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.     

Mass spectrometric and ab initio study of the interaction between 9-methylguanine and amino acid amide group

The temperature dependent field ionization mass spectrometry method combined with ab initio calculations was used to determine the interaction energies and the structures of 9-methylguanine-acrylamide dimers. Acrylamide mimics the side chain amide group of the natural amino acids asparagine and glutamine. The experimental enthalpy of the dimer formation derived from the van't Hoff plot is ?59.5 ± 3.8 kJ mol^?1. The value is higher than interaction energies between acrylamide and other nucleic acid bases which were determined to be ?57.0 for 1-methylcytosine, ?52.0 for 9-methyladenine, and ?40.6 kJ mol^?1 for 1-methyl-uracil. In total, eight hydrogen bonded dimers formed by the three lowest energy 9-methylguanine tautomers and acrylamide were found in the quantum chemical calculations performed at the DFT/B3LYP/6-31++G?? and MP2/6-31++G?? levels of theory. The relative stability and the interaction energies of the dimers were calculated accounting for the basis set superposition error and the zero-point vibrational energy correction. The lowest energy dimer found in the calculations is formed by acrylamide (Ac) with the keto tautomer of 9-methylguanine (Gk). It is stabilized by two intermolecular H bonds, C6=O(Gk) · · · H—N(Ac) and Nl—H(Gk) · · ·O(Ac), and it is more stable than the second lowest energy dimer by ≈ 25 kJ mol^?1. The calculated interaction energies of the lowest energy 9-methylguanine-acrylamide dimer are ?65.0 kJ mol^?1 and ?67.7 kJ mol^?1 at the MP2 and DFT levels of theory, respectively. The experimental enthalpy of the dimer formation is in good agreement with both the calculated interaction energies of the GkAc dimer and much higher than the interaction energies calculated for all other 9-methylguanine-acrylamide dimers. This proved that only one dimer was present in the experimental samples. To verify whether acrylamide is a good model of the amino acid-amide group, we performed direct calculations of the 9-methylguanine-glutamine dimers at the same levels of theory as used for the complexes involving acrylamide. The interaction energies found for the lowest energy 9-methylguanine-glutamine dimer are ?65.1 kJ mon^?1 (MP2/6-31++G??) and ?66.2 kJ mol^?1 (DFT/B3LYP/6-31++G??) and these values are very close (within 0.5 kJ mol^?1) to the interaction energies obtained for the 9-methylguanine-acrylamide dimers.     

O3与O3分子间相互作用的理论研究

采用从头算方法,在B3LYP水平下对O3分子单体及其二聚体进行了几何结构优化,得到四种O3分子二聚体的稳定构型,并经MP2法、均衡法(Massage)分别校正了电子相关和基组叠加误差(BSSE),通过对分子中原子间的最短距离,分子间质心距离与各构型相互作用能的关系进行了分析、比较,得到了最稳定的构型,其对应的O3分子二聚体相互作用能为:-8.788 kJ/mol.     

Enthalpy difference between conformations of normal alkanes: effects of basis set and chain length on intramolecular basis set superposition error

The quantum chemistry of conformation equilibrium is a field where great accuracy (better than 100?cal?mol^?1) is needed because the energy difference between molecular conformers rarely exceeds 1000–3000?cal?mol^?1. The conformation equilibrium of straight-chain (normal) alkanes is of particular interest and importance for modern chemistry. In this paper, an extra error source for high-quality ab initio (first principles) and DFT calculations of the conformation equilibrium of normal alkanes, namely the intramolecular basis set superposition error (BSSE), is discussed. In contrast to out-of-plane vibrations in benzene molecules, diffuse functions on carbon and hydrogen atoms were found to greatly reduce the relative BSSE of n-alkanes. The corrections due to the intramolecular BSSE were found to be almost identical for the MP2, MP4, and CCSD(T) levels of theory. Their cancelation is expected when CCSD(T)/CBS (CBS, complete basis set) energies are evaluated by addition schemes. For larger normal alkanes (N?>?12), the magnitude of the BSSE correction was found to be up to three times larger than the relative stability of the conformer; in this case, the basis set superposition error led to a two orders of magnitude difference in conformer abundance. No error cancelation due to the basis set superposition was found. A comparison with amino acid, peptide, and protein data was provided.     

