Zero-point Energy Corrections Research Articles

Silanes and germanes as free-radical reducing agents: an ab initio study of hydrogen atom transfer from some trialkylsilanes and germanes to alkyl radicals

Ab initio molecular orbital calculations using a (valence) double-ζ pseudopotential (DZP) basis set, with (MP2, QCISD) and without (SCF) the inclusion of electron correlation predict that hydrogen atoms, methyl, ethyl, isopropyl and tert-butyl radicals abstract hydrogen atom from silane, methylsilane, dimethylsilane, trimethylsilane, trisilylsilane and the analogous germanes via transition states in which the attacking and leaving radicals adopt colinear (or nearly so) arrangements. Except for reactions involving trisilylsilane which are predicted at the MP2/DZP level to involve transition states with Si–C distances of about 3.19 A, transition states which have (overall) Si–C and Ge–C separations of 3.12–3.15 and 3.24–3.26 A respectively are calculated; these distances appear to be independent of the number of methyl substituents on the group(IV) element, but appear to be slightly sensitive to the nature of the attacking radical, with marginally earlier transition states calculated as the degree of alkyl substitution on the attacking radical is increased. At the highest level of theory (QCISD/DZP//MP2/DZP), energy barriers (ΔE1‡) of 27–57 (Si) or 26–44 (Ge) kJ mol–1 are predicted for the forward reactions, while the reverse reactions (ΔE2‡) are calculated to require 85–134 (Si) or 102–138 (Ge) kJ mol–1. These values are marginally affected by the inclusion of zero-point vibrational energy correction. Importantly, QCISD and MP2 calculations appear to predict correctly the relative ordering of activation energies for alkyl radical reduction by silanes: tertiary < secondary < primary; SCF/DZP, AM1 and AM1 (CI = 2) calculations perform somewhat more poorly in their prediction of relative radical reactivity.

Density functional theory and ab initio study of oxywater isomerization into hydrogen peroxide

Density functional theory (DFT) methods have been applied to study the stability of the oxywater molecule through its 1,2-hydrogen shift to hydrogen peroxide. All 12 DFT methods found oxywater molecules to be a minimum on the potential energy surfaces (PESs) for the isomerization reaction. The computed activation energies were between 1.5 and 4.8 kcal mol −1. The best estimation was the one obtained with G2 and hybrid DFT methods with a zero-point energy correction. It was estimated that the activation barrier was around 4 kcal mol −1 and that oxywater lies above hydrogen peroxide by 46 kcal mol −1. In this way, the existence of oxywater molecules was confirmed. Furthermore, it was demonstrated that hybrid DFT methods could accurately compute the PESs for low barrier, highly exothermic reactions. The energies obtained were in qualitative agreement with experimental results.

Ab Initio Study of the Isomers: HNNSi, HSiNN, and HNSiN

Abstract We report on new structural, energetics, and vibrational frequency data for three isomers on the potential energy surface [H, Si, N, N] calculated at the UHF, MP2, and CCSD(T)/6-311G(2d) levels of theory. Similarly to SiNN, conventional methods fail to predict a thermodynamic stability for the isomer HSiNN. However, at the CCSD(T) level, the species HSiNN was found to lie 13.63 kcal mol−1 lower in energy than HNNSi; the isomer HNSiN was located 47.62 kcal mol−1 above the global minimum. After including the zero-point energy corrections, the isomer HSiNN becomes almost isoenergetic with its dissociation products HSi and N2; its detection might be likely only at low temperatures.

A correlated ab initio study of the [formula omitted] transition in MgCCH

The A ̃ 2Π ← X ̃ 2Σ + transition in MgCCH was studied with correlation consistent basis sets and single- and multireference correlation methods. The à 2Π excited state was characterized in detail; the X ̃ 2Σ + ground state has been described elsewhere recently. The estimated complete basis set (CBS) limits for valence correlation, including zero-point energy corrections, are 22668, 23191, and 22795 cm −1 for the RCCSD(T), MRCI, and MRCI + Q methods, respectively. A core-valence correction of +162 cm −1 shifts the RCCSD(T) value to 22830 cm −1, in good agreement with the experimental result of 22807 cm −1.

Theoretical studies of the decyclization /cyclization of the C 6H 5 radical

The decyclization/cyclization reactions of the phenyl radical have been investigated by means of ab initio theory. The geometries and structures of the phenyl radical, the open-chain radical and also the transition state were optimized at the UHF/6-31G ∗ level, and their relative energies refined by the spin-projected (UMP3(PUMP3) method with UHF/6-31G ∗ zero-point energy corrections. Evaluations of the unimolecular rate constant for both directions of this isomerization reaction were carried out in terms of Rice-Ramsperger-Kassel-Marcus theory.

