Zero-point Energy Corrections Research Articles

Structures and energies of AlOOH and FeOOH polymorphs from plane wave pseudopotential calculations

Plane wave pseudopotential methods are used to investigate the structures and total energies of AlOOH and FeOOH in the five canonical oxyhydroxide structures: diaspore (goethite), boehmite (lepidocrocite), akaganeite, guyanaite, and grimaldiite. The local density approximation was used in conjunction with ultrasoft pseudopotentials in full optimizations of both AlOOH and FeOOH in each of these structures. Structures are in reasonably good agreement with experiment, with lattice parameters and bond lengths within 3% of experimental values. Neither AlOOH nor FeOOH have been identified in the grimaldiite or guyanaite structures, however we find that total energies for AlOOH and FeOOH in these structures are comparable to or lower than the total energies of the commonly observed polymorphs (with the exception of FeOOH in the grimaldiite structure, which is anomalously high energy). Estimated zero-point energy corrections do not alter this result. For diaspore and boehmite, we also provide calculations using the generalized gradient approximation and norm-conserving pseudopotentials to assess the extent to which the results depend on the particular level of theory used. We find that diaspore is predicted to have a lower energy, consistent with experimental observation, using all but one methodological combination where the generalized gradient approximation is combined with ultrasoft pseudopotentials. Thus, although one may reasonably conclude that the differences in total energies of the various (Al,Fe)oxyhydroxide polymorphs are small, current electronic structure methods do not appear to be fully capable of accurately resolving these small differences. These findings provide further confirmation that the structures of oxyhydroxide polymorphs and surface precipitates are more likely to be a function of kinetics than of intrinsic lattice stability.

Concerted Use of Slab and Cluster Models in an ab Initio Study of Hydrogen Desorption from the Si(100) Surface

Slab and cluster models are used to study H2 desorption from a single dimer of the Si(100)−2 × 1 surface. The cluster models are constructed using geometries obtained from slab-model optimizations. The largest cluster model considered, Si89H62, contains eight surface dimers and gives reaction and activation energies for desorption nearly identical with the slab-model values when the same electronic structure method is used. The barrier for H2 desorption, calculated using the Si89H62 cluster model and the Becke3LYP functional, is 64.3 kcal/mol. When this result is corrected for the effects of basis set expansion and vibrational zero-point energy correction, the barrier decreases to about 61.0 kcal/mol, which is only 4.0 kcal/mol greater than the observed desorption barrier.

Nitrenes as intermediates in the thermal decomposition of aliphatic azides

AbstractN2 extrusion from hydrazoic acid, methyl azide, and ethyl azide to yield the corresponding nitrene has been studied with high‐level ab initio calculations. Geometry optimizations of stationary points and surfaces crossing seams were carried out with the complete active space self‐consistent field (CASSCF) method, and their energies were reevaluated with the second‐order multireference perturbation (CASPT2) theory and corrected by the zero‐point energy (ZPE). The analytic harmonic frequencies calculated at the CASSCF level have been used in the ZPE corrections. The decomposition reaction is a competitive mechanism between a spin‐allowed and a spin‐forbidden channel, giving the nitrene either in the singlet or triplet states. The energy barrier height for XNN2 bond fission is approximately the same in both channels for each azide, respectively. The spin‐orbit (HSO) interactions were determined at the minimum energy point on the seam of crossing between the singlet and triplet surfaces, the value ranges from 43.9 cm−1 in hydrazoic acid to 43.3 cm−1 in ethyl azide. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem 84: 241–248, 2001

Electron Affinities of Polycyclic Aromatic Hydrocarbons

The electron affinities of benzene and four polycyclic aromatic hydrocarbons (PAHs), naphthalene, anthracene, tetracene, and the perinaphthenyl radical, have been obtained using six common density functional theory (DFT) methods. When compared to experiment, the BHLYP, BLYP, and B3LYP functionals have average absolute errors of 0.17, 0.18, and 0.19 eV, respectively. The success of the BHLYP functional is dubious due to a fortuitous cancelation in error between the tendency for BHLYP to underestimate electron affinities and zero-point vibrational energy (ZPVE) corrections. We recommend the BLYP and B3LYP functionals for future studies of PAH anions. However, the computation of ZPVE corrections may be a limiting factor in the accuracy of any method seeking to predict electron affinities for large PAHs.

