An Ab Initio Molecular Orbital Study of Valence Bond Isomers of Silabenzene and Phosphabenzene

Ab initio molecular orbital calculation at HF/6-31G*, HF/6-31G**, HF/6-311G**, HF/6-311++G**, RMP2-FC/6-31G*, and B3LYP/6-31G* levels of theory for geometry optimization and MP4(SDQ)/6-31G* for a single point total energy calculation are reported for silabenzene ( 7 ), phosphabenzene ( 8 ) and 16 valence bond isomers of silabenzene and phosphabenzene ( 9-24 ). The calculated energy difference (19.78 kcal mol m 1 ) between silabenzene and the most stable valence bond isomer of silabenzene (1-silabenzvalene, 9 ) is much smaller than the difference (73.60 kcal mol m 1 ) between benzene and benzvalene ( 2 ). The energy difference between phosphabenzene and the most stable valence bond isomer of phosphabenzene (1-phosphabenzvalene, 17 ) is calculated to be 43.29 kcal mol m 1 .     

An Ab Initio Molecular Orbital Study of Isophosphinines

Ab initio molecular orbital calculation at HF/6-31G*, HF/6-31G**, HF/6-311G**, HF/6-311++G**, RMP2-FC/6-31G*, and B3LYP/6-31G* levels of theory for geometry optimization and MP4(SDQ)/6-31G* for a single-point total energy calculation are reported for phosphinine and 13 isophosphinines 7-19 . Isomers 7-11 with an allenic system are calculated to be 8-18 kcal mol m 1 more stable than structures 12-17 with an acetylenic moiety. The calculated energy difference (66.19 kcal mol m 1 ) between phosphinine and the most stable isophosphinine (1-phospha-1,2,4-cyclohexatriene, 10 ) is smaller than the difference (78.96 kcal mol m 1 ) between benzene and the most stable isobenzene (cyclohexa-1,2,4-triene, 2 ). The isophosphinines 18 and 19 , with a butatriene moiety, are calculated to be the least stable isomers.     

Comparison of Some Computational Methods for Geometry Optimisation of Phosphorus Acid Derivatives

Several economical methods for geometry optimization, that should be applicable to larger molecules, have been evaluated for 19 phosphorus acid derivatives. MP2/cc-pVDZ geometry optimizations are used as reference points and the geometries obtained from the other methods are evaluated with respect to deviations in bond lengths and angles, from the reference geometries. The geometry optimization methods are also compared to the much used B3LYP/6-31G(d) method. Single point energies obtained by subsequent EDF1/6-31+G(d) or B3LYP/6-31+G(d,p) calculations on the respective equilibrium geometries are also reported relative to the energies obtained from the reference geometries. The geometries from HF/MIDI! optimizations were closer to those of the references than the geometries of the HF/3-21G(d), HF/6-31G(d), and B3LYP/MIDI! optimizations. The EDF1/6-31+G(d) or B3LYP/6-31+G(d,p) single point energies obtained from the HF/3-21G(d), HF/6-31G(d), and B3LYP/MIDI! geometries gave a mean absolute deviation (MAD) from that of the reference geometries of 1.4-3.9 kcal mol m 1 . The HF/MIDI! geometries, however, gave EDF1/6-31+G(d) and B3LYP/6-31+G(d,p) energies with a MAD of only about 0.5 and 0.55 kcal mol m 1 respectively from the energies obtained with the reference geometries. Thus, use of HF/MIDI! for geometry optimization of phosphorus acids is a method that gives geometries of near-MP2 quality, resulting in a fair accuracy of energies in subsequent single point calculations, at a much lower computational cost other methods that give similar accuracies.     

Investigation of the use of B3LYP zero-point energies and geometries in the calculation of enthalpies of formation

The use of B3LYP/6–31G^* zero-point energies and geometries in the calculation of enthalpies of formation has been investigated for the enlarged G2 test set of 148 molecules [J. Chem. Phys. 106 (1997) 1063]. A scale factor of 0.96 for the B3LYP zero-point energies gives an average absolute deviation nearly the same as scaled HF/6–31G^* zero-point energies for G2, G2(MP2), and B3LYP/6–311 + G(3df,2p) enthalpies. A scale factor of 0.98, which has been recommended in some studies, increases the average absolute deviation by about 0.2 kcal/mol. Geometries from B3LYP/6–31G^* are found to do as well as MP2/6–31G^* geometries in the calculation of the enthalpies of formation.     