Theoretical study of rearrangements in water dimer and trimer

The global minimum and transition states for the acceptor-tunnelling, donor-acceptor interchange and bifurcation tunnelling rearrangements of the water dimer, and the single-flip, bifurcation and concerted proton transfer processes in the water trimer have been reinvestigated. Our analysis of the tunnelling splittings and spectroscopy is based on ab initio calculations at the computational level of second-order M?ller-Plesset (MP2) theory with basis sets of aug-cc-pVXZ quality (X = D, T, Q for the dimer; X = D, T for the trimer). In both water dimer and trimer, the binding energy, barrier heights, intermonomer distances, and harmonic frequencies converge smoothly as the size of the basis set increases. In the water dimer, the binding energy was evaluated as 5.09kcal mol^?1, while the activation energies are 0.52 (acceptor-tunnelling) 0.79 (donor-acceptor interchange), and 1.94 kcal mol^?1 (bifurcation tunnelling) at the MP2/aug-cc-pVQZ level. In the water trimer, the binding energy was evaluated as 16.29 kcal mol^?1, while the activation energies are 0.28 (single-flip), 2.34 (bifurcation), and 26.36 (proton transfer) kcal mol^?1 at the MP2/aug-cc-pVTZ level.     

Computational studies of the halooxyhalocarbenes XOCX (X = F,Cl)

Ab initio calculations at the B3LYP, MP2, MP4 and CCSD(T) levels of theory were performed to predict the stability of the halooxyhalocarbenes, XOCX (X = F, Cl). The calculations indicate that the nonlinear FOCF molecule is stable with an energy 16 kJ mol^?1 below the energy of possible reacting fragments F₂ and CO. However, a nonlinear equilibrium structure for ClOCCl was located, but it was found to be about 192 kJ mol^?1 higher in energy than the energy of Cl₂ and CO. The charge distribution in these molecules was analysed using the atoms in molecules (AIM) method.     

Intramolecular BSSE and dispersion affect the structure of a dipeptide conformer

B3LYP and MP2 calculations with the commonly-used 6-31+G(d) basis set predict qualitatively different structures for the Tyr–Gly conformer book1, which is the most stable conformer identified in a previous study. The structures differ mainly in the ψ_tyr Ramachandran angle (138° in the B3LYP structure and 120° in the MP2 structure). The causes for the discrepant structures are attributed to missing dispersion in the B3LYP calculations and large intramolecular BSSE in the MP2 calculations. The correct ψ_tyr value is estimated to be 130°. The MP2/6-31+G(d) profile identified an additional conformer, not present on the B3LYP surface, with a ψ_tyr value of 96° and a more folded structure. This minimum is, however, likely an artefact of large intramolecular BSSE values. We recommend the use of basis sets of at least quadruple-zeta quality in density functional theory (DFT), DFTaugmented with an empirical dispersion term (DFT-D) and second-order Møller-Plesset perturbation theory (MP2 ) calculations in cases where intramolecular BSSE is expected to be large.     

A computational characterization of N2@C60

Recent observations of N₂@C₆₀ are supported computationally. The geometry is optimized at the B3LYP/3-21G and PW91/3-21G levels. The lowest-energy structure has the N₂ unit oriented towards a pair of parallel pentagons so that the complex exhibits D_5d symmetry. Single-point energy calculations are further carried out at the B3LYP/6-31G*, PW91/6-31G* and MP2?=?FC/6-31G* levels and corrected for the basis set superposition error (BSSE). The MP2?=?FC/6-31G* treatment with the BSSE correction gives a stabilization energy of -9.3?kcal?mol^?1, whereas DFT approaches mostly fail to produce a stabilization. The entropy term for the encapsulation is also evaluated and leads to a standard Gibbs energy change upon encapsulation at room temperature of -3.3?kcal?mol^?1. The computed structural and vibrational characteristics are also reported.     

A computational study of N2···HHeF: comparison with N2···HArF and N2···HKrF

A weakly bound linear complex of N₂ and HHeF was found to be stable with respect to the constituent monomers by ab initio calculations at various levels of theory (MP2, MP3, MP4(SDQ) and QCISD) using a 6-311++G(2d,2p) basis set. The complex N₂···HHeF was found to have a zero-point vibrational energy corrected binding energy of 14.5?kJ mol^?1 (QCISD) and exhibits a large harmonic vibrational frequency blue shift of 375?cm^?1 for the He–H stretching vibration mode, with a diminished infrared intensity for this mode on formation of the complex. The frequency shift for this mode was also found to be very sensitive to the level of theory employed for the calculation, and is rationalized by considering intermolecular electrostatic and charge-transfer effects. The results for N₂···HHeF are compared with corresponding results for the related complexes N₂···HArF and N₂···HKrF, both of which contain the same proton acceptor molecule.     