An ab initio study of water clusters in gas phase and bulk aqueous media: (H2O)n, n=1–12

Geometries of several clusters of water molecules including single minimum energy structures of n-mers (n=1–5), several hexamers and two structures of each of heptamer to decamer derived from hexamer cage and hexamer prism were optimized. One structural form of each of 11-mer and 12-mer were also studied. The geometry optimization calculations were performed at the RHF/6-311G* level for all the cases and at the MP2/6-311++G** level for some selected cases. The optimized cluster geometries were used to calculate total energies of the clusters in gas phase employing the B3LYP density functional method and the 6-311G* basis set. Frequency analysis was carried out in all the cases to ensure that the optimized geometries corresponded to total energy minima. Zero-point and thermal free energy corrections were applied for comparison of energies of certain hexamers. The optimized cluster geometries were used to solvate the clusters in bulk water using the polarized continuum model (PCM) of the self-consistent reaction field (SCRF) theory, the 6-311G* basis set, and the B3LYP density functional method. For the cases for which MP2/6-311++G** geometry optimization was performed, solvation calculations in water were also carried out using the B3LYP density functional method, the 6-311++G** basis set, and the PCM model of SCRF theory, besides the corresponding gas-phase calculations. It is found that the cage form of water hexamer cluster is most stable in gas phase among the different hexamers, which is in agreement with the earlier theoretical and experimental results. Further, use of a newly defined relative population index (RPI) in terms of successive total energy differences per water molecule for different cluster sizes suggests that stabilities of trimers, hexamers, and nonamers in gas phase and those of hexamers and nonamers in bulk water would be favored while those of pentamer and decamer in both the phases would be relatively disfavored. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 81: 90–104, 2001

C–H⋯O H-bonded complexes: How does basis set superposition error change their potential-energy surfaces?

Geometries, vibrational frequencies, and interaction energies of the CNH⋯O3 and HCCH⋯O3 complexes are calculated in a counterpoise-corrected (CP-corrected) potential-energy surface (PES) that corrects for the basis set superposition error (BSSE). Ab initio calculations are performed at the Hartree–Fock (HF) and second-order Mo/ller–Plesset (MP2) levels, using the 6-31G(d,p) and D95++(d,p) basis sets. Interaction energies are presented including corrections for zero-point vibrational energy (ZPVE) and thermal correction to enthalpy at 298 K. The CP-corrected and conventional PES are compared; the uncorrected PES obtained using the larger basis set including diffuse functions exhibits a double well shape, whereas use of the 6-31G(d,p) basis set leads to a flat single-well profile. The CP-corrected PES has always a multiple-well shape. In particular, it is shown that the CP-corrected PES using the smaller basis set is qualitatively analogous to that obtained with the larger basis sets, so the CP method becomes useful to correctly describe large systems, where the use of small basis sets may be necessary.

Li+Ion Affinities of Global-Warming Perfluorocarbons

Density functional theory studies were performed for the first time to obtain the Li+ ion affinities of various perfluorocarbons (PFCs) that cause global-warming. Becke's three-parameter hybrid density functional, B3LYP combined with 6-31G(d), 6-311+G(2d), and 6-311+G(3df) basis sets were utilized for this purpose. We present optimized geometries of PFC−Li+ ion complexes at B3LYP/6-311+G(2d) level. The frequencies obtained at the same level were used to verify all the optimized geometries are minima. The following PFCsCF4, CHF3, CH2F2, CH3F, C2F6, C4F8, with SF6were considered in the present study. The calculated Li+ affinities for CF4, CHF3, CH2F2, CH3F, C2F6, C4F8, and SF6 are 12.31, 19.64, 26.84, 30.10, 17.20, 21.09, and 16.92 kcal/mol, respectively at B3LYP/6-311+G(3df) after zero-point energy and thermal energy corrections. The large Li+ affinities indicate the validity of our proposed Li+ ion attachment mass spectrometry to quantify the emission of these greenhouse gases from semiconductor industries. Complex geometries were obtained and the ion−molecular bonding nature was discussed on the basis of atomic charge, electron density ρ, and its Laplacian.

