How well can new-generation density functional methods describe stacking interactions in biological systems?

We compare the performance of four recently developed DFT methods (MPW1B95, MPWB1K, PW6B95, and PWB6K) and two previous, generally successful DFT methods (B3LYP and B97-1) for the calculation of stacking interactions in six nucleic acid bases complexes and five amino acid pairs and for the calculation of hydrogen bonding interactions in two Watson-Crick type base pairs. We found that the four newly developed DFT methods give reasonable results for the stacking interactions in the DNA base pairs and amino acid pairs, whereas the previous DFT methods fail to describe interactions in these stacked complexes. We conclude that the new generation of DFT methods have greatly improved performance for stacking interaction as compared to previously available methods. We recommend the PWB6K method for investigating large DNA or protein systems where stacking plays an important role.     

A computational proposal for the experimentally observed discriminatory behavior of hypoxanthine, a weak universal nucleobase

A computational model composed of six nucleobases was used to investigate why hypoxanthine does not yield duplexes of equal stability when paired opposite each of the natural DNA nucleobases. The magnitudes of all nearest-neighbor interactions in a DNA helix were calculated, including hydrogen-bonding, intra- and interstrand stacking interactions, as well as 1-3 intrastrand stacking interactions. Although the stacking interactions in DNA relevant arrangements are significant and account for at least one third of the total stabilization energy in our nucleobase complexes, the trends in the magnitude of the stacking interactions cannot explain the relative experimental melting temperatures previously reported in the literature. Furthermore, although the total hydrogen-bonding interactions explain why hypoxanthine preferentially pairs with cytosine, the experimental trend for the remaining nucleobases (A, T, G) is not explained. In fact, the calculated pairing preference of hypoxanthine matches that determined experimentally only when the sum of all types of nearest-neighbor interactions is considered. This finding highlights a strong correlation between the relative magnitude of the total nucleobase-nucleobase interactions and measured melting temperatures for DNA strands containing hypoxanthine despite the potential role of other factors (including hydration, temperature, sugar-phosphate backbone). By considering a large range of sequence combinations, we reveal that the binding preference of hypoxanthine is strongly dependent on the nucleobase sequence, which may explain the varied ability of hypoxanthine to universally bind to the natural bases. As a result, we propose that future work should closely examine the interplay between the dominant nucleobase-nucleobase interactions and the overall strand stability to fully understand how sequence context affects the universal binding properties of modified bases and to aid the design of new molecules with ambiguous pairing properties.     

Computational study of noncovalent complexes between formamide and formic acid

The geometries and binding energies of 1:1, 1:2, and 1:4 formic acid-formamide complexes (FA-FMA) are calculated by quantum chemical procedures. Vibrational spectra and intermolecular distances of the most stable FA-FMA dimers as well as the influence of the basis set superposition error (BSSE) on the geometries and energies of the dimers are also discussed. All FA-FMA dimers are optimized at the B3LYP/cc-pVTZ, the MP2/cc-pVDZ, aug-cc-pVDZ, cc-pVTZ, and aug-cc-pVTZ levels of theory to study the influence of the level of theory on the calculated geometries and energies. CCSD(T)/cc-pVTZ single-point calculations at the MP2/aug-cc-pVTZ-optimized geometries were performed as reference for estimating the quality of lower level calculations. These calculations allow us to qualitatively describe the competition between different types of hydrogen-bonding interactions in FA-FMA complexes. FA-FMA dimers are compared to other formamide complexes and to the FA-FMA crystal structure.     

How do size-expanded DNA nucleobases enhance duplex stability? Computational analysis of the hydrogen-bonding and stacking ability of xDNA bases

Computational chemistry (B3LYP, MP2) is used to study the properties of size-expanded DNA nucleobases generated by inserting a benzene spacer into the natural nucleobases. Although the addition of the spacer does not significantly affect the hydrogen-bonding properties of natural nucleobases, the orientation of the base about the glycosidic bond necessary for Watson-Crick binding is destabilized, which could have implications for the selectivity of expanded bases, as well as the stability of expanded duplexes. Consideration of the (stacked) binding energies in the preferred relative orientation of natural and expanded nucleobases aligned according to their centers of mass reveals that the stacking within natural dimers can be increased by up to 50% upon expansion of one nucleobase and up to 90% upon expansion of two nucleobases. The implications of these findings to the stability of expanded duplexes were revealed by considering simplified models of natural and mixed duplexes composed of four nucleobases. Although intra- and interstrand interactions within double helices are typically less than those predicted when nucleobases are stacked according to their centers of mass, some nucleobases utilize their full stacking potential within double helices, where both intra- and interstrand interactions can be significant. Most importantly, increasing the size of nucleobases within the duplex significantly increases both intra- and interstrand stacking interactions. Specifically, some interactions are double the magnitude of the corresponding intrastrand interactions in natural helices, and even greater increases in interstrand interactions are sometimes found. Thus, our work suggests that mixed duplexes composed of natural bases hydrogen bound to expanded bases may exploit the increase in the inherent stacking ability of the expanded bases in more than one way and thereby afford duplexes with greater stability than natural DNA.     