The energetics of the isomeric anthrols

We report the results of geometry optimized MP2(FULL)/6-31G(d) quantum chemical calculations with zero-point vibrational energies and thermal corrections of the isomeric 1-, 2- and 9-anthrols and the tautomeric anthrone. We find that 1- and 2-anthrols have nearly the same enthalpy of formation and are some 6?kJ?mol^?1 more stable than their 9-isomer in accord with intuition based on steric hindrance. We find that anthrone is more stable than 9-anthrol by 13.7 ± 6.4?kJ?mol^?1, in satisfactory agreement with the value of 23 ± 8?kJ?mol^?1 suggested elsewhere by experiment and its associated analysis.     

Infrared and Raman Spectra,conformations, ab initio calculations and spectral assignments of 1,3‐disilabutane (SiH3CH2SiH2CH3)

Raman spectra of 1,3‐disilabutane (SiH₃CH₂SiH₂CH₃) as a liquid were recorded at 293 K and as a solid at 78 K. In the Raman cryostat at 78 K an amorphous phase was first formed, giving a spectrum similar to that of the liquid. After annealing to 120 K, the sample crystallized and large changes occurred in the spectra since more than 20 bands present in the amorphous solid phase vanished. These spectral changes made it possible to assign Raman bands to the anti or gauche conformers with confidence. Additional Raman spectra were recorded of the liquid at 14 temperatures between 293 and 137 K. Some Raman bands changed their peak heights with temperature but were countered by changes in linewidths, and from three band pairs assigned to the anti and gauche conformers, the conformational enthalpy difference Δ_confH(gauche–anti) was found to be 0 ± 0.3 kJ mol⁻¹ in the liquid. Infrared spectra were obtained in the vapor and in the liquid phases at ambient temperature and in the solid phases at 78 K in the range 4000–400 cm⁻¹. The sample crystallized immediately when deposited on the CsI window at 78 K, and many bands present in the vapor and liquid disappeared. Additional infrared spectra in argon matrixes at 5 K were recorded before and after annealing to temperatures 20–34 K. Quantum chemical calculations were carried out at the HF, MP2 and B3LYP levels with a variety of basis sets. The HF and DFT calculations suggested the anti conformer as the more stable one by ca 1 kJ mol⁻¹, while the MP2 results favored gauche by up to 0.4 kJ mol⁻¹. The Complete Basis Set method CBS‐QB3 gave an energy difference of 0.1 kJ mol⁻¹, with anti as the more stable one. Scaled force fields from B3LYP/cc‐pVQZ calculations gave vibrational wavenumbers and band intensities for the two conformers. Copyright © 2007 John Wiley & Sons, Ltd.     

Atomic additivity of the correlation energy in molecules—an ab initio MP4 and G3 study

It is shown that the closed shell valence electron molecular correlation energy of organic molecules in their ground states is a homogeneous multilinear function of the numbers of neutral atoms in their canonical hybridization state. The additivity is a robust feature, which holds for MP2(fc), MP3(fc) and MP4(fc) model calculations. The latter results obtained on a test set of 91 widely different organic molecules, exhibiting a whole gamut of electronic structure patterns, are excellent as evidenced by the absolute average deviation from the additivity values (AAD) of only 1.4 kcal mol^?1 and R ² = 0.999 93. The maximum absolute deviation (MAD) is 5.3 kcal mol^?1. The additivity formula for the total molecular electron correlation retrieved from G3 calculations also has an excellent performance (AAD = 1.2 kcal mol^?1, R ² = 0.999 98 and MAD = 7.2 kcal mol^?1). If it is taken into account that the additivity formulae require only back of the envelope calculations, these results are remarkable indeed, in particular since the G3 correlation energies span a very large range from 180.7 (methane) to 1642.8 (hexafluorocyclopropane) kcal mol^?1. Comparison of the exact electron correlation energies in free atoms with the corresponding average correlation energies in molecules reveals that a substantial increase in the latter provides an important contribution in overcoming a very strong Coulomb repulsion between the nuclei. It is shown that the additivity formulae are useful in detecting some special molecular features such as strong resonance and anti-aromaticity.     

A high level computational study of the CH4/CF4 dimer: how does it compare with the CH4/CH4 and CF4/CF4 dimers?

