The effective fragment potential: small clusters and radial distribution functions

The effective fragment potential (EFP) method for treating solvent effects provides relative energies and structures that are in excellent agreement with the analogous fully quantum [i.e., Hartree-Fock (HF), density functional theory (DFT), and second order perturbation theory (MP2)] results for small water clusters. The ability of the method to predict bulk water properties with a comparable accuracy is assessed by performing EFP molecular dynamics simulations. The resulting radial distribution functions (RDF) suggest that as the underlying quantum method is improved from HF to DFT to MP2, the agreement with the experimental RDF also improves. The MP2-based EFP method yields a RDF that is in excellent agreement with experiment.     

Solvent effects on the S(N)2 reaction: Application of the density functional theory-based effective fragment potential method

The performance of the density functional theory (DFT)-based effective fragment potential (EFP) method is assessed using the S(N)2 reaction: Cl- + nH2O + CH3Br = CH3Cl + Br- + nH2O. The effect of the systematic addition of water molecules on the structures and relative energies of all species involved in the reaction has been studied. The EFP1 method is compared with second-order perturbation theory (MP2) and DFT results for n = 1, 2, and 3, and EFP1 results are also presented for four water molecules. The incremental hydration effects on the barrier height are the same for all methods. However, only full MP2 or MP2 with EFP1 solvent molecules are able to provide an accurate treatment of the transition state (TS) and hence the central barriers. Full DFT and DFT with EFP1 solvent molecules both predict central barriers that are too small. The results illustrate that the EFP1-based DFT method gives reliable results when combined with an accurate quantum mechanical (QM) method, so it may be used as an efficient alternative to fully QM methods in the treatment of larger microsolvated systems.     

A DFT study on the dimerization of C62, H2-C62, and F2-C62

On the basis of calculations using the density functional theory, we show that C(62), a recently synthesized nonclassical fullerene, will presumably undergo dimerization with various isomers at elevated temperatures. This is shown by calculating the dimerization energy and the activation barrier of the dimerization. Eight possible isomers of the dimer were identified, all of which are more stable than the two isolated monomers. The relative stability of various isomers depends upon the kind of C=C bonds within the four-membered carbon ring involved in the dimerization. In addition, similar calculations were performed for the monomers and dimers of H(2)-C(62) and F(2)-C(62). Six isomers were identified for each of the dimers. Although less pronounced than the case of the C(62) dimer, all isomers of the H(2)-C(62) dimer are appreciably more stable than the individual monomers. Although a large steric repulsion due to F atoms significantly reduces the stability of F(2)-C(62) dimer, its two isomers are still more stable than separate monomers.     

Highly Accurate CCSD(T) and DFT–SAPT Stabilization Energies of H‐Bonded and Stacked Structures of the Uracil Dimer

The CCSD(T) interaction energies for the H‐bonded and stacked structures of the uracil dimer are determined at the aug‐cc‐pVDZ and aug‐cc‐pVTZ levels. On the basis of these calculations we can construct the CCSD(T) interaction energies at the complete basis set (CBS) limit. The most accurate energies, based either on direct extrapolation of the CCSD(T) correlation energies obtained with the aug‐cc‐pVDZ and aug‐cc‐pVTZ basis sets or on the sum of extrapolated MP2 interaction energies (from aug‐cc‐pVTZ and aug‐cc‐pVQZ basis sets) and extrapolated ΔCCSD(T) correction terms [difference between CCSD(T) and MP2 interaction energies] differ only slightly, which demonstrates the reliability and robustness of both techniques. The latter values, which represent new standards for the H‐bonding and stacking structures of the uracil dimer, differ from the previously published data for the S22 set by a small amount. This suggests that interaction energies of the S22 set are generated with chemical accuracy. The most accurate CCSD(T)/CBS interaction energies are compared with interaction energies obtained from various computational procedures, namely the SCS–MP2 (SCS: spin‐component‐scaled), SCS(MI)–MP2 (MI: molecular interaction), MP3, dispersion‐augmented DFT (DFT–D), M06–2X, and DFT–SAPT (SAPT: symmetry‐adapted perturbation theory) methods. Among these techniques, the best results are obtained with the SCS(MI)–MP2 method. Remarkably good binding energies are also obtained with the DFT–SAPT method. Both DFT techniques tested yield similarly good interaction energies. The large magnitude of the stacking energy for the uracil dimer, compared to that of the benzene dimer, is explained by attractive electrostatic interactions present in the stacked uracil dimer. These interactions force both subsystems to approach each other and the dispersion energy benefits from a shorter intersystem separation.     