Effects of Hydrogen on the Three-Dimensional Epitaxial Growth of Ni(100), (110), and (111)

The effects of hydrogen on Ni homoepitaxy have been investigated by examining rate constants for mobility of Ni during the Ni-growth process with and without the presence of a small amount of hydrogen impurity which is found to act primarily as a catalyst. The rate constant activation energies are determined by classical-potential total-energy calculations with semiclassical zero-point energy corrections for the hydrogen atom. This work extends previous work in which we have examined the effects of H on submonolayer (two-dimensional) Ni(100) growth in Haug, K.; Zhang, Z.; John, D.; Walters, C. F.; Zehner, D. M.; Plummer, W. E. Phys. Rev. B. 1997, 55, R10233−R10236 and Haug, K.; Do, N. K. N. Phys. Rev. B. 1999, 60, 11095. We find that fast diffusion of H atoms occurs on the flat Ni surfaces and the presence of these highly mobile H atoms is found to have significant effects on the mobility of lone Ni adatoms on Ni(100), but not on the Ni(110) and Ni(111) surfaces. The H atoms are also found to have significant catalytic effects lowering the step edge (Ehrlich−Schwoebel descent) barrier and therefore accelerating breakdown of three-dimensional Ni islands which form during the epitaxial growth on the Ni(100) surfaces, and to a very modest extent on the Ni(111) surface, but this net catalytic effect is not found on the Ni(110) surfaces. While the overall H atom effects on the Ni mobility in these cases are primarily catalytic, the kinetically determined Ni island morphologies may differ substantially over time periods which are long on the deposition time scale, and therefore the morphology differences can become frozen in place.

Theoretical Investigation of Reaction Mechanisms for Carboxylic Acid Formation in the Atmosphere

Theoretical calculations have been carried out to investigate the mechanism of several chemical reactions that may explain the formation of formic acid in the atmosphere. All the envisaged processes involve the so-called Criegee intermediate, H2COO, which is generated in the course of the ozonolysis reaction. We focus on isomerization of carbonyl oxide through bimolecular reactions with H2CO, H2O, SO2, and CO2. The results are compared with those obtained for unimolecular isomerization mechanisms previously reported in the literature. In the bimolecular processes, there is always formation of an intermediate adduct, the stability of which increases in the order CO2 (−24.5 kcal/mol) < SO2 (−43.1 kcal/mol) < H2O (−45 kcal/mol) < H2CO (−49 kcal/mol) (values at the CCSD(T) level with zero-point energy correction at the B3LYP level). Note that the formation of this adduct may or may not be preceded by the formation of a stable complex. Afterward, the adduct decomposes to form the final products according to a ...

CCNN: The last kinetically stable isomer of cyanogen

The dissociation and isomerization stability of the linear cyanogen isomer CCNN, a formally charge-transfer species comprising C2− and N2+, is theoretically investigated by means of ab initio methods, including the Hartree–Fock (HF), the Mo/ller–Plesset perturbation theory from second through fourth order (MP2, MP4SDQ, MP4SDTQ), the configuration interaction with singles and doubles (CISD), the quadratic configuration interaction with singles and doubles (QCISD) as well as with triples [QCISD(T)], and the density functional theory (DFT) including Beck’s three parameter hybrid methods with the Lee–Yang–Parr correlation functional (B3LYP) and with the Perdew–Wang 91 correlation functional (B3PW91) methods. At the QCISD(T)/6-311G(3df)//QCISD(T)/6-311G(d) level with QCISD/6-311G(d) zero-point vibrational energy (ZPVE) correction, the barriers from CCNN to the NNC three-membered ring structure with exocyclic C–C bonding and to the dissociation products C2 and N2 are predicted to be 42.1 and 51.8 kcal/mol, respectively. The QCISD(T)/6-311G(3df) potential energy surface of C2N2 indicates that CCNN may be kinetically more stable than the other two well-studied isomers CNCN and CNNC. Thus, although CCNN is thermodynamically less favorable due to its high energy, it is still experimentally observable. Moreover, a barrier of 5.5 kcal/mol is predicted for the reverse association reaction between C2 and N2 to produce CCNN at the QCISD(T)/6-311G(3df)//QCISD(T)/6-311G(d)+ZPVE level, while both B3LYP and B3PW91 methods erroneously predict a barrierless association process. Finally, the possible strategy for the formation of CCNN in laboratory and in interstellar space is discussed in detail. The calculated results may provide a useful guide for future laboratory and interstellar identification of the last kinetically stable isomer of cyanogen, CCNN.