The interaction within the methane–methane (CH₄/CH₄), perfluoromethane–perfluoromethane (CF₄/CF₄) methane–perfluoromethane dimers (CH₄/CF₄) was calculated using the Hartree–Fock (HF) method, multiple orders of Møller–Plesset perturbation theory [MP2, MP3, MP4(DQ), MP4(SDQ), MP4(SDTQ)], and coupled cluster theory [CCSD, CCSD(T)], as well as the PW91, B97D, and M06-2X density functional theory (DFT) functionals. The basis sets of Dunning and coworkers (aug-cc-pVxZ, x?=?D, T, Q), Krishnan and coworkers [6-311++G(d,p), 6-311++G(2d,2p)], and Tsuzuki and coworkers [aug(df, pd)-6-311G(d,p)] were used. Basis set superposition error (BSSE) was corrected via the counterpoise method in all cases. Interaction energies obtained with the MP2 method do not fit with the experimental finding that the methane–perfluoromethane system phase separates at 94.5?K. It was not until the CCSD(T) method was considered that the interaction energy of the methane–perfluoromethane dimer (?0.69?kcal?mol^?1) was found to be intermediate between the methane (?0.51?kcal?mol^?1) and perfluoromethane (?0.78?kcal?mol^?1) dimers. This suggests that a perfluoromethane molecule interacts preferentially with another perfluoromethane (by about 0.09?kcal?mol^?1) than with a methane molecule. At temperatures much lower than the CH₄/CF₄ critical solution temperature of 94.5?K, this energy difference becomes significant and leads perfluoromethane molecules to associate with themselves, forming a phase separation. The DFT functionals yielded erratic results for the three dimers. Further development of DFT is needed in order to model dispersion interactions in hydrocarbon/perfluorocarbon systems.     

Intermolecular potentials for ammonia based on the test particle model and the coupled pair functional method

The intermolecular interaction ΔE in (NH₃)₂ is investigated on the SCF level, with inclusion of correlation effects by means of the CPF method and within the simple test particle model. Whereas the linear hydrogen bonded structure is favoured on the SCF level, ΔE = -7·65 kJ mol^-1, the most stable geometry on the highest level of theory is a cyclic structure, ΔE = -12·96 kJ mol^-1. The minimum is very shallow and allows for appreciable angular motions. The test particle model reproduces the general features of ΔE but shows deviations in details. The computed potentials are used in MD simulations to compute static and dynamic properties of liquid NH₃. Good agreement with available experimental results is obtained throughout.     

Structure and bonding of the (C6H6)+ 2 radical

To elucidate the relative stability of various structures of the benzene dimer cation radical, (C₆H₆)⁺ ₂ in its ground and low-lying excited states, ab initio complete active space self-consistent field (CASSCF), multi-reference singly and doubly excited configuration interaction (MRSDCI), and multi-reference coupled pair approximation (MRCPA) calculations were performed. Full optimization was performed at the CASSCF level for various structures of the dimer cation, followed by MRSDCI and MRCPA calculations. It was found that the global minimum of the cation is at a slipped C_2h sandwich structure but there are some other sandwich structures with almost the same stability, being within about kcal mol^?1. T-shape structures are less stable than the sandwich structures, by more than 5 kcal mol^?1 by MRCPA calculations. Low lying electronic excited states in various structures are also discussed.     

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.     

The energetics of naphthalene derivatives. II. The isomeric 1— and 2—naphthyl acetates

The isomeric 1- and 2-naphthyl acetates (acetoxynaphthalenes) are at the confluence of diverse concepts, techniques and classes of organic compounds. Summing the results of literature measurements of the enthalpy of formation of their solids and of our new sublimation enthalpies reported herein, we derive gas phase enthalpies of formation of ?209.9 ± 1.4 and ?213.3 ± 1.3 kJ mol^?1 respectively. This corresponds to 2-naphthyl acetate being more stable than its 1-isomer by 3.4 ± 1.9 kJ mol^?1. We also performed MP2(full)/6-31G(d) calculations on these species, resulting in enthalpies of formation of ?212.9 ± 3.9 and ?212.2 ± 3.9 kJ mol^?1 for 1- and 2-naphthyl acetate and a difference of ?0.7 kJ mol^?1 respectively in satisfactory agreement with the above experimental results.     