The gas-phase conformations of valine: an ab initio study

A survey of 108 possible gas-phase conformations of valine led to 26 unique conformers at the HF/6-31G ∗ level. Relative energies are reported at the MP2/6-31+G ∗//HF/6-31G ∗ level with corrections for zero-point vibrational energies. The results indicate that the preferred orientation of the isopropyl group depends on the interaction between the carboxyl and the amino group. In comparison to alanine, it does not appear that the larger size of the side chain significantly biases the conformational preferences.

Staggered and eclipsed conformations of C 2F 6: A systematic ab initio study

Molecular geometries, energies, and vibrational frequencies for eclipsed and staggered conformers of perfluoroethane were determined by ab initio calculations. Basis set effects were investigated systematically with progressively larger basis sets, up to triple zeta, d and f polarization functions plus diffuse functions on all atoms. Electron correlation was included by means of Møller-Plesset perturbation calculations to the third order. Vibrational frequencies, calculated at both Hartree-Fock (HF) and second order Møller-Plesset perturbation (MP2) methods, were used to make zero-point energy and thermal corrections to electronic energies. Some semi-empirical methods and molecular mechanics force fields were also employed for comparison. The rotational barrier (3.81 kcal mol −1) predicted from the HF/6-311 + G(3df) method is close to the measured electron diffraction value of 4.40 kcal mol −1 (−0.90, + 1.10). The MP2/6-31 1G(d) level gives a lower barrier of 3.33 kcal mol −1, and the best MP3 calculation, MP3/6-311 + G(3df)//MP2/6-311G(d), a value of 3.55 kcal mol −1.

Violations of Hund's rule in molecules — where to look for them and how to identify them

Violations of Hund's rule are predicted to be found in D 4 h cyclobutadiene (CBD), D 8 h cyclooctatetraene (COT), and in non-Kekulé hydrocarbon diradicals that have disjoint NBMOs. In D 4 h CBD the singlet is calculated to lie below the triplet by − ΔE ST = 6.3 kcal mol −1 at the CAS-SDCI + (Q)/6-31G ∗ level of theory. This value is bracketed by the CASSCF and CASPT2N values of, respectively, − ΔE ST = 10.6 and 4.0 kcal mol −1. For D 8 h COT CASSCF, CASPT2N and MR-(π-SD, σ-S)CI + (Q)/6-31G ∗ calculations give, respectively, − ΔE ST = 15.8, 6.7 and 8.5 kcal mol −1. In both [4 n]annulenes the geometry of highest symmetry is the equilibrium geometry of the triplet but the transition state for bond shifting in the singlet. Consequently, the “bond-alternation” vibration, which shortens half the CC bonds and lengthens the other half, has a relatively high frequency in the triplet but an imaginary frequency in the singlet. As a result, zero-point vibrational energy corrections increase − ΔE ST by ca. 2 kcal mol −1 in both antiaromatic annulenes. The role of calculations in assigning the electron photodetachment spectrum of COT − and thereby confirming experimentally that D 8 h COT really does violate Hund's rule is discussed. CASPT2N calculations of UV spectra are shown to be useful for deciding whether the singlet or triplet state is responsible for the UV-Vis spectrum of non-Kekulé hydrocarbon diradicals. Comparison of the spectra calculated for the singlet and the triplet states of 1,2,4,5-tetramethylenebenzene (TMB), 4,5-dimethylenecyclopentane-1,3-diyl (DMCPD) and 2,3-dimethylenecyclohexane1,3-diyl (DMCHD) with those observed indicates that TMB has a singlet ground state but that DMCPD and DMCHD both have triplet ground states.