6-甲基-4-羟基嘧啶单体及二聚体质子转移过程的理论研究

应用密度泛函理论的B3LYP/6-311+G(d)方法研究了6-甲基-4-羟基嘧啶单体及二聚体质子转移的异构化反应.对反应势能面的研究发现,该化含物可能存在9种单体异构体,对其最稳定的单体构型进行分析.各单体间异构化反应的过渡态共有9种,反应的活化能最小为22.06 kJ/mol,最大为356.55 kJ/mol,最可能的反应路径在室温下即可进行. 研究了2种二聚体及其异构化反应的过渡态,发现二聚体均比其对应的单体稳定,而且质子转移所需要的活化能仅为20.13 kJ/mol,比单体低很多. 氢键在这种变化中起了主要作用,由单体和二聚体的总能量计算了氢键的键能.     

Noncovalent interactions in extended systems described by the effective fragment potential method: theory and application to nucleobase oligomers

The implementation of the effective fragment potential (EFP) method within the Q-CHEM electronic structure package is presented. The EFP method is used to study noncovalent π-π and hydrogen-bonding interactions in DNA strands. Since EFP is a computationally inexpensive alternative to high-level ab initio calculations, it is possible to go beyond the dimers of nucleic acid bases and to investigate the asymptotic behavior of different components of the total interaction energy. The calculations demonstrated that the dispersion energy is a leading component in π-stacked oligomers of all sizes. Exchange-repulsion energy also plays an important role. The contribution of polarization is small in these systems, whereas the magnitude of electrostatics varies. Pairwise fragment interactions (i.e., the sum of dimer binding energies) were found to be a good approximation for the oligomer energy.     

Analysis of non-covalent interactions in (bio)organic molecules using orbital-partitioned localized MP2

Localized molecular orbitals (LMO) are used as basis for an MP2 treatment (LMP2) of electron correlation energies. The major aim is an improved understanding of the non-covalent interactions in large molecules with an emphasis on intra-molecular dispersion effects. A partitioning of the inter-fragment electron correlation energy into electron pairs of different orbital type (i.e., sigma, pi, lone-pairs) is presented. The benzene dimer, 1,4-diphenylbutane conformations, and the tyrosine-glycine dipeptide are used as model systems. For the benzene dimer, comparisons with CCSD(T) data are made in order to analyse the MP2 problems for pi-pi stacking. A comparison of phenyl-phenyl interactions in the benzene dimer and for 1,4-diphenylbutane conformations reveals a very good transferability of dispersion-type contributions to binding from an inter-molecular to an intra-molecular situation. In both systems, the relative (percentage) contributions of sigma-sigma, sigma-pi, and pi-pi pairs to the total inter-fragment correlation energy is a clear signature for the binding mode (pi-stacked vs. T-shaped). For various benzene dimer conformations, we find a linear relation between the MP2 interaction energy error and the correlation contribution from pi-pi pairs. In the dipeptide, also dispersion-type electron correlations between the glycyl amino acid residue and the phenol group are most relevant for folding. This convincingly explains problems of DFT with such systems reported previously. Although in this case only one aromatic ring (and a glycyl moiety) is involved, the same sigma-sigma, sigma-pi, and pi-pi correlations seem to dominate the shape of the potential energy surface.     

An ab initio intermolecular potential energy surface for the F(2) dimer

Two analytical representations for the potential energy surface of the F(2) dimer were constructed on the basis of ab initio calculations up to the fourth-order of M?ller-Plesset (MP) perturbation theory. The best estimate of the complete basis set limit of interaction energy was derived for analysis of basis set incompleteness errors. At the MP4/aug-cc-pVTZ level of theory, the most stable structure of the dimer was obtained at R = 6.82 au, theta(a) = 12.9 degrees , theta(b) = 76.0 degrees , and phi = 180 degrees , with a well depth of 716 microE(h). Two other minima were found for canted and X-shaped configurations with potential energies around -596 and -629 microE(h), respectively. Hexadecapole moments of monomers play an important role in the anisotropy of interaction energy that is highly R-dependent at intermediate intermolecular distances. The quality of potentials was tested by computing values of the second virial coefficient. The fitted MP4 potential has a more reasonable agreement with experimental values.     