Enthalpies of formation and isomerization of cis‐ and trans‐decalin,and their oxa‐analogs by G3(MP2)//B3LYP calculations

G3(MP2)//B3LYP calculations have been carried out on trans‐ and cis‐decalin, and their mono‐, di‐, tri‐, and tetraoxa‐analogs. The main purpose of the work was to obtain enthalpies of formation for these compounds, and to study the relative stabilities of the cis–trans and positional isomers of the various (poly)oxadecalins. Comparison of the computational enthalpies of formation with the respective experimental ones, known only for the decalins and 1,3,5,7‐tetraoxadecalins, shows that in both cases the computational values are more negative than the experimental ones, the deviations being ?5 to ?7 kJ mol^?1 for the decalins and ?12 to ?17 kJ mol^?1 for the 1,3,5,7‐tetraoxadecalins. The respective computational enthalpies of cis–trans isomerization, however, are in excellent to satisfactory agreement with the experimental data. The cis–trans enthalpy differences vary from +11.0 kJ mol^?1 for decalin to ?15.4 kJ mol^?1 for 1,4,5,8‐tetraoxadecalin. Low relative enthalpy values were also calculated for the cis isomers of 1,8‐dioxadecalin (?3.7 kJ mol^?1), 1,3,6‐trioxadecalin (?4.6 kJ mol^?1), 1,3,8‐trioxadecalin (?9.7 kJ mol^?1), 1,4,5‐ trioxadecalin (?5.6 kJ mol^?1), 1,3,5,8‐tetraoxadecalin (?7.3 kJ mol^?1), and 1,3,6,8‐tetraoxadecalin (?14.5 kJ mol^?1). Copyright © 2009 John Wiley & Sons, Ltd.     

The intermolecular potential of NH+ 4-Ar I. Calculations for the internal rotor structure of the v 3 band

The intermolecular potential energy surface of the electronic ground state of the ammonium-argon ionic dimer, NH⁺ ₄-Ar, is calculated by ab initio methods using different levels of theory (MP2, MP4) and basis sets (aug-cc-pVXZ, X = D/T/Q). The deformation of the ammonium ion in the complex is shown to be small and its geometry is therefore fixed in these calculations to the tetrahedral structure optimized for the bare ion. The global minimum of the potential corresponds to a proton-bound structure with C_3v symmetry (R_e ≈ 3.4 Å, D_e ≈ 950 cm^?1) and the barrier to internal rotation between the four equivalent minima is around 200 cm^?1. The three-dimensional potential is expanded in tetrahedral harmonics whose radially dependent coefficients, V_i (R), are compared for the considered levels of theory. The rotation-intermolecular vibration Hamiltonian is solved using a two-dimensional fixed-R representation of the calculated potentials, V_i , ≡ V_i (R ^eff), where the effective intermolecular separation, RR^eff, is determined from the experimental rotational constants of the complex. The accuracy of these parametrized potential energy surfaces is judged by their ability to reproduce the hindered rotor subband structure in the experimental v ₃(t ₂) infrared band of the complex. The simulations using the potentials calculated at the MP2/aug-cc-pVTZ or higher levels of theory reproduce the coarse structure of the experimental spectrum well. Further improvement could be achieved by least-squares fitting the potential parameters to the observed subband positions. The fitted V ₃ and V ₄ parameters remain in close agreement with those determined from the ab initio calculations but the anisotropy of the potential is significantly different from that in a previous least-squares fit of V ₃ alone.     

Accurate ground-state potential energy surfaces of the C2H2–Kr and C2H2–Xe van der Waals complexes

Accurate ab initio intermolecular potential energy surfaces (IPES) have been obtained for the first time for the ground electronic state of the C₂H₂–Kr and C₂H₂–Xe van der Waals complexes. Extensive tests, including complete basis set and all-electron scalar relativistic results, support their calculation at the CCSD(T) level of theory, using small-core relativistic pseudopotentials for the rare-gas atoms and aug-cc-pVQZ basis sets extended with a set of 3s3p2d1f1g mid-bond functions. All results are corrected for the basis set superposition error. The importance of the scalar relativistic and rare-gas outer-core (n–1)d correlation effects is investigated. The calculated IPES, adjusted to analytical functions, are characterized by global minima corresponding to skew T-shaped geometries, in which the Jacobi vector positioning the rare-gas atom with respect to the center of mass of the C₂H₂ moiety corresponds to distances of 4.064 and 4.229?Å, and angles of 65.22° and 68.67° for C₂H₂–Kr and C₂H₂–Xe, respectively. The interaction energy of both complexes is estimated to be ?151.88 (1.817?kJ?mol^?1) and ?182.76?cm^?1 (2.186?kJ?mol^?1), respectively. The evolution of the topology of the IPES as a function of the rare-gas atom, from He to Xe, is also discussed.