The performance of the rapid estimation of basis set error and correlation energy from partial charges method on new molecules of the G3/99 test set

Experimental enthalpies of formation have been approximated using single-point Hartree–Fock (HF)–self-consistent-field (SCF) total energies plus the rapid estimation of basis set error and correlation energy from partial charges (REBECEP) energy corrections. The energy corrections are calculated from the HF–SCF partial atomic charges and optimized atomic energy parameters. The performance of the method was tested on 51 closed-shell neutral molecules (50 molecules from the G3/99 thermochemistry database plus urea, composed of H, C, N, O, and F atoms). The predictive force of the method is demonstrated, because these larger molecules were not used for the optimization of the atomic parameters. We used the earlier RECEP-3 [HF/6-311+G(2d,p)] and REBECEP [HF/6-31G(d)] atomic parameter sets obtained from the G2/97 thermochemistry database (containing small molecules) together with natural population analysis and Mulliken partial charges. The best results were obtained using the natural population analysis charges, although the Mulliken charges also provide useful results. The root-mean-square deviations from the experimental enthalpies of formation for the selected 51 molecules are 1.15, 3.96, and 2.92 kcal/mol for Gaussian-3, B3LYP/6-11+G(3df,2p), and REBECEP (natural population analysis) enthalpies of formation, respectively (the corresponding average absolute deviations are 0.94, 7.09, and 2.27 kcal/mol, respectively). The REBECEP method performs considerably better for the 51 test molecules with a moderate 6-31G(d) basis set than the B3LYP method with a large 6-311+G(3df,2p) basis set. Received: 10 March 2001 / Accepted: 5 July 2001 / Published online: 11 October 2001     

Prediction of the 13C NMR Chemical Shifts of Fluorenone Analogues by the GIAO Method

After the geometry optimization at B3LYP/6-31+G(d,p) level,the NMR calcula-tions of a series of fluorenone analogues have been carried out by GIAO method at HF/6-31+G(d) level and B3LYP/6-311G+(2d,p) level,respectively.The 13C NMR chemical shifts calculated at HF/6-31+G(d) level show better agreement with the observed values.By a series of linear correction equations (δpred=a + bδcalc),accurate prediction of 13C chemical shifts was achieved for the new fluorenone compound.The linear correlation of δpred with δexptl is excellent,and the square of correlation coefficient,r2,is up to 0.994.The maximum absolute difference between δpred and δexptl,Δδ,is 4.6 ppm,and the root-mean-square error between δpred and δexptl is only 2.6 ppm.     

A new scheme for determining the intramolecular seven-membered ring N-H...O=C hydrogen-bonding energies of glycine and alanine peptides

In this paper a new scheme was proposed to calculate the intramolecular hydrogen-bonding energies in peptides and was applied to calculate the intramolecular seven-membered ring N-H...O=C hydrogen-bonding energies of the glycine and alanine peptides. The density-functional theory B3LYP6-31G(d) and B3LYP6-311G(d,p) methods and the second-order Moller-Plesset perturbation theory MP26-31G(d) method were used to calculate the optimal geometries and frequencies of glycine and alanine peptides and related structures. MP26-311++G(d,p), MP26-311++G(3df,2p), and MP2/aug-cc-pVTZ methods were then used to evaluate the single-point energies. It was found that the B3LYP6-31G(d), MP26-31G(d), and B3LYP6-311G(d,p) methods yield almost similar structural parameters for the conformers of the glycine and alanine dipeptides. MP2/aug-cc-pVTZ predicts that the intramolecular seven-membered ring N-H...O=C hydrogen-bonding strength has a value of 5.54 kcal/mol in glycine dipeptide and 5.73 and 5.19 kcal/mol in alanine dipeptides, while the steric repulsive interactions of the seven-membered ring conformers are 4.13 kcal/mol in glycine dipeptide and 6.62 and 3.71 kcal/mol in alanine dipeptides. It was also found that MP26-311++G(3df,2p) gives as accurate intramolecular N-H...O=C hydrogen-bonding energies and steric repulsive interactions as the much more costly MP2/aug-cc-pVTZ does.     