How well can density functional methods describe hydrogen bonds to pi acceptors?

We employed four newly developed density functional theory (DFT) methods for the calculation of five pi hydrogen bonding systems, namely, H2O-C6H6, NH3-C6H6, HCl-C6H6, H2O-indole, and H2O-methylindole. We report new coupled cluster calculations for HCl-C6H6 that support the experimental results of Gotch and Zwier. Using the best available theoretical and experimental results for all five systems, our calculations show that the recently proposed MPW1B95, MPWB1K, PW6B95, and PWB6K methods give accurate energetic and geometrical predictions for pi hydrogen bonding interactions, for which B3LYP fails and PW91 is less accurate. We recommend the most recent DFT method, PWB6K, for investigating larger pi hydrogen bonded systems, such as those that occur in molecular recognition, protein folding, and crystal packing.     

Effects of hydrogen-bonding and stacking interactions with amino acids on the acidity of uracil

The effects of hydrogen-bonding interactions with amino acids on the (N1) acidity of uracil are evaluated using (B3LYP) density functional theory. Many different binding arrangements of each amino acid to three uracil binding sites are considered. The effects on the uracil acidity are found to significantly depend upon the nature of the amino acid and the binding orientation, but weakly depend on the binding site. Our results reveal that in some instances small models for the amino acids can be used, while for other amino acids larger models are required to properly describe the binding to uracil. The gas-phase acidity of uracil is found to increase by up to approximately 60 kJ mol(-1) due to discrete hydrogen-bonding interactions. Although (MP2) stacking interactions with aromatic amino acids decrease the acidity of uracil, unexpected increases in the acidity are found when any of the aromatic amino acids, or the backbone, hydrogen bond to uracil. Consideration of enzymatic and aqueous environments leads to decreases in the effects of the amino acids on the acidity of uracil. However, we find that the magnitude of the decrease varies with the nature of the molecule bound, as well as the (gas-phase) binding orientations and strengths, and therefore solvation effects should be considered on a case-by-case basis in future work. Nevertheless, the effects of amino acid interactions within enzymatic environments are as much as approximately 35 kJ mol(-1). The present study has general implications for understanding the nature of active site amino acids in enzymes, such as DNA repair enzymes, that catalyze reactions involving anionic nucleobase intermediates.     

Tridentate ionic hydrogen-bonding interactions of the 5-fluorocytosine cationic dimer and other 5-fluorocytosine analogues characterized by IRMPD spectroscopy and electronic structure calculations

Ionic hydrogen-bonding interactions have been found in several clusters formed by 5-fluorocytosine (5-FC). The chloride and trimethylammonium cluster ions, along with the cationic (proton-bound) dimer have been characterized by infrared multiple-photon dissociation (IRMPD) spectroscopy and electronic structure calculations performed at the B2PLYP/aug-cc-pVTZ//B3LYP/6-311+G(d,p) level of theory. IRMPD action spectra, in combination with calculated spectra and relative energetics, indicate that it is most probable that predominantly a single isomer exists in each experiment. For the 5-FC-trimethylammonium cluster specifically, the calculated spectrum of the lowest-energy isomer convincingly matches the experimental spectrum. Interestingly, the cationic dimer of 5-FC was found to have a single energetically relevant isomer (Cationic-IV) involving a tridentate ionic hydrogen-bonding interaction. The three sites of intermolecular ionic hydrogen bonds in this isomer interact very efficiently, leading to a significant calculated binding energy of 180 kJ/mol. The magnitude of the calculated binding energy for this species, in combination with the strong correlation between the simulated and IRMPD spectra, suggests that a tridentate-proton-bound dimer was observed predominantly in the experiments. Comparison of the calculated relative Gibbs free energies (298 K) for this species and several of the other isomers considered also supports the likelihood of the dominant protonated dimer existing as Cationic-IV.     

