b initio molecular orbital calculations at the HF/4-21G level, are reported of the structure, the molecular force field, and the methyl torsional potential energy curve of acetophenone in an attempt to interpret the observed tunneling and rotamer splittings in the S0→T(nπ*) excitation spectra of methyl-deuterated acetophenone-d1 and -d2. It is found that the angular dependence of the torsional kinetic energy operator does not contribute significantly to the rotamer splittings, which instead are mainly due to the angular dependence of the overall zero-point energy. The calculated zero-point energy differences between the two rotamers in the ground state are 14 cm−1 for acetophenone-d1 and 12 cm−1 for -d2. To account for the observed rotamer splittings of 7.5 and 4 cm−1, respectively, the corresponding zero-point energy difference in the triplet state must be about 9 cm−1 for both isotopomers. Comparison with experimental results for isotopomers of acetaldehyde indicates that these values are reasonable and support the notion that the level of theory used yields relevant results in the case at hand. The similarity of the zero-point difference between the rotamers in the ground and excited state contrasts strongly with the large difference in torsional barrier: 700–800 cm−1 for the ground state and 95 cm−1 for the triplet state of acetophenone-d0; the latter value is derived from the tunneling splitting observed in the excitation spectrum. These contrasting results are due to the fact that the barrier is an electronic effect whereas the rotamer splitting is a purely vibrational effect.

Isotope substitution effects on preferred conformations of some hydrocarbon radical cations

The stability of different conformational isomers of partially deuterated radical cations of ethane, butane, and cyclopropane is studied at the HF/6-31G** and MP2/6-31G** levels. It is shown that the superposition patterns of spectra corresponding to different isomers, observed in ESR spectroscopy, are accurately reproduced by Boltzmann statistics based on differences in vibrational zero-point energies (ZPE), provided that the temperature is high enough to overcome existing barriers toward internal pseu-dorotation in the cations. For the ethane and butane cations, the most stable conformations are, as expected, those which are deuterated in the short CH bonds, while this is found not to be the case for the cyclopropane cation. The latter result is explained by shifts in the low-frequency bending modes, which counteract the anticipated isotope effect on the CH stretching modes. © 1992 John Wiley & Sons, Inc.

Is the carbon monoxide—acetylene dimer semirigid? Evidence from its rotational spectrum

The ground-state rotational spectra of ten isotopomers of the carbon monoxide—acetylene dimer are reported and the spectroscopic constants B O and D J determined in the usual way in a semirigid rotor fit for a linear molecule. The B O values are consistent with a simple linear model of the dimer with nuclei in the order OC…HCCH. The failure to observe the isotopomer OC…HCCD in mixtures of CO and HCCD is interpreted in terms of a zero-point energy difference rather than in terms of a nearly free internal rotation of the acetylene subunit.

Electron transfer in mixed-valence biferrocenium salts: effect of zero-point energy difference and pronounced anion dependence

that the photoreaction is strongly inhibited in the en complex and that nonradiative decay to the ground state is a more effective competitor. Part of this rate inhibition in the en complex could arise prior to reverse intersystem crossing because the larger energy barrier for the activated route allows more competitive doublet nonradiative decay. However, the extent to which such decay can be accommodated is restricted by the observed linearity of the Arrhenius plot. At the transition-state level, other possible reasons are easy to imagine. If the transition state is seven-coordinate, then it may be more sterically crowded and have higher strain energy for the en complex than for the diammine. Alternatively, it may be that the required migration of the whole en ligand is a difficult and slow process so that deactivation and/or recoordination have a greater opportunity to compete. Finally, the diammine complex reactsz7 via a seven-coordinate species of microsecond lifetime. If the en complex behaves similarly, then its intermediate might be more likely to revert to starting material because of the bidentate nature of the leaving ligand. Concluding Remarks. We have presented evidence that after photochemical Cr-N bond breaking has occurred, it is possible for the reacting bidentate ligand to migrate from one coordination site to another in an edge displacement reaction. Since our proof relies on the assumption of stereochemical change, in the future additional evidence will be sought. It is fairly straightforward to design experiments with appropriate stereochemical sign-posting to prove group migration incontrovertably. Unfortunately, it is difficult to identify systems in which the starting compound can be prepared and unambiguously characterized and its photochemistry explored with product identification including stereochemistry. The work has shown, however, that complex ligand motions are likely and that further study of such phenomena is tractable and worth pursuing.