Quantum Chemical Study of the Lithium Cation Coordination by Dimethylsulfoxide Molecules

A quantum chemical study of the lithium ion coordination by dimethylsulfoxide molecules has been performed by HF/6-31G (d), HF/6-311+(d,p), and B3LYP/6-311+(d,p) methods with full geometry optimization. The coordination number of Li⁺ in the dimethylsulfoxide was found to be equal to 4. Heats of the complex formation at each stage of the process were calculated (in kJ/mol); these are 267.2, 203.0, 122.8, and 90.5 in HF/6-31G(d); 270.6, 200.5, 108.8, and 82.9 in HF/6-311+(d,p); 256.3, 186.8, 100.8, and 80.1 in B3LYP/6-311+(d,p) for 1-4 DMSO molecules, respectively. The paper reports on the structure parameters of the complexes formed, and the corresponding charge distributions. The solvation of the lithium cation with dimethylsulfoxide molecules was shown to be more preferable than that with water molecules in the gas phase. A possibility for an Li⁺·(4DMSO)·OH^- associate to form in the DMSO medium was examined using the HF/6-311+(d,p) method.     

Influence of diffuse and polarization functions on the second-order Møller–Plesset optimized dihedral angle of biphenyl

 Using 6-31G and 6-311G basis sets to which diffuse and polarization functions were added in a stepwise fashion (a total of 16 basis sets), Hartree–Fock (HF), MP2 and B3LYP geometry optimizations were performed on biphenyl. With the MP2 method, diffuse functions raise the dihedral angle φ, for example, from 46.3° for 6-31G to 54.1° for 6-311++G, while polarization functions lower it, for example, from 54.1° for 6-311++G to 42.1° for 6-311++G(2d,2p). For a single set of polarization functions, φ(MP2) lies close to or above φ(HF) (44–47°), but for a double set it is below φ(HF) and is close to B3LYP values (38–42°) which show little basis set dependence. The most reliable value for φ, 42.1° [MP2/6-311++G(2d,2p)], is expected to increase slightly by adding more diffuse functions. The corresponding best calculated energy barrier at 0° (coplanar conformation) is 2.83 kcal/mol, much higher than the experimental estimate (1.4 ± 0.5 kcal/mol). The barrier at 90° is 1.82 kcal/mol, in line with the experimental estimate (1.6 ± 0.5 kcal/mol) and with previous theoretical results. Received: 9 September 2002 / Accepted: 15 November 2002 / Published online: 1 April 2003 Correspondence to: Friedrich Grein e-mail: fritz@unb.ca Acknowledgement. The author would like to thank NSERC (Canada) for financial support.     

苯并氧化呋咱稳定性和异构化的DFT和ab initio研究

运用B3LYP/6-31G(d)密度泛函理论（DFT）方法对苯并氧化呋咱、邻二亚硝基苯及其间的异构化反应进行了计算研究。结果表明,苯并氧化呋咱的分子总能量比邻二亚硝基苯的低;由苯并氧化呋咱异构为邻二亚硝基苯的正向反应活化能（Ea+=51.0kJ/mol）,与文献实测值（58.6kJ/mol）较接近,而其逆向反应活化能（Ea-=4.6kJ/mol）很小,从而揭示了苯并氧化呋咱比邻二亚硝基苯更稳定·此外,进行了HF/3-21G、HF/6-31G(d)和MP2/6-31G(d)//6-31G(d)水平下相应的计算,发现B3LYP-DFT的结果较abinitio为优。谐振动频率的B3LYP/6-31G(d)计算还支持了邻二亚硝基苯为苯并氧化呋咱“自-自”互变重排反应的中间体。     

The X1 method for accurate and efficient prediction of heats of formation

We propose the X1 method which combines the density functional theory method with a neural network (NN) correction for an accurate yet efficient prediction of heats of formation. It calculates the final energy by using B3LYP6-311+G(3df,2p) at the B3LYP6-311+G(d,p) optimized geometry to obtain the B3LYP standard heats of formation at 298 K with the unscaled zero-point energy and thermal corrections at the latter basis set. The NN parameters cover 15 elements of H, Li, Be, B, C, N, O, F, Na, Mg, Al, Si, P, S, and Cl. The performance of X1 is close to the Gn theories, giving a mean absolute deviation of 1.43 kcalmol for the G399 set of 223 molecules up to 10 nonhydrogen atoms and 1.48 kcal/mol for the X107 set of 393 molecules up to 32 nonhydrogen atoms.     