Ab Initio and DFT Potential Energy Surfaces for Cyanuric Chloride Reactions

Ab initio and nonlocal density functional theory (DFT) calculations were performed to determine reaction mechanisms for formation of the six-membered ring C3N3Cl3 (cyanuric chloride) from the monomer cyanogen chloride (ClCN). MP2 geometry optimizations followed by QCISD(T) energy refinements and corrections for zero-point energies for critical points on the potential energy surface were calculated using the 6-31G* and 6-311+G* basis sets. DFT (B3LYP) geometry optimizations and zero-point corrections for critical points on the potential energy surface were calculated with the 6-31G*, 6-311+G*, and cc-pVTZ basis sets. Good agreement is found for MP2 and DFT geometries and frequencies of cyanuric chloride and ClCN when compared with experimental values. Two formation mechanisms of cyanuric chloride were investigated, the concerted triple association (3 ClCN → cyanuric chloride) and the stepwise association (3ClCN → Cl2C2N2 + ClCN → cyanuric chloride). All calculations show that the lower energy path to formation of cyanuric chloride is the concerted triple-association. MP2 and DFT intrinsic reaction coordinate calculations starting from the transition state for concerted triple association reaction proceeding toward the isolated monomer resulted in the location of a local minimum, stable by as much as 8.0 kcal/mol, that corresponds to a weakly-bound cyclic (ClCN)3 cluster. The existence of this cluster on the reaction path for the concerted triple association could lower the entropic hindrance to this unusual association reaction mechanism. The DFT/cc-pVTZ barrier to concerted triple association relative to isolated ClCN is 42.9 kcal/mol. The QCISD(T)//MP2/6-311+G* barrier to concerted triple association is 41.0 kcal/mol. The DFT/cc-pVTZ barrier to formation of the dimer (stepwise association reaction) is 63.4 kcal/mol while the QCISD(T)//MP2/6-311+G* barrier is 76.7 kcal/mol. The barrier to formation of cyanuric chloride relative to the (ClCN)3 minimum requires ∼46−49 kcal/mol, indicating that the concerted triple-association reaction via formation of the (ClCN)3 prereaction intermediate is the lower energy path to formation of cyanuric chloride. The temperature-corrected (T = 298 K) heats of reaction for formation of cyanuric chloride from ClCN are −63.4 and −61.2 kcal/mol for the B3LYP/cc-pVTZ and the QCISD(T)//MP2/6-311+G* predictions, respectively.

Kinematic mass model of activated bimolecular reactions: Molecular shape effects and zero-point energy corrections

The recently proposed simple collision model of activated bimolecular reactions which takes into account the nonspherical shape of molecules and includes the effects of reagent rotation has been studied in considerable detail, in order to determine its range of applicability. By taking the limit of hard nonspherical molecules in which the formulation becomes rigorous it is possible to show that the model is likely to work well if the shape of the potential surface is prolate in the region of the reaction barrier, as long as a direct reaction mechanism is involved. The model cannot be expected to work for diatomic reactants if the shape of the potential surface is pronouncedly oblate because of the complicated reorientation effects which such a surface exerts on the trajectories and which do not appear amenable to simple modeling. The original model is improved by including the zero-point energy corrections on the assumption of vibrational adiabaticity en route to the barrier. With the improved model, cross-sections are calculated for the reactions: H+F2, O+H2, N+O2, O+HBr, O+HCl, O+DCl, and the results are compared with those of quasiclassical trajectory calculations and, in the last two cases, also with those of quantum mechanical calculations. The possible origins of the significant discrepancies which occur in some cases are also discussed.

Transition state barrier height for the reaction H2CO→H2+CO studied by multireference Mo/ller–Plesset perturbation theory

The second-order multireference Mo/ller–Plesset perturbation method (MRMP) was applied to the accurate estimation of the transition state barrier height of H2CO→H2+CO reaction. The best estimate for the classical barrier height is 84.5 kcal/mol at the highest level of MRMP theory with the quadruple zeta plus triple polarization basis set and with the active space of 12 electrons in 11 active orbitals. The inclusion of zero-point vibrational energy correction reduces the activation energy to 79.1 kcal/mol, which is in excellent agreement with the experimental value of 79.2±0.8 kcal/mol [Polik, Guyer, and Moore, J. Chem. Phys. 92, 3453 (1990)]. Analysis of the second-order energies in terms of internal, semi-internal, and external contributions shows that the present MRMP provides a well balanced treatment for the estimation of the energy difference between the equilibrium and transition state structures.

Extended ab initio studies of the vinylidene–acetylene rearrangement

The ground state vinylidene–acetylene isomerization was investigated by ab initio molecular electronic structure theory. The coupled-cluster method with single, double, and noniterative inclusion of triple excitations [CCSD(T)]; with single, double, and noniterative inclusion of triple and quadruple excitations [CCSD(TQ)]; and with full single, double, and triple excitations (CCSDT) were used to treat the effect of electron correlation. Several correlation-consistent polarized valence basis sets, cc-pVXZ, were employed. Theoretical limiting values of the energetics of the reaction were then deduced from the series of computations. With zero-point energy correction, the energy of reaction is −42.95 kcal/mol and the reaction barrier is 1.5 kcal/mol. Both agree excellently with experimental values.