Dimethyldioxirane, Carbonyl Oxide, and the Transition State Connecting Them: Electronic Structures, Relative Energies, and Vibrational Frequencies

The electronic structures and vibrational frequencies of dimethyl-substituted carbonyl oxide and its cyclic isomer dimethyldioxirane have been investigated using high-level ab initio quantum mechanical techniques with large basis sets. The equilibrium geometries have been optimized at the self-consistent field (SCF), the single and double excitation configuration interaction (CISD), the coupled cluster with single and double excitation (CCSD), and the CCSD with connected triple excitations [CCSD(T)] levels of theory. The absolute and relative energies of carbonyl oxide, dimethyldioxirane, and the transition state between them have also been computed. At the highest level of theory employed in this study, TZP CCSD(T), dimethyldioxirane is predicted to be lower in energy than the carbonyl oxide by 23.2 kcal/mol with the inclusion of zero-point vibrational energy (ZPVE) corrections. The energy barrier for the cyclization of carbonyl oxide becomes 19.5 kcal/mol at the same level of theory. Harmonic vibrational frequencies and infrared (IR) intensities are determined at the DZP SCF and TZP SCF levels of theory for the dimethyl-substituted carbonyl oxide and the transition state, and at correlated levels (CISD and CCSD) with DZP and TZP basis sets for dimethyldioxirane. The experimental vibrational frequencies of dimethyldioxirane are assigned using the present theoretical predictions. It is hoped that the theoretical frequencies for the dimethyl carbonyl oxide isomer will stimulate new experiments.

The most stable isomers in HC4N and HC6N

The relative stability of the triplet-linear A to the singlet B with a C3-ring in an HC4N molecule was investigated at the density functional level of theory with Becke's three parameters (B3LYP) and the coupled-cluster singles and doubles with triple contributions (CCSD(T)). The various qualities of the correlation-consistent basis sets were used. After the zero-point vibrational energy corrections, the singlet B is by 4.2kcal/mol lower in energy than the triplet A at the present highest level of theory (CCSD(T)/cc-pCVTZ with core electron correlations (CCSD(T)(full)/cc-pCVTZ)). The B3LYP calculations failed to predict the relative stability, however, the optimized geometries even with the cc-pVDZ basis set are in good agreement with the accurate CCSD(T)/cc-pVTZ ones. For the larger HC6N molecule, the CCSD(T)/cc-pVTZ and cc-pCVDZ energy calculations (with and without core electron correlations) on the basis of the B3LYP optimized parameters were performed to predict the relative stabilities of the triplet-linear C to the two singlet-rings (D and E). The triplet C is the most stable isomer, which are by 2.4 and 4.0kcal/mol lower in energy than the singlets D and E, respectively, after the corrections due to the zero-point vibrational energies.

Infrared Depletion Spectroscopy Suggests Mode-Specific Vibrational Dynamics in the Hydrogen-Bonded Aniline−Diethyl Ether (C6H5−NH2···OC4H10) Complex