Accurate prediction of heats of formation by a combined method of B3LYP and neural network correction

Recently, we proposed the X1 method which combines the B3LYP/6‐311+G(3df,2p)//B3LYP/6‐311+G(d,p) method with a neural network correction for an accurate yet efficient prediction of heats of formation (Wu and Xu, J Chem Phys 2007, 127, 214105). In this contribution, we discuss in detail how to set up the X1 neural network. We give examples, showing how to apply the X1 method and how the applicability of X1 can be extended. The overall mean absolute deviation of the X1 method from experiment for the 488 heats of formation is 1.52 kcal/mol compared with 9.44 kcal/mol for the original B3LYP results. © 2008 Wiley Periodicals, Inc. J Comput Chem 2009     

The rate enhancement for prolyl cis-to-trans isomerization of cyclic CPFC peptide is caused by an increase in the vibrational entropy of the transition state

The conformational preferences and prolyl cis-trans isomerization of oxidized and reduced Ac-Cys-Pro-Phe-Cys-NH2 (CPFC peptides) have been carried out using the ab initio HF/6-31+G(d) and hybrid density functional B3LYP/6-311++G(d,p) levels of theory. The most preferred conformations of oxidized and reduced CPFC peptides with the trans prolyl peptide bond have a type-I beta-turn for the Pro-Phe sequence in common. In particular, the transition states for both forms are stabilized by the intramolecular hydrogen bonds between the prolyl nitrogen and the N-H group of the Phe3 residue. The rotational barrier DeltaGct to the cis-to-trans isomerization for the oxidized CPFC peptide is calculated to be 19.37 kcal/mol at the B3LYP/6-311++G(d,p)//HF/6-31+G(d) level of theory, which is lower by 0.88 kcal/mol than that of the reduced CPFC peptide. This may indicate that the rate constant kc-->t of the prolyl cis-to-trans isomerization for the oxidized form is about 4 times larger than that of the reduced form, which is reasonably consistent with the value deduced from NMR experiments. In particular, the increase in vibrational entropy for the transition state of the oxidized form over that of the reduced form contributes to enhance the rate constant for the prolyl cis-to-trans isomerization of the oxidized form.     

Corannulene as a Lewis base: computational modeling of protonation and lithium cation binding.

A computational modeling of the protonation of corannulene at B3LYP/6-311G(d,p)//B3LYP/6-311G(d,p) and of the binding of lithium cations to corannulene at B3LYP/6-311G(d,p)//B3LYP/6-31G(d,p) has been performed. A proton attaches preferentially to one carbon atom, forming a sigma-complex. The isomer protonated at the innermost (hub) carbon has the best total energy. Protonation at the outermost (rim) carbon and at the intermediate (bridgehead rim) carbon is less favorable by ca. 2 and 14 kcal mol(-)(1), respectively. Hydrogen-bridged isomers are transition states between the sigma-complexes; the corresponding activation energies vary from 10 to 26 kcal mol(-)(1). With an empirical correction obtained from calculations on benzene, naphthalene, and azulene, the best estimate for the proton affinity of corannulene is 203 kcal mol(-)(1). The lithium cation positions itself preferentially over a ring. There is a small energetic preference for the 6-ring over the 5-ring binding (up to 2 kcal mol(-)(1)) and of the convex face over the concave face (3-5 kcal mol(-)(1)). The Li-bridged complexes are transition states between the pi-face complexes. Movement of the Li(+) cation over either face is facile, and the activation energy does not exceed 6 kcal mol(-)(1) on the convex face and 2.2 kcal mol(-)(1) on the concave face. In contrast, the transition of Li(+) around the corannulene edge involves a high activation barrier (24 kcal mol(-)(1) with respect to the lowest energy pi-face complex). An easier concave/convex transformation and vice versa is the bowl-to-bowl inversion with an activation energy of 7-12 kcal mol(-)(1). The computed binding energy of Li(+) to corannulene is 44 kcal mol(-)(1). Calculations of the (7)Li NMR chemical shifts and nuclear independent chemical shifts (NICS) have been performed to analyze the aromaticity of the corannulene rings and its changes upon protonation.     