Structure and vibrations of catechol(methanol)1 in the S and S1 state

The structure as well as the inter- and intramolecular vibrations of the catechol (methanol)1 cluster are investigated both experimentally and theoretically. By using resonant two-photon ionization (R2PI) and dispersed fluorescence (DF) spectroscopy, the vibrational transitions of the S0 and S1 state are obtained. In order to find the corresponding vibrations of the S0 and S1 state, DF spectra are recorded by pumping the electronic origin and the most intense vibrations of the R2PI spectrum. According to ab initio calculations performed at the Hartree–Fock level [6-31G(d,p) basis], including MP2, BSSE, and ZPE (zero point energy) corrections, the most stable structure turns out to be translinear. The calculated vibrational frequencies are in close agreement to the experimental values. Since the catechol(methanol)1 cluster has no symmetry, all intermolecular fundamental vibrations of the S0 and S1 state spectra can be assigned. A large number of combination bands and overtone vibrations are observed in the low frequency region (&amp;lt;200 cm−1) of the S0 and S1 state spectra. From the DF spectrum obtained by pumping the low frequency ρ1 vibration, it can be concluded that the catechol(methanol)1 cluster undergoes a geometry change in the S1 state. The OH…O bond turns out to be nonplanar with respect to the aromatic plane. This confirms the results reported for catechol and the catechol(H2O)1 cluster.

Zero-point energy correction for trajectory rate data

K. F. Lim, J. Chem. Soc., Faraday Trans., 1997, 93, 669 DOI: 10.1039/A608119C

A CASSCF study of the S 0 and S 1 states of phenol

Different basis sets and active spaces have been employed to determine the geometries and vibrational frequencies of phenol in its electronic ground and first excited state at the CASSCF level of theory. Good agreement with experimentally determined rotational constants was achieved using Dunning's correlation consistent cc-pVDZ basis set. The electronic origin of the S 1 ← S 0 excitation has been calculated with an accuracy of 0.1 eV considering zero-point energy corrections for both the S 0 and S 1 states. Additionally, S 1 state frequencies were calculated at the CIS/cc-pVDZ level of theory.

Towards the accurate computation of properties of transition metal compounds: the binding energy of ferrocene

Recently published ab initio computations on ferrocene in the framework of coupled-cluster as well as multireference perturbation theory are exploited to obtain a theoretical best estimate of 655 ± 15 kcal/mol for the heterolytic bond disruption enthalpy. This best estimate was obtained by establishing the complete atomic orbitals basis set limit at the level of single-reference second-order perturbation theory, and computing corrections for relativistic effects, semicore (3s/3p) electron correlation effects, vibrational zero-point energy corrections, and structural relaxation energies of the fragments. Agreement with the experimental value of 635 ± 6 kcal/mol is unsatisfactory.

Chloromethyldichloromethylsilane and chloromethyldimethylchlorosilane: structure, conformational composition and torsional potential determined by gas-phase electron diffraction and ab initio molecular orbital calculations

