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.     

异硫氰酸与甲亚胺环加成反应机理的理论研究

对异硫氰酸与甲亚胺形成四元或六元环产物的环加成反应进行了理论研究,结果表明,一分子异硫氰酸与一分子甲亚胺形成四元环(1:1)产物P1的反应(1)为经过一个两性离子中间体的分步反应,其中第二步为速控步骤,其活化热垒为107.86kJ/mol.此外,反应(1)的中间体还可与另一甲亚胺或异硫氰酸分子继续反应形成两个不同的六元环(1:2或2:1)产物P2或P3;这两个反应均为协同反应,其活化势垒分别为15.88和21.82kJ/mol.这些结果与当异硫氰酸酯与亚胺发生环加成反应时,只有类似于P2和P3的两种六元环产物生成的实验事实一致。     

1. 5-环辛二烯-3, 7-二炔(C~8H~4)结构和光谱性质的理论研究

采用量子化学从头算方法研究了1,5-环辛二烯-3,7-二炔(C~8H~4)的结构和光谱性质,根据等键反应分析和自然键轨道方法研究了它的稳定性、成键情况和共轭性。结果表明1,5-环辛二烯-3,7-二炔(C~8H~4)分子为平面刚性结构,可能稳定存在。分子中C≡C键与C=C键存在一定程度的共轭,可能具有芳香性。     

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.     

Theoretical study of geometrical effect on the deoxygenation of epoxide by singlet carbenes

The mechanism of the abstraction of oxygen from epoxide by carbenes has been investigated using the B3LYP/6-31G* and MP2/6-311++G(d,p)//B3LYP/6-31G* levels of theory. According to our model calculations, the reactivity of carbene decreases in the order: four-membered ring carbene > six-membered ring carbene > three-membered ring carbene > five-membered ring carbene vinylidene. Moreover, the present work shows that the singlet–triplet splitting of a carbene can be used as a guide for the prediction of its reactivity.     

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.     

吡啶-BH~3相互作用复合物的理论研究

对吡啶-BH~3复合物分别用MP2/6-31+G^*和B3LYP/6-31+G^*进行理论计算以预测该复合物的构型及解离能，得到四种构型，在MP2优化构型基础上作CCSD/6-31+G^*单点能量计算以验证MP2与B3LYP结果的可靠性，然后用B3LYP作振动频率分析，计算了各构型的垂直电离势，最后用更大基组作单点能量计算和自然键轨道(NBO)分析。结果表明，N-B直接相连的构型最稳定，其解离能为141.50kJ/mol,MP2和B3LYP对N-H接近的构型结果相关较大，另外两种构型稳定性介于二者之间，解离能分别为15.18kJ/mol,14.06kJ/mol(MP2/6-31+G^*)。     

Novel H-bonded base dimers as repeat units for information-bearing self-associative duplexes: a B3LYP/6-31G* search

Density functional theory at the B3LYP/6-31G* level with counterpoise correction has been employed to study six sets of nitrogenous bases for the capacity of each to form H-bonded dimers restricted to a chosen pairing configuration. These results are augmented by MP2/6-311++G(d,p) single point calculations on the B3LYP/6-31G* optimized geometries. Each set has two bases, including substituted azoles, imidazoles, pyrimidines, and fused ring systems. This study aims to determine the suitability of each set to furnish H-bonded base pairs which may serve as repeat units for self-associative H-bonded macromolecular duplexes with the capacity to store and replicate information at the molecular level. Out of the various possibilities tested here, a set of two substituted pyrimidines best satisfies the prescribed criteria and may be put forward as a good candidate to yield isomorphic repeat units for designing such synthetic information-bearing macromolecular duplexes. The optimized configurations of these chosen base pairs as calculated at the B3LYP/6-31G* level compare well with those calculated at the B3LYP/6-31++G(d,p) and MP2/6-31G(d,p) levels, and indicate that isomorphism of the two base pairs is independent of method used. Assuming a one-to-one correspondence for encoding information in the macromolecule, such a set of two bases can allow the macromolecule to encode up to 8 types of encrypted species.     