On the validity of the Buckingham-liu rule for water-dimer isotopomers AOB.OXY (A ≠ B; A, B, X, Y=1H,2D,3T)

Using 8 modifications of recently developed flexible water potentials, zeropoint energy differences between the isomeric water-dimer isotopomers differing in the hydrogen isotope involved in the hydrogen bond have been evaluated. In all the 18 possible pairs, the species bound through the heavier isotope is always lower in the energy term.

Comparison of the calculated acidity of cubane with that of other strained and unstrained hydrocarbons

Gas-phase acidities of some strained and unstrained hydrocarbons were calculated. The resulting deprotonation enthalpies (DPE's) are within 2-3 kcal mol{sup {minus}1} of those observed when extended basis sets are employed, some accounting of the correlation energy is made, and zero-point energy differences are considered. The best calculated DPE for cubane (406.4 {plus minus} 3 kcal mol{sup {minus}1}) is significantly greater than that calculated for benzene (397 kcal mol{sup {minus}1}) and bicyclobutane (395.4 kcal mol{sup {minus}1}), but less than that for cyclopropane (413 kcal mol{sup {minus}1}). This result shows that the enhanced kinetic acidity of cubane is reflected in its thermodynamic acidity as well. It is noted that the quantity {triangledown}{sup 2}{sub {rho}}{sub c}(C-H) predicts cubane to be less acidic than cyclopropane, as would correlations against J{sub 13{sub C-H}}. Changes of angles between bond paths at carbon upon ionization were calculated. It is found that the change for cubane is unusually large for formal sp{sup 3} centers, thus corroborating the unusual hybridization in the cubyl anion as suggested by Luh and Stock.

Infrared intensities of CH stretching bands in partially deuterated compounds, and effects of conformation and substitution

Integrated infrared intensities were measured in the gas phase for the CH stretching bands in the following compounds: C 2H 6, C 2D 5H, CH 3CH 2CH 3, CD 3CD 2CHD 2, (CD 3) 2CHD, (CH 3) 3CH, (CD 3) 3CH, (CH 3) 3CD, (CD 3) 2CHD 2CD, c-C 6D 11H*, c-C 6H 12, CHD 2Cl, CHD 2I, CHD 2CD 2Cl*, CHD 2CHDCl, CH 3CH 2Cl, CHD 2CD 2Br*, CH 3CH 2Br, CHD 2OH*, (CHD 2) 2O* and CHD 2NH 2*. For the asterisked species, separate intensities were determined for each of the two bands seen. The additivity of νCH intensity, in inverse relation to the degree of deuteration of the bonds of a given type, appears to be good. In nearly every case, the undeuterated species has an intensity slightly greater than that predicted from the partially deuterated species. This is useful for checking the internal consistency of the intensity data, and for identifying likely error in earlier data for c-CH 6H 12. Intensities per CH bond in the methyl and methylene groups of acyclic alkanes agree well with the gas phase ones derived indirectly from a series of undeuterated alkanes. Marked effects of conformation on νCH intensities are found in cyclohexane, ethyl halides and in the CH 3O and CH 3N compounds. In the latter the high intensities associated with CH bonds trans to lone pairs of electrons can be understood in terms of the Gussoni—Zerbi electrooptical parameter theory. The lowering effect of halogen on αCH bond intensity in ethyl chloride and bromide is similar to that in the corresponding methyl compounds. Marked, but differing lowering of intensity is also found in the βCH bonds in the methyl groups which are gauche and trans to halogen, respectively. The abundances of conformers of CHD 2O- and CHD 2N- species are significantly affected by zero-point energy differences.

