A theoretical conformational study on the structural parameters involved in the ring strain of exo-unsaturated four-membered heterocycles,Y = CCH2CH2X

The effect of ring-puckering angle on the structural parameters (bond lengths and angles) involved in the ring strain of a series of four-membered heterocycles (1–16) was theoretically demonstrated by using the ab initio methods MP2 and HF, and the DFT methods PBE1PBE, B3LYP, SVWN5 with 6-31+G(d,p) as basis set. The results revealed that the bonds within the ring (C–X and C–C) are the most sensitive to puckering angle changes. The variation of the C–X and C=Y bond lengths as function of puckering angle are determined by a balance between the 1,3 repulsive interactions and the electronic nature of the heteroatoms X and Y. Particularly, for azetidines and phosphetanes, the C–X and C=Y bond lengths exhibit a major increase at axial conformations. In general, the C–C bond length decreases with the puckering angle for all heterocycles. While the heteroatom–H bonds (in the ring skeleton) are very sensitive to geometric changes, exhibiting an increasing behaviour for equatorial conformations and a decreasing behaviour for axial conformations highly puckered (? > ?20°). The C–X–C angle decreases monotonically with the puckering angle, increasing the Baeyer strain on the studied molecules. Finally, all methods predicted a similar behaviour for the studied parameters as function of the puckering angle, although some smaller differences in the predictions of their respective values, especially at HF level, were observed.     

Potential use of small basis set on the calculations of electronic properties of some four-membered heterocycles: a conformational study

The potential use of small basis sets upon a low level of theory was studied on the calculations of electronic properties (dipole moment, static polarisability and static hyperpolarisabilities) of a series of 16 four-membered heterocycles with an exocyclic double bond at the position 3 (1–16). First, the calculations were performed within the Hartree–Fock (HF) approximation using 6-31G, 6-31G(d,p) and 6-31+G(d,p) as basis sets for the different conformational states of each molecule, and the results obtained were compared with the MP2/6-31+G(d,p) results reported. In the second place, in order to know the real potential of HF calculations, these were compared with those calculated using larger approaches such as MP2/6-311+G(d,p), MP2/aug-cc-pVDZ, CCS/6-311+G(d,p), CCS/aug-cc-pVDZ, CCS/aug-cc-pVTZ, CCSD/6-31+G(d) and CCSD/cc-pVDZ, taken into account only the planar and equilibrium geometries of each molecules. The HF approaches permit us to obtain a good qualitative representation of the dipole moment as a function of puckering angle in comparison with MP2, CCS and CCSD levels for all tested molecules. However, only HF/6-31+G(d,p) provides quantitative values of dipole moment for the heterocycles 1, 5 and 13 in comparison with MP2, CCS and CCSD levels. On the other hand, the polarisability and hyperpolarisabilities were quite sensitive to the quality of level of theory and basis sets. In particular, HF/6-31+G(d,p) predicted a representative approximation of alpha for the molecule 16 in comparison with larger methods as MP2/aug-cc-pVDZ, CCS/aug-cc-pVDZ and CCS/aug-cc-pVTZ, while a detailed analysis showed that HF can be used in the calculation of alpha for the molecules 3, 7, 11 and 15, but it requires the use of extended basis sets. Also, HF/6-31+G(d,p) predicted values of beta very similar to those calculated at the MP2 and CCSD levels used, for the planar and equilibrium geometry of the molecules 10 and 14. Furthermore, HF/6-31+G(d,p) described a representative dependence of this property with the puckering angle for the heterocycles 9, 10 and 14, compared with the MP2 curves.     

Anatomy of molecular properties evaluated with explicitly correlated electronic wave functions

Static electric dipole and quadrupole moments were evaluated at the explicitly correlated second-order Møller–Plesset (MP2-F12) level for BH, CO, H₂O, and HF molecules. The electron correlation contributions to the multipole moments were further decomposed into the direct (unrelaxed) and indirect (orbital response) components; we found that both components are equally important for the conventional (MP2) contribution, whereas the F12 correction to these properties originates primarily from the orbital response effects. Finally, the direct contribution dominates in the perturbative Hartree–Fock basis set incompleteness (CABS singles) correction. Two basis set families were employed: the standard aug-cc-pVXZ series and the cc-pVXZ-F12 series designed specifically for the F12 methods. The aug-cc-pVXZ MP2-F12 multipole moments usually have smaller basis set errors than the cc-pVXZ-F12 counterparts, albeit their differences are small at the triple (X = T) and quadruple (X = Q) zeta level. With the MP2-F12 calculations, the basis set errors of dipole and quadrupole moments can be reduced to ～0.001 a.u., or roughly 0.1%, at the aug-cc-pVDZ and aug-cc-pVTZ levels, respectively.     