Molecular structure and conformational stability of allylisocyanate—post-Hartree–Fock and density functional theory studies

The molecular structure and conformational stability of allylisocyanate (CH₂CHCH₂NCO) molecule was studied using the ab initio and DFT methods. The geometries of possible conformers, C-gauche (δ=120°, θ=0°) (δ=C=C–C–N and θ=C–C–N=C) and C-cis N-trans (δ=0° and θ=180°) were optimized employing HF/6-31G^*, MP2/6-31G^* levels of theory of ab initio and BLYP, B3LYP, BPW91 and B3PW91 methods of DFT implementing the atomic basis set 6-311+G(d,p). The structural and physical parameters of the above conformers were discussed with the experimental and theoretical values of the related molecules, methylisocyanate and 3-fluoropropene. It has been found that the N=C=O bond angle is not linear as the experimental result for both the conformers and the theoretical bond angle is 173°. The rotational potential energy surfaces have been performed at the HF/6-31G^*, and MP2/6-31G^* levels of theory. The Fourier decomposition potentials were analysed at the HF/6-31G^*, and MP2/6-31G^* levels of theory. The HF/6-31G^* level of theory predicted that the C-gauche conformer is more stable than the C-cis N-trans conformer by 0.41 kJ/mol, but the MP2 and DFT methods predicted the C-cis N-trans conformer is found to be more stable than the C-gauche conformer. The calculated chemical hardness value at the HF/6-31G^* level of theory predicted the C-cis N-trans form is more stable than C-gauche form, whereas the chemical hardness value at the MP2/6-31G^* level of theory favours the slight preference towards the C-gauge conformer.     

Conformational study of the structure of 12-crown-4-alkali metal cation complexes

A conformational search was performed for the 12-crown-4 (12c4)-alkali metal cation complexes using two different methods, one of them is the CONFLEX method, whereby eight conformations were predicted. Computations were performed for the eight predicted conformations at the HF/6-31+G*, MP2/6-31+G*//HF/6-31+G*, B3LYP/6-31+G*, MP2/6-31+G*//B3LYP/6-31+G*, and MP2/6-31+G* levels. The calculated energies predict a C4 conformation for the 12c4-Na+, -K+, -Rb+, and -Cs+ complexes and a C(s) conformation for the 12c4-Li+ complex to be the lowest energy conformations. For most of the conformations considered, the relative energies, with respect to the C4 conformation, at the MP2/6-31+G*//B3LYP/6-31+G* are overestimated, compared to those at the MP2/6-31+G* level, the highest level of theory considerd in this report, by 0.2 kcal/mol. Larger relative energy differences are attributed to larger differences between the B3LYP and MP2 optimized geomtries. Binding enthalpies (BEs) were calculated at the above-mentioned levels for the eight conformations. The agreement between the calculated and experimental BEs is discussed.     

Rearrangement of azirine intermediates to nitriles: Theoretical study of cleavage of 3,4-dihydro-1aH-azirine[2,3-c]pyrrol-2-one to cyanoketene–formaldimine complex

A detailed investigation of the reaction path for the thermal rearrangement of 3,4-dihydro-1aH-azirine[2,3-c]pyrrol-2-one to yield a cyanoketene–formaldimine complex is carried out at the MP2/6-31G* and B3LYP/6-31G* levels of theory. The ring opening of the five-membered pyrrolinone ring and the formation of the nitrile group takes place in a concerted manner, presenting a significant strain energy release and allowing for an electronic stabilization by coarctate conjugation of the transition structure (TS). These two factors make possible a moderate energy barrier. Although the structural features B3LYP/6-31G* theoretical levels, it is found that the MP2 energy barrier (28.8) CCSD(T)/6-31G*//MP2/6-31G* value (17.1 kcal/mol). The complex electronic rearrangement can be rationalized using the theory of coarctate transition structures developed by Herges as the evolution of an azirine structure without referring to a hypothetical vinyl nitrene intermediate. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 912–922, 1998     

Ab initio studies on mechanisms of cycloaddition reaction between dichloro-vinylidene and ethylene

Mechanisms of cycloaddition reaction between singlet dichloro-vinylidene (R1) and ethylene (R2) have been investigated with MP2 and B3LYP /6-31G* methods, including geometry optimization, vibrational analysis, and energy for the involved stationary points on the potential energy surface. CCSD(T)/6-31G* single point calculations are also applied to the geometries from both methods. CCSD(T) relative energies for the stationary points predicted by MP2 and B3LYP are in a very good agreement. Three reaction pathways are located. Along the first one, one intermediate (INT1) is firstly generated, which then rearranges into a three-membered ring compound (P1) via a small barrier of 5.4 kJ/mol; the other two paths share the other intermediate (INT2), which isomerizes into two four-membered ring compounds (P2 and P3) via a chlorine and a hydrogen transfer, respectively. The barriers of the latter two paths are significantly higher by approximately 25 kJ/mol than that of the former (27.2 and 28.8 vs 5.4 kJ/mol), the major reaction is therefore the formation of P1.     