Isotopic fractionation in low temperature ion–molecule exchange reactions: Enrichment of 22Ne in Ne+n clusters formed by association in an ionized free jet

Cationic clusters of neon atoms (Ne+n ) formed by association of neutrals onto seed ions in an ionized supersonic expansion are found to favor incorporation of the heavier isotope (22Ne) by as much as a factor of 15 (in the dimer and trimer ions) when compared to a simple statistical distribution based on natural abundances. This enrichment is attributed to the small difference in zero-point energies among species formed with the two major isotopes of neon (20Ne and 22Ne), which is of the same order as the collisional energy of particles in the expanding jet. This enrichment is anticipated by current models of isotope exchange which are invoked to explain the anomalous isotope abundance patterns in interstellar clouds.

Rotational barriers. 2. Energies of alkane rotamers. An examination of gauche interactions

The barrier to rotation about the C2-C3 bond in n-butane has been calculate using several basis sets, complete geometry optimization, and correction for electron correlation. Neither the basis set size nor inclusion of electron correlation has a large effect on the magnitude of the rotational barrier or the trans/gauche energy difference. After correction for zero-point energy differences, the former is found to be 6.34 kcal/mol, while the latter is 0.86, in very good agreement with the experimental value. The trans/gauche energy difference in n-pentane is the same as that for butane, and similar values are found for the two gauche forms of n-hexane and the symmetrical gauche form of octane. The structures and energies of several conformers of pentane and hexane with two and three gauche fragments also have been obtained. It is found that the pentane rotamer with two consecutive gauche kinks has roughly twice the gauche energy, but the hexane conformer with three consecutive gauche kinks has considerably less than 3 times that value. The energy differences for the rotamers of 2-methylbutane and 2,3-dimethylbutane are well reproduced by the calculations. Vibrational frequencies are estimated at the 3-21G level for all species, and the zero-point energies and enthalpy changesmore » (H{sub 298}-H{sub 0}) are calculated. The difference in enthalpy between an axial and equatorial methyl substituent on cyclohexane is calculated to be 2.17 kcal/mol after correcting for vibrational energy differences. The relationship between the energy of a methylene group in cyclohexane and in trans-n-alkanes is examined. 49 refs., 9 tabs.« less

Internal rotation in nitrosomethane and acetaldehyde: incremental effect of deuterium substitution on the potential for methyl torsion

Torsional splittings and zero-point conformational energy differences have been fitted for all forms of nitrosomethane and acetaldehyde substituted with deuterium in the methyl group. A single degree of freedom potential function, ▪, has been used with the isotopic data accommodated by allowing incremental changes in the potential according to the position of substitution. Coefficients up to and including V 6 have been considered. This approach has allowed rationalisation of the unusually small amount of cis-gauche perturbation observed in the microwave spectrum of CHD 2CHO. The incremental behaviour of the potential function relates closely to the conformational dependence of the CH stretching force constants. The difference in CH force constants also accounts largely for the zero-point energy differences reported here. The same ideas applied to methylamine lead to a revision of potential coefficients for CH 2DNH 2.

Surface diffusion of hydrogen and CO on Rh(111): Laser-induced thermal desorption studies

Surface diffusion of hydrogen, deuterium, and CO on Rh(111) has been investigated by laser-induced thermal desorption (LITD) and compared with previous results for these species on Pt(111) and on other metals. As the coverage θ of deuterium increases from 0.02 to 0.33, the preexponential factor D0 remains constant at 8×10−2 cm2/s, but the diffusion activation energy Ediff rises from 3.7 to 4.3 kcal/mol. Ediff for hydrogen is 0.6 kcal/mol lower than for deuterium, consistent with the difference in zero-point energy. For CO, Ediff =7 kcal/mol at all coverages, but D0 rises from 10−3 to 10−2 cm2/s between θ=0.01 and 0.40. Values of Ediff for these adsorbates vary by several orders of magnitude for surfaces on which heats of adsorption are essentially identical. These differences appear to correlate with differences in heats of adsorption in different binding states which form saddle point configurations in surface diffusion. Ediff is found to be nearly identical to the reaction activation energies for the CO and hydrogen oxidation reactions on Rh and on several other transition metal surfaces. This suggests that surface diffusion of the reducing agent may be the rate-limiting step in their bimolecular surface reactions.