The vibrational frequencies of the N−H stretching modes of aniline, after forming a strong H-bonded complex with diethyl ether (DEE), are measured with infrared depletion spectroscopy that uses cluster-size-selective REMPI time-of-flight mass spectrometry. Two strong absorption features observed at 3372 and 3478 cm-1 are assigned to the H-bonded and free N−H stretching vibrations of the 1:1 aniline−DEE complex. The spectral broadening observed for the free and H-bonded N−H stretching modes indicates mode-specific vibrational energy dynamics. While the narrow bandwidth (≈3 cm-1) of the N−H stretch at 3478 cm-1 incorporates all the common broadening mechanisms including IVR, the broader (≈10 cm-1) absorption feature at 3372 cm-1 suggests vibrational predissociation/IVR of the H-bonded complex, with a subpicosecond lifetime. The red shifts of the N−H stretching vibrations of aniline agree with the ab initio calculated (MP2/6-31G**) aniline−DEE structure in which one of the N−H bonds of aniline interacts with the oxygen atom of DEE through a hydrogen bond, giving a binding energy of 13 kJ mol-1 with due corrections for BSSE and zero-point energy. The electronic 0−0 band origin for the S1 ← S0 transition is observed at 33292 cm-1, giving a significant red shift of 737 cm-1 from that of the bare aniline. The vibrational bands associated with the R2PI spectrum are assigned to the intermolecular modes of the complex.

Influence of the vibrational zero-point energy correction on the amine inversion barrier and the far-infrared spectrum of methylamine

The vibrational zero-point energy correction is determined for the methyl torsion and amine hydrogen wagging potential energy function. It is found that the amine inversion barrier increases from 1727.27 cm −1 up to 1850.65 cm −1 which is in better agreement with the value of 1937 cm −1 deduced from experiment. In addition, the splittings calculated for the fundamental band reproduce fairly well the experimental data.

Mechanisms of Hydrogen Exchange of Methane with H-Zeolite Y: An ab Initio Embedded Cluster Study

We present ab initio embedded cluster studies on the mechanism of hydrogen exchange of methane with H-Zeolite Y. We found that inclusion of the Madelung field stabilizes the formation of a carbonium-like transition state, and consequently reduces the reaction barrier by 17−23 kJ/mol, relative to the corresponding bare cluster predictions. Using the CCSD(T)/6-31G(d,p) level of theory, including zero-point energy (∼10 kJ/mol) and tunneling (1.6 kJ/mol) corrections, the activation energy is predicted to be 124 ± 5 and 137 ± 5 kJ/mol for hydrogen exchange from two different binding sites. These predictions agree well with the experimental estimate of 122−130 kJ/mol. We also found that it is necessary to include the Madelung potential to find preferrential proton siting at site O1 versus site O4, in agreement with experimental observation.

Theoretical Study of the Thermal Decomposition of N,N‘-Diacyl-N,N‘-Dialkoxyhydrazines: A Comparison of HF, MP2, and DFT

The thermal decomposition of N,N‘-diacyl-N,N‘-dialkoxyhydrazines, (N(COR1)(OR2))2, to the corresponding ester and dinitrogen was investigated with high-level ab initio and density functional calculations. The results suggest that the decomposition proceeds via a two step 1,1-elimination. Coupled cluster calculations on several model systems (R1R2H; R1CH3, R2H; R1R2CH3) at the density functional geometry (CCSD(T)//B3P86) with zero-point energy and thermal corrections at the B3P86 level show that the barrier for the first elimination, the rate-determining step, is 24−34 kcal/mol, while the barrier for the second step in the two step 1,1-elimination is only 1−3 kcal/mol, a value that is much smaller than the exothermicity of the first step. This result explains why experimentalists have been unable to trap the intermediate nitrene. The critical point associated with the concerted elimination is shown to be a second-order saddle point on the potential energy surface at the HF and density functional levels of ...

Cation π interaction between acetylcholine and the benzene ring

Ab initio self-consistent-field second-order Moller–Plesset perturbation theory computations including basis set superposition error and zero-point vibrational energy corrections have been performed on the complexation of benzene with the polar head of acetylcholine (ACh). The ACh–benzene complex is about 0.5 kcal/mol less stable than the corresponding tetramethylammonium (TMA)–benzene complex, with a structure a little distorted with respect to the latter. The electronic structure of ACh is little modified by the ligand. Overall, the replacement of one methyl group of TMA by the acetyl tail of ACh does not affect strongly the complexation to benzene, as far as the main interaction is concerned.