Experimental and Theoretical Investigation of the Proton-Bound Dimer of Lysine

The structure of the proton-bound lysine dimer has been investigated by infrared multiple photon dissociation (IRMPD) spectroscopy and electronic structure calculations. The structures of different possible isomers of the proton-bound lysine dimer have been optimized at the B3LYP/6-31 + G(d) level of theory and IR spectra calculated using the same computational method. Based on relative Gibbs free energies (298 K) calculated at the MP2/aug-cc-pVTZ//B3LYP/6-31 + G(d) level of theory, LL-CS01, and followed closely (1.1 kJ mol^–1) by LL-CS02 are the most stable non-zwitterionic isomers. At the MP2/aug-cc-pVTZ//6-31 + G(d) and MP2/aug-cc-pVTZ//6-31 + (d,p) levels of theory, isomer LL-CS02 is favored by 3.0 and 2.3 kJ mol^–1, respectively. The relative Gibbs free energies calculated by the aforementioned levels of theory for LL-CS01 and LL-CS02 are very close and strongly suggest that diagnostic vibrational signatures found in the IRMPD spectrum of the proton-bound dimer of lysine can be attributed to the existence of both isomers. LL-ZW01 is the most stable zwitterionic isomer, in which the zwitterionic structure of the neutral lysine is well stabilized by the protonated lysine moiety via a very strong intermolecular hydrogen bond. At the MP2/aug-cc-pVTZ//B3LYP/6-31 + G(d), MP2/aug-cc-pVTZ//6-31 + G(d) and MP2/aug-cc-pVTZ//6-31 + G(d,p) levels of theory, the most stable zwitterionic isomer (LL-ZW01) is less favored than LL-CS01 by 7.3, 4.1 and 2.3 kJ mol^–1, respectively. The experimental IRMPD spectrum also confirms that the proton-bound dimer of lysine largely exists as charge-solvated isomers. Investigation of zwitterionic and charge-solvated species of amino acids in the gas phase will aid in a further understanding of structure, property, and function of biological molecules.     

On the keto-enol tautomerization of malonaldehyde: an effective fragment potential study

Recent studies have mapped the keto-enol tautomerization of malonaldehyde through a general transition structure that leads exclusively to the Z isomer of the enol. However, it will be shown that a competing general transition structure exists that leads to both the E and Z isomers of the enol at the B3LYP/6-31G(d,p) and MP2/6-31G(d,p) levels of theory. Both the RHF- and DFT-based effective fragment potential methods have been used to model solvation effects, and the results are compared with full ab initio calculations. It is found that two bridging water molecules with two discrete DFT-based effective fragment potential solvent waters at the MP2/6-31G(d,p) level of ab initio theory provides the most computationally effective model for solvent effects in this system. It is shown that the relative energies for this QM/MM model differ from the full MP2/6-31G(d,p) energies by an average absolute relative difference of 2.2 kcal mol-1 across the reaction path when the zero-point vibrational energy correction is included.     

An ab initio benchmark study of hydrogen bonded formamide dimers

The five singly and doubly hydrogen bonded dimers of formamide are calculated at the correlated level by using resolution of identity M?ller-Plesset second-order perturbation theory (RIMP2) and the coupled cluster with singles, doubles, and perturbative triples [CCSD(T)] method. All structures are optimized with the Dunning aug-cc-pVTZ and aug-cc-pVQZ basis sets. The binding energies are extrapolated to the complete basis set (CBS) limit by using the aug-cc-pVXZ (X = D, T, Q) basis set series. The effect of extending the basis set to aug-cc-pV5Z on the geometries and binding energies is studied for the centrosymmetric doubly N-H...O bonded dimer FA1 and the doubly C-H...O bonded dimer FA5. The MP2 CBS limits range from -5.19 kcal/mol for FA5 to -14.80 kcal/mol for the FA1 dimer. The DeltaCCSD(T) corrections to the MP2 CBS limit binding energies calculated with the 6-31+G(d,p), aug-cc-pVDZ, and aug-cc-pVTZ basis sets are mutually consistent to within < or =0.03 kcal/mol. The DeltaCCSD(T) correction increases the binding energy of the C-H...O bonded FA5 dimer by 0.4 kcal/mol or approximately 9% over the distance range +/-0.5 Angstrom relative to the potential minimum. This implies that the ubiquitous long-range C-H...O interactions in proteins are stronger than hitherto calculated.     