Molecular properties with dual basis set methods

The dual basis set approach has proven to be very successful for accurately estimating total energies with large basis sets. This study extends the applications of this technique to the calculation of molecular properties, including energy derivatives with respect to nuclear positions and to an external electric field. All energy derivatives have been calculated numerically via finite-differences. Molecular gradients and Hessians as well as dipole moments and polarizabilites have been calculated at the HF and MP2 levels using two alternative versions of the dual basis set method. The accuracy of these approaches is discussed in the context of quality of basis sets used in calculations. It is shown that even quite poor results obtained with the 6-311G basis set are significantly improved in dual basis set calculations with the 6-311G(d,p) and 6-311G(3df,3dp) basis sets.     

New basis sets for the evaluation of the CO–Ne van der Waals complex interaction induced electric dipole moment and polarizability surfaces

Using the coupled cluster singles and doubles method together with the recently developed LPol-n (n?=?ds, dl, fs, fl), the aug-pc-2, the SVPD, the TZVPD and Dunning's x-aug-cc-pVXZ basis sets, we calculate the interaction induced electric dipole moment and polarizability of the CO–Ne van der Waals complex. We consider the effect of extending the bases with different sets of mid-bond functions, and after a systematic basis set study carried out at a representative set of intermolecular geometries, we select the aug-cc-pVTZ, the aug-pc-2, the LPol-fs and the TZVPD bases with a set of 3s3p2d1f1g mid-bond functions placed in the middle of the van der Waals bond for the evaluation of the whole interaction induced property surfaces. After having determined the optimal parameters of appropriate analytical functions fitting the interaction induced properties, the resulting surfaces are used in semiclassical calculations of the dielectric and refractivity second virial coefficients of the system. All through this study the results obtained with Dunning's basis set hierarchy and reported in Phys. Chem. Chem. Phys., 11, 9871 (2009) are taken as reference.     

The keto-enol equilibrium in substituted acetaldehydes: focal-point analysis and ab initio limit

High-level ab initio electronic structure calculations up to the CCSD(T) theory level, including extrapolations to the complete basis set (CBS) limit, resulted in high precision energetics of the tautomeric equilibrium in 2-substituted acetaldehydes (XH₂C-CHO). The CCSD(T)/CBS relative energies of the tautomers were estimated using CCSD(T)/aug-cc-pVTZ, MP3/aug-cc-pVQZ, and MP2/aug-cc-pV5Z calculations with MP2/aug-cc-pVTZ geometries. The relative enol (XHC?=?CHOH) stabilities (ΔE _{e,CCSD(T)/CBS}) were found to be 5.98?±?0.17, ?1.67?±?0.82, 7.64?±?0.21, 8.39?±?0.31, 2.82?±?0.52, 10.27?±?0.39, 9.12?±?0.18, 5.47?±?0.53, 7.50?±?0.43, 10.12?±?0.51, 8.49?±?0.33, and 6.19?±?0.18?kcal?mol^?1 for X?=?BeH, BH₂, CH₃, Cl, CN, F, H, NC, NH₂, OCH₃, OH, and SH, respectively. Inconsistencies between the results of complex/composite energy computations methods Gn/CBS (G2, G3, CBS-4M, and CBS-QB3) and high-level ab initio methods (CCSD(T)/CBS and MP2/CBS) were found. DFT/aug-cc-pVTZ results with B3LYP, PBE0 (PBE1PBE), TPSS, and BMK density functionals were close to the CCSD(T)/CBS levels (MAD?=?1.04?kcal?mol^?1).     

HArF和HNO二聚体相互作用氢键的理论研究

用二阶微扰理论结合6-311+G**、6-311++G**和6-311++G(2d,2p)基组对氢键相互作用二聚体HNO···HArF进行研究．在MP2/6-311+G**、MP2/6-311++G**和MP2/6-311++G(2d,2p)水平上，利用标准方法和均衡校正方法对二聚体进行了几何优化、振动频率和相互作用能的计算．对于相互作用能采用G2MP2方法计算．计算结果表明存在两种稳定的二聚体HNO···HArF结构，在这两种结构中，Dimer I(H···F)比Dimer II(H···O)更加稳定．通过振动频率的计算表明，在Dimer I(H···F)中存在N-H···F蓝移氢键，在DimerII(H···O)中存在Ar-H···O红移氢键，并对蓝移氢键加以确认．利用电子密度拓扑学分析和自然键轨道分析对于氢键红移和蓝移进行了合理解释．     

从头计算研究超共轭效应对2-氯乙醇电子波函数的影响

运用从头算的B3LYP和MP2方法研究了2-氯乙醇分子五种构象的电子结构．在自然键轨道理论分析的基础上讨论了存在的分子内氢键和超共轭作用对构象稳定性的影响,结果说明后者是构象稳定性的主要因素．结合电子动量谱学研究了这种超共轭作用对最外价壳层轨道(HOMO)的电子波函数的影响,演示了动量空间HOMO波函数的不同．     