The molecular structure and conformation of chloromethyldichloromethylsilane (TCS), ClH 2CSiCl 2CH 3, and chloromethyldimethylchlorosilane (DCS), ClH 2CSiCl(CH 3) 2, have been studied using gas-phase electron diffraction at 24°C and ab initio molecular orbital calculations. These molecules exist in the gas phase as a mixture of two conformers, anti (A, torsion angle ∅(ClCSiX) = 180°, X = CH 3 (TCS) or Cl (DCS)) and gauche (G, torsion angle (∅(ClCSiX) close to 60°). Some relevant structural parameters for TCS (gauche) are: bond lengths ( r g), r( SiC(Cl)) = 1.877(5) A ̊ , r( SiCH 3) = 1.854(5) A ̊ , r( CCl) = 1.787(7) A ̊ , r( 〈 SiCl 〉 ) = 2.046(3) A ̊ (average value); bond angles (∠ α), ∠CSiC = 113.6(23)°, ∠SiCCl = 110.4(6)°, ∠ 〈 CSiCl 〉 = 108.8(5)°, ∠ClSiCl = 107.9(12)°; torsion angle, ∅(G) = 51(5)°. For TCS the experimental gas-phase composition (%) was (anti/gauche) 16 84 with error limits ± 15%. With ΔS° A-G = −R ln 2 + ΔS∗ , where ΔS∗ is the entropy difference from vibrational and rotational partition functions calculated from ab initio, an estimated conformational energy difference ΔE° A-G = 0.6(± 0.7) kcal mol −1 was obtained for TCS. Some relevant structural parameters for DCS (anti) are: bond lengths ( r g), r( SiC(Cl)) = 1.888(3) A ̊ , r( SiCl) = 2.078(5) A ̊ , r( CCl) = 1.793(14) A ̊ ; bond angles (∠ α), ∠ CSiC = 111.5°(assumed), ∠SiCCl = 110.7(10)°, ∠ClSiC(Cl) = 104.0°(assumed), ∠SiCH = 112.3(15)°; torsion angles, ∅(A) = 161(3)°, ∅(G) = 70(8)°. For DCS the anti conformer showed an apparent deviation from the exactly staggered value of 180°, but this is a result of large-amplitude torsional motion about the SiC bond. For DCS the experimental composition was (anti/gauche) 59 41 with error limits ± 16%. Using ΔS° A-G = −R ln 2 + ΔS∗ an estimated conformational energy difference ΔE° A-G = −0.6(± 0.4) kcal mol −1 was obtained from this composition. Error limits are given as 2σ (σ includes estimates of uncertainties in voltage/height measurements and correlation in the experimental data). Full geometry optimizations were performed for all conformers of both molecules employing ab initio molecular orbital HF/6–31G(d) level of theory, while conformational energy calculations were performed at the MP2(fc)/6–311 + G(d,p)//HF/6–31G(d) level, with scaled zero-point vibrational energy corrections from frequency calculations at the HF/6–31G(d) level. The theoretical energies and geometries are compared with the experimental results.

Theoretical studies of the interactions of singlet carbenes with water and alcohols

Results are presented from ab initio calculations which explore the interactions of singlet carbenes with water and alcohols. The carbenes investigated include methylene and carbomethoxycarbene. A number of different minima on the potential energy surfaces have been located and characterized. These minima correspond to oxonium ylide-type structures as well as to hydrogen-bonded structures. Equilibrium geometries, binding energies, and vibrational frequencies have been determined. We also report on the results of preliminary studies of the geometries and energetics of transition states for rearrangement of the oxonium ylides to alcohols or ethers. Calculations were performed at levels of theory ranging from HF/3-21G to MP2/6-311G ∗∗ , and include zero-point energy corrections, as well as basis set superposition error corrections.

Isomerization of SiOH +, HSiOH and H 2SiO: a density functional study

Density functional theory (DFT) is used to investigate the isomerization reactions of SiOH +, and of HSiOH. Linear SiOH + is predicted to be more stable than linear HSiO + by 65.1 kcal mol −1. This energy difference becomes 63.5 kcal mol −1 after zero-point vibrational energy (ZPVE) correction. The barrier height for the endothermic isomerization is predicted to be 96.7 kcal mol −1 (93.1 kcal mol −1 after ZPVE correction). The calculated total energies for HSiOH (cis), HSiOH (trans) and H 2SiO are very close to each other. HSiOH (trans) is predicted to be more stable than the cis-isomer by 0.2 kcal mol −1. HSiOH (trans) is predicted to be more stable than H 2SiO by 2.0 kcal mol −1. Zero-point vibrational energy correction changes the relative stability of HSiOH (cis) and HSiOH (trans) by making the cis-isomer to be more stable than the trans-isomer (0.02 kcal mol −1). ZPVE correction decreases the energy difference between HSiOH (trans) and H 2SiO but does not lead to a reversal of relative stabilities. The predicted barrier height for HSiOH (cis) → HSiOH (trans) reaction is 8.1 kcal mol −1. A much larger barrier height (56.3 kcal mol −1) is predicted for the reaction H 2SiO → HSiOH (trans). Calculated equilibrium geometries, activation energies and vibrational frequencies are shown to be in good agreement with the results of high quality ab initio studies.

Theoretical studies of the interactions of singlet carbenes with water and alcohols

Results are presented from ab initio calculations which explore the interactions of singlet carbenes with water and alcohols. The carbenes investigated include methylene and carbomethoxycarbene. A number of different minima on the potential energy surfaces have been located and characterized. These minima correspond to oxonium ylide-type structures as well as to hydrogen-bonded structures. Equilibrium geometries, binding energies, and vibrational frequencies have been determined. We also report on the results of preliminary studies of the geometries and energetics of transition states for rearrangement of the oxonium ylides to alcohols or ethers. Calculations were performed at levels of theory ranging from HF/3-21G to MP2/6-311G ∗∗, and include zero-point energy corrections, as well as basis set superposition error corrections.