Glycine Dimers: Structure,Stability, and Medium Effects

We report a study on different ionization states and conformations of the bimolecular (Gly)₂ system by means of quantum mechanical calculations. Optimized geometries for energy minima of the glycine dimer, as well as relative energies and free energies were computed as a function of the medium: gas phase, nonpolar polarizable solvent, and aqueous solution. The polarizable continuum model was employed to account for solvation effects. Energy calculations were done using the MP2/aug‐cc‐pVTZ and B3LYP/6‐311+G(2df,2p) methods on B3LYP/6‐31+G(d,p) optimized structures (some single‐point energy calculations were also done using the B3PW91 and PBE1KCIS methods). Ionized forms of the glycine dimer (either zwitterion–zwitterion or neutral–zwitterion) are predicted to exist in all media, in contrast to amino acid monomers. In aqueous solution, dimerization is an exergonic process (?4 kcal mol^?1). Thus, according to our results, zwitterion–zwitterion Gly dimers might be abundant in supersaturated glycine aqueous solutions, a fact that has been connected with the structure of α‐glycine crystals but that remains controversial in the literature. Another noticeable result is that zwitterion–zwitterion interactions are substantially underestimated when computed using methods based on density functional theory. For comparison, some calculations for the dimer of the simplest chiral amino acid alanine were done as well and differences to the glycine dimer are discussed.     

Improvement of the coupled-cluster singles and doubles method via scaling same- and opposite-spin components of the double excitation correlation energy

There has been much interest in cost-free improvements to second-order M?ller-Plesset perturbation theory (MP2) via scaling the same- and opposite-spin components of the correlation energy (spin-component scaled MP2). By scaling the same- and opposite-spin components of the double excitation correlation energy from the coupled-cluster of single and double excitations (CCSD) method, similar improvements can be achieved. Optimized for a set of 48 reaction energies, scaling factors were determined to be 1.13 and 1.27 for the same- and opposite-spin components, respectively. Preliminary results suggest that the spin-component scaled CCSD (SCS-CCSD) method will outperform all MP2 type methods considered for describing intermolecular interactions. Potential energy curves computed with the SCS-CCSD method for the sandwich benzene dimer and methane dimer reproduce the benchmark CCSD(T) potential curves with errors of only a few hundredths of 1 kcal mol(-1) for the minima. The performance of the SCS-CCSD method suggests that it is a reliable, lower cost alternative to the CCSD(T) method.     

A comparative study of the dimers of selected hydroxybenzenes

Hydroxybenzenes are the parent compounds of large classes of derivatives, many of which exhibit biological activities. This work presents the results of a comparative study of the dimers of selected hydroxybenzenes, considering all the possible mutual geometrical arrangements of the two monomers and comparing their relative stabilities and interaction energies. The OH···OH hydrogen bond between the two monomers is the dominant stabilizing factor, with frequent preference for mutual perpendicularity of the two aromatic rings. C? H···O unconventional H‐bonds, OH···π unconventional H‐bonds, H···π interactions and π··π interactions also may play significant roles. The factors stabilizing individual hydroxybenzenes (presence of intramolecular hydrogen bonds; number, positioning and orientation of the OH groups; symmetry features) have greater influence on the dimers' relative energy than on the interaction energy between monomers. While results from different calculations methods (HF, MP2, and DFT/B3LYP) show consistency for all the features just‐mentioned, they show some relevant differences in the way they take into account different types of interactions between monomers, resulting in some differences in the geometry arrangements of the monomers in the lowest energy dimers and in differences in the relative preferences among higher‐energy dimer geometries. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