Electric Multipole Moments for Some First—Row Diatomic Hydride Molecules

As an example of the use of the analytical formulas derived for electric multipole moment integrals over STOs in our previous work(I.I.Guseinov,et al.,J.Mol.Struct(Theochem)465(1999)5),the 2ν-pole electric moments have been calculated for the ground electronic states of LiH,BH and FH of the first-row diatomic hydride molecules,Calculated electric multipole moment values are in agteement with literatures.By the use of these analytical formulas the 2^ν-pole moments for multiatomic molecules can be evaluated most efficiently and accurately by employing STOs as basis sets.     

Effect of electron-donating and electron-withdrawing atoms on the C–H…Y hydrogen bond in model X3CH…YZ (X = B,F; YZ = BF,CO, N2) complexes

A computational study of model complexes X₃CH…YZ (X = B, F; YZ = BF, CO, N₂) was undertaken to assess the effect of electron-donating and electron-withdrawing X atoms on the properties of the C–H…Y hydrogen bond. Sequential substitution of the B atoms in B₃CH by F atoms to produce F₃CH allowed for the elucidation of interesting trends in the corresponding hydrogen-bonded complexes. The dipole moments and the dipole moment derivative with respect to C–H bond displacement for the proton donors and the chemical hardness of the Y atom of the proton acceptor YZ were found to be useful parameters for understanding these trends. It was found that a positive dipole derivative favours red-shifted hydrogen bonds, whereas a negative dipole derivative favours blue-shifted hydrogen bonds. However, decreasing hardness of Y (which correlates with increasing intermolecular attraction) modifies the interaction such that either greater C–H bond extensions/red shifts or smaller C–H bond compressions/blue shifts are obtained.     

The accuracy of local MP2 methods for conformational energies

The relative energies of 95 conformers of four peptide models are studied using MP2 and LMP2 methods and correlation consistent basis sets ranging from double-zeta to augmented quintuple-zeta quality. It is found that both methods yield quite similar results, and the differences between MP2 and LMP2 decrease systematically with increasing basis set. Due to reduced intramolecular basis set superposition effects (BSSE), the LMP2 results converge more slowly to the basis set limit for most of these rather small systems. However, for larger peptides, the BSSE has a very large effect on the energy difference between extended and helical structures, leading to a very strong basis set dependence of the canonical MP2 results. It is demonstrated for alanine octapeptides that the basis set error exceeds 30 and 20kJ mol^?1, respectively, if augmented double-zeta and triple-zeta basis sets are used. On the other hand, the LMP2 results are only slightly affected by the basis set size, and, even with augmented double-zeta basis sets, reasonably accurate results are obtained. Furthermore, for the larger systems, the computation times for the LMP2 calculations are shown to be up to one order or magnitude shorter than for canonical MP2 calculations with the same basis set.     

水二聚体分子间相互作用势

利用超分子二阶到四阶多体微扰理论和扩展的相关一致基组(aug-cc-pVTZ)结合有效的中点键函数(3s3p2d1f1g)计算水二聚物的平衡结构和分子间相互作用势,并用平衡方法修正基组重叠误差.在MP2/aug-cc-pVTZ理论级别优化水二聚物几何构型.与正常优化的结果相比,平衡修正优化得到的RO-O和α值分别轻微的增加0.002 nm和0.19°,同时,θ值减小0.013°.在MP2水平利用扩展的相关一致基组结合有效键函数,预言了RO-O和ΔECP值分别为0.0923 nm和-4.86 kcal/mol,计算结果与实验值符合得很好.用exp-4.2势函数拟合分子间相互作用能的离散点,拟合结果与从头算计算的结果一致.     

Cooperativity between the hydrogen bonding and halogen bonding in F3CX ··· NCH(CNH) ··· NCH(CNH) complexes (X=Cl,Br)

MP2 calculations with the cc-pVTZ basis set were used to analyse the intermolecular interactions in F₃CX?···?NCH(CNH)?···?NCH(CNH) triads (X=Cl, Br), which are connected via hydrogen and halogen bonds. Molecular geometries, binding energies, and infrared spectra of the dyads and triads were investigated at the MP2/cc-pVTZ computational level. Particular attention was given to parameters such as the cooperative energies, cooperative dipole moments, and many-body interaction energies. All studied complexes, with the simultaneous presence of a halogen bond and a hydrogen bond, show cooperativity with energy values ranging between ?1.32 and ?2.88?kJ?mol^?1. The electronic properties of the complexes were analysed using the Molecular Electrostatic Potential (MEP), electron density shift maps and the parameters derived from the Atoms in Molecules (AIM) methodology.     