Theoretical studies on the conformations of selenamides

Ab initio HF/6-31+G*, MP2/6-31+G*, B3LYP/6-31+G* level calculations have been performed on HSe-NH₂ to estimate the Se-N rotational barriers and N-inversion barriers. Two conformers have been found withsyn andanti arrangement of the NH₂ hydrogens with respect to Se-H bond. The N inversion barriers in selenamide are 1.65, 2.47, 1.93 kcal/mol and the Se-N rotational barriers are 6.58, 6.56 and 6.12 kcal/mol respectively at HF/6-31+G*, MP2/6-31+G* and B3LYP/6-31+G* levels respectively. The n_N →Σ *_Se-H negative hyperconjugation is found to be responsible for the higher rotational barriers.     

Mechanistic insights into triterpene synthesis from quantum mechanical calculations. Detection of systematic errors in B3LYP cyclization energies

Most quantum mechanical studies of triterpene synthesis have been done on small models. We calculated mPW1PW91/6-311+G(2d,p)//B3LYP/6-31G* energies for many C30H51O+ intermediates to establish the first comprehensive energy profiles for the cationic cyclization of oxidosqualene to lanosterol, lupeol, and hopen-3beta-ol. Differences among these 3 profiles were attributed to ring strain, steric effects, and proton affinity. Modest activation energy barriers and the ample exothermicity of most annulations indicated that the cationic intermediates rarely need enzymatic stabilization. The course of reaction is guided by hyperconjugation of the carbocationic 2p orbital with parallel C-C and C-H bonds. Hyperconjugation for cations with a horizontal 2p orbital (in the plane of the ABCD ring system) leads to annulation and ring expansion. If the 2p orbital becomes vertical, hyperconjugation fosters 1,2-methyl and hydride shifts. Transition states leading to rings D and E were bridged cyclopropane/carbonium ions, which allow ring expansion/annulation to bypass formation of undesirable anti-Markovnikov cations. Similar bridged species are also involved in many cation rearrangements. Our calculations revealed systematic errors in DFT cyclization energies. A spectacular example was the B3LYP/6-311+G(2d,p)//B3LYP/6-31G* prediction of endothermicity for the strongly exothermic cyclization of squalene to hopene. DFT cyclization energies for the 6-311+G(2d,p) basis set ranged from reasonable accuracy (mPW1PW91, TPSSh with 25% HF exchange) to underestimation (B3LYP, HCTH, TPSS, O3LYP) or overestimation (MP2, MPW1K, PBE1PBE). Despite minor inaccuracies, B3LYP/6-31G* geometries usually gave credible mPW1PW91 single-point energies. Nevertheless, DFT energies should be used cautiously until broadly reliable methods are established.     

Reaction of hypochlorous acid with imidazole: formation of 2-chloro- and 2-oxoimidazoles

Reaction of hypochlorous acid (HOCl) with imidazole (Im) taken as a model for the 5-membered ring of guanine, leading to the products 2-chloro- and 2-oxo-imidazoles was investigated at the B3LYP/6-31+G* and B3LYP/AUG-cc-pVDZ levels of density functional theory. For all cases, single point energy calculations were performed at the MP2/AUG-cc-pVDZ level of theory using the geometries optimised at the B3LYP/AUG-cc-pVDZ level. Intrinsic reaction coordinate calculations were performed to ensure genuineness of all the calculated transition states. Effect of aqueous media was investigated by solvating all the species involved in the reactions using the polarizable continuum model. It is found that 2-chloroimidazole (2-ClIm) can be formed following three different reaction schemes while 2-oxoimidazole (2-oxoIm) can be formed following two different reaction schemes. The calculated barrier energies show that formation of 2-oxoIm would be less favored than that of 2-ClIm, which explains the experimental observations on relative yields of 8-chlorodeoxyguanosine and 8-oxodeoxyguanosine.     

The C7-C10 cycloalkanes revisited

The conformers of cycloheptane through cyclodecane have been examined at the B3LYP/6-311+G* and MP2/6-311+G* theoretical levels, with some additional calculations at the CCD/6-311+G* and CCSD(T)/6-311++G** levels. With cyclooctane, B3LYP predicts that the boat-chair and crown conformers have similar energies, whereas MP2 and CCSD(T) predict that the crown conformer is 2 kcal/mol higher in energy. The latter is in agreement with the electron diffraction data. With cyclononane, B3LYP predicts that two of the higher-energy conformers found in molecular mechanics calculations should convert to one of the lower-energy conformers. However, MP2/6-311+G* optimizations find them to be true minima on the potential energy surface. B3LYP systematically predicts larger C-C-C bond angles for these compounds than either MP2 or CCD. The results of molecular mechanics MM4 calculations are generally in good agreement with those obtained using MP2.     