Investigations on stabilities and intermolecular interactions of different naphthalene derivatives dimers by using B3LYP and M06-2X density functional calculations

In this paper, the stabilities and hydrogen bond interactions of 4-chloro-1-naphthol, 1-hydrox-ynaphthalene and 1,4-dihydroxynaphthalene dimers have been theoretically investigated by means of study on binding energies with nonlocal hybrid three-parameter Lee-Yang-Parr, B3LYP, and M06-class functional calculations. Calculations on dimers aim to provide as a test of the efficacy of M06 calculations for intermolecular interaction calculations and more strongly bound systems. For hydroxyl- and halo-substituted derivatives of naphthalene, total electronic energies, their correction for the zero point vibrational energies with some calculated thermodynamic properties and their relative differences are together in order to discuss the rotamer structures. Static (hyper) polarizabilities and the electric dipole moments, frontier molecular orbital energy gaps and the relationships between them have been interpreted. Generally, they are seen that the calculated geometric parameters and spectral results were in a good agreement with the corresponding experimental data.     

Design of density functionals that are broadly accurate for thermochemistry, thermochemical kinetics, and nonbonded interactions

This paper develops two new hybrid meta exchange-correlation functionals for thermochemistry, thermochemical kinetics, and nonbonded interactions. The new functionals are called PW6B95 (6-parameter functional based on Perdew-Wang-91 exchange and Becke-95 correlation) and PWB6K (6-parameter functional for kinetics based on Perdew-Wang-91 exchange and Becke-95 correlation). The resulting methods were comparatively assessed against the MGAE109/3 main group atomization energy database, against the IP13/3 ionization potential database, against the EA13/3 electron affinity database, against the HTBH38/4 and NHTBH38/04 hydrogen-transfer and non-hydrogen-transfer barrier height databases, against the HB6/04 hydrogen bonding database, against the CT7/04 charge-transfer complex database, against the DI6/04 dipole interaction database, against the WI7/05 weak interaction database, and against the new PPS5/05 pi-pi stacking interaction database. From the assessment and comparison of methods, we draw the following conclusions, based on an analysis of mean unsigned errors: (i) The PW6B95, MPW1B95, B98, B97-1, and TPSS1KCIS methods give the best results for a combination of thermochemistry and nonbonded interactions. (ii) PWB6K, MPWB1K, BB1K, MPW1K, and MPW1B95 give the best results for a combination of thermochemical kinetics and nonbonded interactions. (iii) PWB6K outperforms the MP2 method for nonbonded interactions. (iv) PW6B95 gives errors for main group covalent bond energies that are only 0.41 kcal (as measured by mean unsigned error per bond (MUEPB) for the MGAE109 database), as compared to 0.56 kcal/mol for the second best method and 0.92 kcal/mol for B3LYP.     

Intra- and intermolecular interactions between cyclic-AMP receptor protein and DNA: ab initio fragment molecular orbital study

The ab initio fragment molecular orbital (FMO) calculations were performed for the cAMP receptor protein (CRP) complexed with a cAMP and DNA duplex to elucidate their sequence-specific binding and the stability of the DNA duplex, as determined by analysis of their inter- and intramolecular interactions. Calculations were performed with the AMBER94 force field and at the HF and MP2 levels with several basis sets. The interfragment interaction energies (IFIEs) were analyzed for interactions of CRP-cAMP with each base pair, DNA duplex with each amino acid residue, and each base pair with each residue. In addition, base-base interactions were analyzed including hydrogen bonding and stacking of DNA. In the interaction between DNA and CRP-cAMP, there was a significant charge transfer (CT) from the DNA to CRP, and this CT interaction played an important role as well as the electrostatic interactions. It is necessary to apply a quantum mechanical approach beyond the "classical" force-field approach to describe the sequence specificity. In the DNA intramolecular interaction, the dispersion interactions dominated the stabilization of the base-pair stacking interactions. Strong, attractive 1,2-stacking interactions and weak, repulsive 1,3-stacking interactions were observed. Comparison of the intramolecular interactions of free and complexed DNA revealed that the base-pairing interactions were stronger, and the stacking interactions were weaker, in the complexed structure. Therefore, the DNA duplex stability appears to change due to both the electrostatic and the CT interactions that take place under conditions of DNA-CRP binding.     