A density functional theory study of the structure and vibrational spectra of beta-carotene, capsanthin, and capsorubin

A theoretical study of the structure and the vibrational spectra of the beta-carotene molecule and its derivatives capsanthin and capsorubin is carried out. We first investigate systematically the theoretical method which provides the best results for beta-carotene by performing ab initio calculations at the HF/6-31G(d), SVWN/6-31G(d), PBE0/6-31G(d), BLYP/6-31G(d), B3LYP/6-31G(d), B3LYP/6-31G(d,p), B3LYP/6-311G(d), and B3LYP/6-311G(d,p) levels and by using previous theoretical results available in the literature obtained at the AM1 and BPW91/6-31G(d) levels. The influence of both the level of calculation and the size of the basis set used in the geometry optimization and in the determination of the IR and Raman spectra of this molecule is thus analyzed. It is confirmed that the hybrid functional B3LYP with the basis 6-31G(d) is the method that gives the best results as a whole. By use of this level of calculation, we next optimize the molecular geometries of related molecules of capsanthin and capsorubin, which to the best of our knowledge have only been studied at the semiempirical AM1 level. In addition we calculate the IR and Raman spectra of these molecules at the B3LYP/6-31G(d) level of theory. The results obtained for capsanthin show on the one hand that the double bond of the beta-ionone ring is outside the polyene chain plane, due to the repulsion between the hydrogen atoms of the ring methyl groups and the hydrogen atoms of the polyene chain, and on the other hand that the carbonyl double bond in the other headgroup is very close to planarity with the polyene chain, since in this case such a repulsion does not exist. For the molecule of capsorubin the two carbonyl groups also take the same coplanar orientation relative to the polyene chain. The IR and Raman spectra theoretically computed for these two molecules are finally compared with their experimental spectra and the vibrational normal modes of the main signals are interpreted.     

Improved modification for the density-functional theory calculation of thermodynamic properties for C-H-O composite compounds

A three-parametric modification equation and the least-squares approach are adopted to calibrating hybrid density-functional theory energies of C(1)-C(10) straight-chain aldehydes, alcohols, and alkoxides to accurate enthalpies of formation DeltaH(f) and Gibbs free energies of formation DeltaG(f), respectively. All calculated energies of the C-H-O composite compounds were obtained based on B3LYP6-311++G(3df,2pd) single-point energies and the related thermal corrections of B3LYP6-31G(d,p) optimized geometries. This investigation revealed that all compounds had 0.05% average absolute relative error (ARE) for the atomization energies, with mean value of absolute error (MAE) of just 2.1 kJ/mol (0.5 kcal/mol) for the DeltaH(f) and 2.4 kJ/mol (0.6 kcal/mol) for the DeltaG(f) of formation.     

Structure and conformational stability of CH2CHCH2X (X=F, Cl and Br) molecules—post Hartree–Fock and density functional theory methods

The molecular structure and conformational stability of CH₂CHCH₂X (X=F, Cl and Br) molecules were studied using ab initio and density functional theory (DFT) methods. The molecular geometries of 3-fluoropropene were optimized employing BLYP and B3LYP levels of theory of DFT method implementing 6-311+G(d,p) basis set. The MP2/6-31G^*, BLYP and B3LYP levels of theory of ab initio and DFT methods were used to optimize the 3-chloropropene and 3-bromopropene molecules. The structural and physical parameters of the molecules are discussed with the available experimental values. The rotational potential energy surface of the above molecules were obtained at MP2/6-31G^* and B3LYP/6-311+G(d,p) levels of theory. The Fourier decomposition of the rotational potentials were analyzed. The HF/6-31G^* and MP2/6-31G^* levels of theory have predicted the cis conformer as the minimum energy structure for 3-fluoropropene, which is in agreement with the experimental values, whereas the BLYP/6-311+G(d,p) and B3LYP/6-311+G(d,p) levels of theory reverses the order of conformation. The ΔE values calculated for 3-chloropropene at MP2/6-31G^*, BLYP/6-311+G(d,p) and B3LYP/6-311+G(d,p) levels of theory show that the gauche form is more stable than the cis form, which is in agreement with the experimental value. The same levels of theory have also predicted that the gauche form is stable than cis for 3-bromopropene molecule. The maximum hardness principle has been able to predict the stable conformer of 3-fluoropropene at HF/6-31G^* level of theory, but the same level of theory reverses the conformational stability of 3-chloropropene and 3-bromopropene molecules and MP2/6-31G^* level of theory predicted the stable conformer correctly.     