Photodissociation dynamics of the D2H+ molecular ion

Using a sudden transition state theory we find that photodissociation of long-lived resonances of D2H+ leads to the H+ fragment for total angular momentum J⩽27 while D+ is formed for J⩾30. This quantum result which is critically dependent on the difference of zero-point energies between D2 and HD explains an additional aspect of the Carrington-Kennedy experiments.

Rotational barriers. 1. 1,2-Dihaloethanes

The rotational barrier about the C-C bond of 1,2-dichloroethane has been calculated by using several basis sets (4-31G, 6-31G*, 6-31+G*, and 6-31++G**) and including electron correlation. Corrections for zero-point energy differences, and the differences in enthalpy change from 0 to 298 K, were made by using the calculated geometries and vibrational frequencies. The trans/gauche energy difference was found to be 1.39 kcal/mol as compared to the observed value, 1.1 +/- 0.1 kcal/mol. The intramolecular interactions in the several rotamers are discussed. The trans/gauche energy difference for 1,2-difluoroethane also was calculated (MP3/6-311++G**) and was found to be 0.76 kcal/mol favoring the gauche conformer, again in good agreement with the experimental value of 0.57 +/- 0.09 kcal/mol. The trend in trans/gauche energy differences in the series n-butane, 1,2-dichloroethane, 1,2-difluoroethane is noted.

Structures and energies for C4

Optimized geometries and relative energies for three states of the C4 molecule have been obtained from single-reference configuration interaction (SRCI) calculations. The 1Σ+g state, which is formed without activation from the dimerization of ground state C2 molecules, is calculated to lie approximately 25 kcal above the 3Σ−g state. At the SRCI level, a rhombic form is calculated to lie 1.2 kcal below the triplet form; consideration of the Davidson correction reduces this difference to 0.4 kcal, inclusion of a second set of diffuse d functions increased the difference only by about 0.2 kcal. Consideration of these effects, the difference in zero-point energy and previous results for methylene leads to a final estimated separation of 4.9 kcal, favoring the rhombus. Electron density distribution analysis for the rhomb is consistent with the existence of a bond between inverted sp2 carbon atoms. To aid the detection of this unusual molecule, preliminary estimates of the lowest optical transitions were obtained from SRCI calculations and vibrational frequencies were obtained from SCF calculations. Comparison of the calculated results with experimentally obtained spectra suggest the possibility that both the linear triplet and the rhombus may have already been observed.

The molecular structure of hydrogen disulfide (H2S2) and barriers to internal rotation

The molecular structure of H/sub 2/S/sub 2/ has been determined by ab initio molecular theory at the SCF and CI-SD levels. The SCF and CI-SD results are in good agreement with each other for all parameters and are in agreement with experiment except for the value of theta(HSS). The calculated value for theta is 98.4/sup 0/ as compared to an experimental value of 91.3/sup 0/. It is suggested that the experimental value is too low. The vibrational frequencies for the optimum skew structure and the cis (tau = 0/sup 0/) and trans (tau = 180/sup 0/) structures have been calculated at the SCF level. The cis and trans structures have one imaginary frequency and are true transition states on the internal rotation energy surface. The barriers to internal rotation were calculated at the SCF and CI-SD levels and were corrected for the difference in zero-point energies; this correction is 0.6-0.7 kcal/mol. The trans barrier is 5.0 +/- 0.15 kcal/mol and the cis barrier is 7.5 +/- 0.15 kcal/mol. 22 references, 3 tables.