三硝基甲烷键离解能和生成焓的理论计算

采用密度泛函(DFT)四种交换/相关函数(B3LYP、B3P86、B3PW91和PBE0)结合不同的基函数,求得了三硝基甲烷C-NO2键的离解能(BDE),并且通过合理选择参考物硝基甲烷,设计等键等电子对反应,计算了气相三硝基甲烷分子的生成焓(HOF).与实验数据进行比较,PBE0/6-31g*计算出的BDE值最好,误差为-2.1 kcal mol-1;PBE0密度泛函结合带极化函数的6-31g基组得到的HOF值与实验值吻合的最好(误差在0.1 kcal mol-1以内).     

Total lattice potential energy of sodium bromide dihydrate NaBr · 2H2O

In addition to presenting comparative calculations by two approaches for the total lattice potential energy of sodium bromide dihydrate, NaBr · 2H₂O, found to take the value 803.9 kJ mol^-1, we investigate the influence of the size and nature of the basis set used to generate multipole moments in a Hartee-Fock calculation which are in turn used to calculate the Madelung constant. The requirement is one of critical size of the basis set and once this is reached the electrostatic energy will be reliable.     

Comparison of hydrogen and halogen bonds between dimethyl sulfoxide and hypohalous acid: competition and cooperativity

A theoretical study of the complexes formed between dimethyl sulfoxide (DMSO) and hypohalous acid (HOX, X = Cl, Br, and I) has been carried out at the MP2/aug-cc-pVTZ level. For each HOX, four minima binary complexes were found, two mainly with an OH???O hydrogen bond and the other two with an OX???O halogen bond. The hydrogen-bonded complexes are more stable than the halogen-bonded analogues for HOCl and HOBr, while both types of complexes have similar stability in the iodine case. A red shift was found for the associated H–O and X–O bond stretch vibrations and a small blue shift for the distant bonds. As the oxygen of DMSO simultaneously binds with two HOCl molecules, the corresponding interactions are weakened with diminutive effect. This diminutive effect is the largest in the complexes with two OH???O hydrogen bonds but the smallest in those with two OCl???O halogen bonds.     

Combining rule for interaction energies of the (CO)2, (N2)2 and CO-N2 complexes

The relationship between interaction energies of the most stable structures of the (CO)₂, (N₂)₂ and CO-N₂ complexes is investigated using the supermolecule CCSD(T) and MP4 methods and aug-cc-pVXZ (X = D,T,Q) basis sets extended by a set of midbond functions centred in the middle of the intermolecular bond. A simple combining rule for interaction energies of this triad of clusters is proposed.     

Gaussian basis sets of triple and quadruple zeta valence quality for correlated wave functions

Contracted basis sets of triple and quadruple zeta (TZ and QZ, respectively) valence quality for the atoms from H to Ar are presented. They have been determined from fully-optimized basis sets of primitive Gaussian-type functions generated in atomic Hartree–Fock (HF) calculations. Sets of Gaussian polarization functions optimized at the Møller–Plesset second-order (MP2) level were added to the TZ and QZ basis sets. This extends earlier work on segmented contracted double zeta valence basis sets. The performance of the basis sets are assessed in molecular HF and MP2 calculations for a sample of diatomic molecules by a comparison of energies, dissociation energies, and dipole moments with results obtained numerically or using basis sets reported in the literature. By fitting the directly calculated values through two extrapolation schemes, estimates of the complete basis set limit for second order correlation energy have been obtained. In addition, results for MP2-R12/A calculations to establish the basis set convergence for the standard calculations are also presented.     

The influence of deformation on the reactivity of C=C bonds in reactions with ozone

The influence of strain in the reaction center containing a double bond on double bond reactivity at the first stage of the reaction with ozone was studied by the B3LYP density functional theory method and ab initio MP2, CCSD, QCISD, and MRMP2 multireference methods. The 6-31+G** and 6-311+G** basis sets were used. The reactions of ozone with ethylene and butylene were studied. Deformation (ɛ) was introduced by using the C=C bond length or the distance between extreme carbon atoms as a coordinate not subjected to optimization. Stretching of the double bond was found to activate the reaction by the mechanisms of symmetrical and nonsymmetrical addition. The sensitivities to deformation were similar in the two channels. When the butene fragment as a whole was stretched, a different picture was observed, and the reaction with ozone was decelerated. In both cases, the logarithms of rate constants linearly depended on ɛ. The calculation results were analyzed using the approach developed earlier, which allowed the calculation results to be used to obtain an analytic form of the dependence of activation energy E _a on the strength of bonds and to relate deformation-induced changes in E _a to the length and rigidity of the initial and transition states.