Empirical force field and ab initio calculations on allyl cations

Allyl cation geometries optimized using an extended version of MMP2, newly parameterized for localized and delocalized classical cations, compare favorably with those obtained at the MP2(full) /6–31G^* level. Hence, the force field should provide good starting structures for ab initio calculations. The π-electron densities obtained by these two very different methods are quite similar. The relative energies of various isomers at MP4/6–31G^*//MP2(full)/6–31G^* are reproduced well by the force-field calculations. The heats of formation calculated by MMP2, as well as those predicted from the ab initio data, agree with experimentally determined values. The force-field method provides interpretive capabilities. Energy differences between isomers can be separated into electronic and steric contributions, reasonable estimates of resonance energies are given, and nonbonded resonance energies in delocalized cations can be evaluated. The stabilizing 1–3 π-interactions in allyl cations are quite significant, but are reduced by alkyl groups hyperconjugatively and sterically. © 1997 by John Wiley & Sons, Inc.     

Ab Initio calculations of the stabilization energies of the conformational and the structural isomers of C(3)H(7)X where X = F,Cl, and Br

HF, MP2, and B3LYP calculations with different basis sets have been used in the computation of the stabilization energies of C(3)H(7)X isomers, where X is F, Cl, and Br. The experimental stabilization energies of the structural isomers of C(3)H(7)Cl and C(3)H(7)Br have been reproduced via B3LYP calculations. However, the calculated stabilization energies of fluoropropane isomers from their reported enthalpies of formation have been reproduced in all methods of calculations in present work. The experimental relative stabilities of the gauche conformers of 1-fluoro-, 1-chloro-, and 1-bromopropanes have been also reproduced via some of the used calculations in the present work. The effect of the geminal interactions on X atomic charges and on the C-X and C-C bond lengths in halopropane isomers are also discussed.     

Cross-checking of nanoelectrospray ionization mass spectrometry and computer simulation for the evaluation of the interaction strength of non-covalently bound enkephalins in solution

Nanoelectrospray ionization mass spectrometry (nanoESI-MS) and computer simulation were applied to the characterization of non-covalent interactions of [Leu5]-enkephalin (LE) and its optical isomers, [D-Tyr1, Leu5]-enkephalin (Y-LE), [D-Phe4, Leu5]-enkephalin (F-LE) and [D-Tyr1, D-Phe4, Leu5]-enkephalin (YF-LE). The dimer formation tendencies of the optical isomers of LE were evaluated by nanoESI-MS using quadruply deuterated LE (H2N-Tyr-(2,2-d2)Gly-(2,2-d2)Gly-Phe-Leu-COOH, d4-LE) as an internal standard. The relative interaction strengths of the optical isomers of LE were estimated to be Y-LE < F-LE < LE < YF-LE. Geometry optimization calculations were performed for interactions in vacuo and in water using a semi-empirical SCF method (PM3). The initial coordinate of the dimer structure of LE was taken from that obtained from single-crystalline x-ray diffraction analysis. Estimates of the interaction strengths of the dimer complexes were based on the heats of formation of a dimer complex (Hd) and the corresponding monomers (Hm) using the equation DeltaH = Hd - 2Hm. The values of DeltaH obtained from the calculations for interactions in water decreased in the order Y-LE > F-LE > LE > YF-LE. Since the smaller values of DeltaH correspond to stronger interactions between peptides, the results from computer simulations were qualitatively consistent with those obtained from the nanoESI experiments. The possibility of cross-checking these independent techniques was demonstrated using medium-sized molecules of biological importance. The agreement of the results from the two techniques suggested that nanoESI experiments, at least qualitatively, reflected the relative interaction strengths of non-covalently bound enkephalins in aqueous solution.     

Toward true DNA base-stacking energies: MP2, CCSD(T), and complete basis set calculations