Ab initio quantum chemical and experimental study of structure, harmonic vibrational frequencies and internal Ph–SO3 torsion of benzenesulfonate anion

A combined quantum chemical and experimental study of the structure, harmonic vibrational frequencies, charge distribution and internal torsional motion of benzenesulfonate anion was performed. The geometry of the anion was optimized at the HF/3-21+G(d) and HF/6-31+G(d) levels of theory, followed by numerical harmonic vibrational analysis. Furthermore, the FT-IR spectra of several metal benzenesulfonate salts were recorded. The computed structural parameters of the anion at both levels of theory are in very good agreement with the X-ray data. Regarding the vibrational analysis, the HF/6-31+G(d) force field is significantly superior over the HF/3-21+G(d). On the basis of the HF/6-31+G(d) vibrational analysis, several important reassignments of the IR bands owing to the benzenesulfonate anion are suggested. The larger basis set methodology gives the correct order of conformational stabilities (staggered vs. eclipsed anion conformation), while the lower basis reproduces the experimental data only upon inclusion of the zero-point energy corrections. On the basis of ab initio HF/6-31+G(d) energetics, the torsional energy levels of the Ph–SO3 rotor were computed within a one-dimensional approach, diagonalizing the torsion Hamiltonian in the free-rotor basis. Both the Mulliken and the NPA charge-partitioning schemes predict a strong delocalization of the anionic charge over the phenyl ring, while the electrostatic potential based schemes (CHelp, CHelpG and MK) predict only a slight delocalization.

A Theoretical Study of the Methyl and Aldehyde Torsion FIR Spectra in Symmetric Propanal Isotopomers

This paper is an extension of the techniques developed by us [A. Vivier-Bunge, V. H. Uc, and Y. G. Smeyers, J. Chem. Phys. 109, 2279 (1998)] for standard propanal. In that paper the potential energy surface for the simultaneous methyl and asymmetric aldehydic torsions was calculated at RHF/MP2 level using the 6-311(3df,p) basis set for propanal. The fit of the energy values to symmetry-adapted functional forms was carried out by using the 28 energy values which retain the C3 dynamical symmetry of the methyl group in the optimization procedure. With this potential, as well as with the kinetic parameters and the electric dipole moment variations, the FIR frequencies and intensities for the methyl and aldehyde torsions of seven symmetric isotopomers of propanal were determined theoretically using two-dimensional calculations. The calculated spectra of propanal and three of its isotopomers were compared with the available experimental data. It is found that the calculations for the cis conformer satisfactorily reproduce the aldehyde and methyl torsion spectra and furnish also methyl torsionally excited progressions for the aldehyde torsion modes. The methyl torsion frequencies agree especially well whenever the methyl group is nondeuterated. The small deviations encountered for the deuterated compound are probably due to some mass effect, such as the zero-point vibrational energy correction, which is not taken into account in the present calculations. Finally, the influence of the deuteration on the intensities is discussed.

Effects of the Complexation by the Mg2+ Cation on the Stereochemistry of the Sugar−Diphosphate Linkage. Ab Initio Modeling on Nucleotide−Sugars

Ab initio molecular orbital calculations of the 2-O-methyldiphosphono-tetrahydropyran dianion (1) and the complex of magnesium with 2-O-methyldiphosphono-tetrahydropyran (2) are used to model the conformational behavior of the sugar−diphosphate linkage in sugar−nucleotides. The geometry and energy of each conformer were calculated at different basis set levels, from 6-31G* to cc-pVTZ(-f)++, using the SCF, DFT/B3LYP, and LMP2 methods. The vibrational frequencies were calculated at the HF/6-31G* level and the zero-point energy, thermal, and entropy corrections were evaluated. The results of conformational analyses of 1 and 2 clearly show that interactions of the diphosphate linkage with the Mg2+ cation alter the conformational preferences about the anomeric and the diphosphate linkages. These changes influence the overall 3D shape adopted by nucleotide−sugars and, therefore, might have consequences for their functions in biological processes. The effects of solvation and of the full first hydration shell of the metal on the stability of relevant conformers have also been calculated. The results show that a delicate balance between intramolecular and intermolecular interactions determines the conformational equilibrium around the sugar−diphosphate linkage. As a result, the sugar−diphosphate linkage can adopt several different conformations depending on the environment.