Comparison of ab initio and DFT electronic structure methods for peptides containing an aromatic ring: effect of dispersion and BSSE

We establish that routine B3LYP and MP2 methods give qualitatively wrong conformations for flexible organic systems containing pi systems and that recently developed methods can overcome the known inadequacies of these methods. This is illustrated for a molecule (a conformer of the Tyr-Gly dipeptide) for which B3LYP/6-31+G(d) and MP2/6-31+G(d) geometry optimizations yield strikingly different structures [Mol. Phys. 2006, 104, 559-570]: MP2 predicts a folded "closed-book" conformer with the glycine residue located above the tyrosine ring, whereas B3LYP predicts a more open conformation. By employing different levels of theory, including the local electron correlation methods LMP2 (local MP2) and LCCSD(T0) (local coupled cluster with single, double, and noniterative local triple excitations) and large basis sets (aug-cc-pVnZ, n=D, T, Q), it is shown that the folded MP2 minimum is an artifact caused by large intramolecular BSSE (basis set superposition error) effects in the MP2/6-31+G(d) calculations. The B3LYP functional gives the correct minimum, but the potential energy apparently rises too steeply when the glycine and tyrosine residues approach each other, presumably due to missing dispersion effects in the B3LYP calculations. The PWB6K and M05-2X functionals, designed to give good results for weak interactions, remedy this to some extent. The reduced BSSE in the LMP2 calculations leads to faster convergence with increasing basis set quality, and accurate results can be obtained with smaller basis sets as compared to canonical MP2. We propose LMP2 as a suitable method to study interactions with pi-electron clouds.     

Theoretical studies on the gas-phase pyrolysis of 2-phenoxycarboxylic acids: an ONIOM approach

Various ONIOM combinations-ONIOM(HF/6-31G*: PM3), ONIOM(B3LYP/6-31G*: PM3), ONIOM(MP2/6-31G*: PM3), and ONIOM(MP2/6-31G*: HF/3-21G)--were applied to investigate thermal decomposition mechanisms of four 2-phenoxycarboxylic acids (2-phenoxyacetic acid, 2-phenoxypropionic acid, 2-phenoxybutyric acid, and 2-phenoxyisobutyric acid) in the gas phase. All the transition states and intermediates of the reaction paths were optimized. The reaction pathway of four reactants yielding the phenol, CO, and the corresponding carbonyl compound was characterized on the potential energy surface and found to proceed stepwise. The first step corresponds to the elimination of phenol and the formation of alpha-lactone intermediate through a five-membered ring transition state, and the second step is the cycloreversion process of alpha-lactone intermediate to form CO and the corresponding carbonyl compound. The reaction pathway of latter three compounds to produce the carboxylic acid and phenol via a four-membered cyclic transition structure was also examined theoretically. Comparison with experiment indicates that the activation parameters for the fist reaction channel are accurately predicted at the ONIOM(MP2/6-31G*: HF/3-21G) level of theory.     

Peculiar basis set dependence of the energetics of C2S2H2 isomers. In search of adequate and affordable basis set for routine calculations

Quantum mechanical calculations using the Hartree-Fock (HF), post-Hartree-Fock {MP2 and CCSD(T)}and gradient-corrected hybrid density functional variant, B3LYP methodology in conjugation with basis sets like 6-31G*, 6-311G** and cc-pVTZ, were employed to critically probe the right quality of basis set and the appropriate level of theory that can be applied in modeling the organo-sulfur compounds. The relative stability ordering of 1,2-dithiete and dithioglyoxal reveal the delicate basis set dependence especially on ‘S’ atom. Single point calculations at the B3LYP, MP2 and CCSD(T) levels using a series of basis set ranging from double ζ quality all the way up to the quintuple ζ quality were done to illustrate the effect of electron correlation and the basis set dependency for these compounds. Basis set requirements are much higher than affordable for medium sized molecules as very slow convergence is seen even when the calculations are carried out with basis set as high as cc-pV5Z at the B3LYP and MP2 level of theories.     

A comparative study on the nature and strength of O–O, S–S, and Se–Se bond

A computational study on dichalcogenide molecules (R₂X₂; X = O, S, Se; R = H, CH₃, NH₂) has been carried out employing B3LYP and MP2 levels using 6-31+G*, 6-311+G*, 6-311++G**, and PVDZ basis sets. The relative energies have been evaluated at G2MP2 also. The rotational barriers and bond dissociation energies indicate that S–S bond is stronger than Se–Se and O–O bond. NBO analysis at MP2/6-31+G* suggest the presence of partial π character between X–X bond that decreases in the order S–S > Se–Se > O–O. Fuki functions for nucleophilic and electrophilic attack fail to distinguish the reactivity of S and Se. The proton affinities of the O₂H₂, S₂H₂, Se₂H₂ decrease in the order Se > S > O.