Stacking energies in low-energy geometries of pyrimidine, uracil, cytosine, and guanine homodimers were determined by the MP2 and CCSD(T) calculations utilizing a wide range of split-valence, correlation-consistent, and bond-functions basis sets. Complete basis set MP2 (CBS MP2) stacking energies extrapolated using aug-cc-pVXZ (X = D, T, and for pyrimidine dimer Q) basis sets equal to -5.3, -12.3, and -11.2 kcal/mol for the first three dimers, respectively. Higher-order correlation corrections estimated as the difference between MP2 and CCSD(T) stacking energies amount to 2.0, 0.7, and 0.9 kcal/mol and lead to final estimates of the genuine stacking energies for the three dimers of -3.4, -11.6, and -10.4 kcal/mol. The CBS MP2 stacking-energy estimate for guanine dimer (-14.8 kcal/mol) was based on the 6-31G(0.25) and aug-cc-pVDZ calculations. This simplified extrapolation can be routinely used with a meaningful accuracy around 1 kcal/mol for large aromatic stacking clusters. The final estimate of the guanine stacking energy after the CCSD(T) correction amounts to -12.9 kcal/mol. The MP2/6-31G(0.25) method previously used as the standard level to calculate aromatic stacking in hundreds of geometries of nucleobase dimers systematically underestimates the base stacking by ca. 1.0-2.5 kcal/mol per stacked dimer, covering 75-90% of the intermolecular correlation stabilization. We suggest that this correction is to be considered in calibration of force fields and other cheaper computational methods. The quality of the MP2/6-31G(0.25) predictions is nevertheless considerably better than suggested on the basis of monomer polarizability calculations. Fast and very accurate estimates of the MP2 aromatic stacking energies can be achieved using the RI-MP2 method. The CBS MP2 calculations and the CCSD(T) correction, when taken together, bring only marginal changes to the relative stability of H-bonded and stacked base pairs, with a slight shift of ca. 1 kcal/mol in favor of H-bonding. We suggest that the present values are very close to ultimate predictions of the strength of aromatic base stacking of DNA and RNA bases.     

Computational study of the release of H2 from ammonia borane dimer (BH3NH3)2 and its ion pair isomers

High-level electronic structure calculations have been used to map out the relevant portions of the potential energy surfaces for the release of H2 from dimers of ammonia borane, BH3NH3 (AB). Using the correlation-consistent aug-cc-pVTZ basis set at the second-order perturbation MP2 level, geometries of stationary points were optimized. Relative energies were computed at these points using coupled-cluster CCSD(T) theory with the correlation-consistent basis sets at least up to the aug-cc-pVTZ level and in some cases extrapolated to the complete basis set limit. The results show that there are a number of possible dimers involving different types of hydrogen-bonded interactions. The most stable gaseous phase (AB)2 dimer results from a head-to-tail cyclic conformation and is stabilized by 14.0 kcal/mol with respect to two AB monomers. (AB)2 can generate one or two H2 molecules via several direct pathways with energy barriers ranging from 44 to 50 kcal/mol. The diammoniate of diborane ion pair isomer, [BH4-][NH3BH2NH3+] (DADB), is 10.6 kcal/mol less stable than (AB)2 and can be formed from two AB monomers by overcoming an energy barrier of approximately 26 kcal/mol. DADB can also be generated from successive additions of two NH3 molecules to B2H6 and from condensation of AB with separated BH3 and NH3 molecules. The pathway for H2 elimination from DADB is characterized by a smaller energy barrier of 20.1 kcal/mol. The alternative ion pair [NH4+][BH3NH2BH3-] is calculated to be 16.4 kcal/mol above (AB)2 and undergoes H2 release with an energy barrier of 17.7 kcal/mol. H2 elimination from both ion pair isomers yields the chain BH3NH2BH2NH3 as product. Our results suggest that the neutral dimer will play a minor role in the release of H2 from ammonia borane, with a dominant role from the ion pairs as observed experimentally in ionic liquids and the solid state.     

Electrostatic energy in the effective fragment potential method: theory and application to benzene dimer

Evaluation of the electrostatic energy within the effective fragment potential (EFP) method is presented. The performance of two variants of the distributed multipole analysis (DMA) together with two different models for estimating the charge penetration energies was studied using six homonuclear dimers. The importance of damping the higher order multipole terms, i.e. charge dipole, was also investigated. Damping corrections recover more than 70% of the charge penetration energy in all dimers, whereas higher order damping introduces only minor improvement. Electrostatic energies calculated by the numerical DMA are less accurate than those calculated by the analytic DMA. Analysis of bonding in the benzene dimer shows that EFP with inclusion of the electrostatic damping term performs very well compared to the high-level coupled cluster singles, doubles, and perturbative triples method. The largest error of 0.4 kcal/mol occurs for the sandwich dimer configuration. This error is about half the size of the corresponding error in second order perturbation theory. Thus, EFP in the current implementation is an accurate and computationally inexpensive method for calculating interaction energies in weakly bonded molecular complexes.