Transition state structure and energetics of the N(2)O + X (X = Cl,Br) reactions

The structural and vibrational properties of the transition state of the N(2)O + X (X = Cl,Br) reactions have been characterized by ab initio methods using density functional theory. We have employed Becke's hybrid functional (B3LYP), and transition state optimizations were performed with 6-31G(d), 6-311G(2d,2p), 6-311+G(3d,2p), and 6-311+G(3df,2p) basis sets. For the chlorine atom reaction the coupled-cluster method (CCSD(T)) with 6-31G(d) basis set was also used. All calculations resulted in transition state structures with a planar cis arrangement of atoms for both reactions. The geometrical parameters of transition states at B3LYP are very similar, and the reaction coordinates involve mainly the breaking of the N-O bond. At CCSD(T)/6-31G(d) level a contribution of the O-Cl forming bond is also observed in the reaction coordinate. In addition, several highly accurate ab initio composite methods of Gaussian-n (G1, G2, G3), their variations (G2(MP2), G3//B3LYP), and complete basis set (CBS-Q, CBS-Q//B3LYP) series of models were applied to compute reaction energetics. All model chemistries predict exothermic reactions. The G3 and G2 methods result in the smallest deviations from experiment, 1.8 and 0 kcal mol(-1), for the enthalpies of reaction for N(2)O reaction with chlorine and bromine, respectively. The G3//B3LYP and G1 methods perform best among the composite methods in predicting energies of the transition state, with a deviation of 1.9 and 3.0 kcal mol(-1), respectively, in the activation energies for the above processes. However, the B3LYP/6-311+G(3df,2p) method gives smaller deviations of 0.4 and -1.0 kcal mol(-1), respectively. The performance of the methodologies applied in predicting transition state energies was analyzed.     

Computational studies of the structure and vibrational spectra of hexafluorodisilane

Ab initio calculations predict that D_3d symmetry of Si₂F₆ is more stable than D_3h symmetry. The calculated potential barrier to internal rotation was 0.77, 0.73 and 0.78 kcal/mol using HF/6-31G*, B3LYP/6-31G* and MP2/6-31G* methods respectively, which was in good agreement with the experimental value between 0.51±0.10 and 0.73±0.14 kcal/mol. The optimized geometries, harmonic force fields, infrared intensities, Raman activities, and vibrational frequencies are reported for D_3d symmetry of Si₂F₆ from HF/6-31G* and B3LYP/6-31G*. A normal coordinate analysis was carried out. The average error between the scaled DFT frequencies obtained from the B3LYP/6-31G* calculation and observed frequencies was 4.2 cm⁻¹ and the average error between the scaled HF and observed frequencies was 2.2 cm⁻¹.     

Conformational studies in the cyclohexane series. 2. Phenylcyclohexane and 1-methyl-1-phenylcyclohexane

The structures and relative energies of the conformers of phenylcyclohexane, and 1-methyl-1-phenylcyclohexane have been calculated at theoretical levels including HF/6-31G, B3LYP/6-311G, MP2/6-311G, MP2/6-311(2df,p), QCISD/6-311G, and QCISD/6-311G(2df,p). The latter gives conformational enthalpy (DeltaH degrees ), entropy (DeltaS degrees ), and free energy (DeltaG degrees ) values for phenylcyclohexane that are in excellent agreement with the experimental data. The calculations for 1-methyl-1-phenylcyclohexane find a free energy difference of 1.0 kcal/mol at -100 degrees C, favoring the conformation having an axial phenyl group, that is in only modest agreement with the experimental value of 0.32 +/- 0.04 kcal/mol. The origin of the phenyl rotational profiles for the conformers of phenylcyclohexane and 1-methyl-1-phenylcyclohexane is discussed.