Theoretical study of excited states of DNA base dimers and tetramers using optimally tuned range‐separated density functional theory

Excited states of various DNA base dimers and tetramers including Watson‐Crick H‐bonding and stacking interactions have been investigated by time‐dependent density functional theory using nonempirically tuned range‐separated exchange (RSE) functionals. Significant improvements are found in the prediction of excitation energies and oscillator strengths, with results comparable to those of high‐level coupled‐cluster (CC) models (RI‐CC2 and EOM‐CCSD(T)). The optimally‐tuned RSE functional significantly outperforms its non‐tuned (default) version and widely‐used B3LYP functional. Compared to those high‐level CC benchmarks, the large mean absolute deviations of conventional functionals can be attributed to their inappropriate amount of exact exchange and large delocalization errors which can be greatly eliminated by tuning approach. Furthermore, the impacts of H‐bonding and π‐stacking interactions in various DNA dimers and tetramers are analyzed through peak shift of simulated absorption spectra as well as corresponding change of absorption intensity. The result indicates the stacking interaction in DNA tetramers mainly contributes to the hypochromicity effect. The present work provides an efficient theoretical tool for accurate prediction of optical properties and excited states of nucleobase and other biological systems. © 2015 Wiley Periodicals, Inc.     

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.     

yDNA versus xDNA pyrimidine nucleobases: computational evidence for dependence of duplex stability on spacer location

The structural and binding properties of the natural and x- and y-pyrimidines were compared using computational methods. Our calculations show that although the x-pyrimidines favor different orientations about the glycosidic bond compared to the natural pyrimidines, which could have implications for the formation and resulting stability of xDNA duplexes and jeopardize the selectivity of expanded nucleobases, y-pyrimidines have rotational profiles more similar to the natural bases. Increasing the pyrimidine size using a benzene spacer leads to relatively minor changes in the hydrogen-bond strength of isolated Watson-Crick base pairs. However, differences in the anomeric carbon distances in pairs composed of x- or y-pyrimidines suggest yDNA may yield a more optimal expanded structure. By stacking two monomers via their centers of mass, we find that the expanded nucleobases stack much stronger than the natural bases. Additionally, although replacing xT by yT changes the stacking energy by less than 5 kJ mol (-1), replacing xC by yC significantly strengthens complexes with the natural nucleobases (by up to 30%). Calculations on larger duplex models composed of four nucleobases reveal that x- and y-pyrimidines can increase duplex stability of natural helices by strengthening both the intra and interstrand stacking interactions. Furthermore, when the total stability (sum of all hydrogen-bonding and (intrastrand and interstrand) stacking interactions) of the larger models is considered, y-pyrimidines lead to more stable complexes than x-pyrimidines for all but three duplex sequences. Thus, through analysis of a variety of properties, our calculations suggest that the location of the benzene spacer affects the properties of expanded nucleobases and the stability of expanded duplexes, and therefore should be carefully considered when designing future expanded analogues.     

Comparative DFT study of van der Waals complexes: rare-gas dimers, alkaline-earth dimers, zinc dimer, and zinc-rare-gas dimers

Recent interest in the application of density functional theory prompted us to test various functionals for the van der Waals interactions in the rare-gas dimers, the alkaline-earth metal dimers, zinc dimer, and zinc-rare-gas dimers. In the present study, we report such tests for 18 DFT functionals, including both some very recent functionals and some well-established older ones. We draw the following conclusions based on the mean errors in binding energies and complex geometries: (1) B97-1 gives the best performance for predicting the geometry of rare-gas dimers, whereas M05-2X and B97-1 give the best energetics for rare-gas dimers. (2) PWB6K gives the best performance for the prediction of the geometry of the alkaline-earth metal dimers, zinc dimers, and zinc-rare-gas dimers. M05-2X gives the best energetics for the metal dimers, whereas B97-1 gives the best energetics for the zinc-rare-gas dimers. (3) The M05 functional is unique in providing good accuracy for both covalent transition-metal dimers and van der Waals metal dimers. (4) The combined mean percentage unsigned error in geometries and energetics shows that M05-2X and MPWB1K are the overall best methods for the prediction of van der Waals interactions in metal and rare-gas van der Waals dimers.     

Theoretical Studies on the Hydrogen‐bonding and π‐Stacking Interactions in the m‐Nisoldipine Polymorphism Dimers

The intermolecular interactions in the dimers of m‐nisoldipine polymorphism were studied by B3LYP calculations and quantum theory of "atoms in molecules" (QTAIM) studies. Four geometries of dimers were obtained: dimer I (a‐dimer, O···H? N), dimer II (b‐dimer, O···H? N), dimer III (b‐dimer, π‐stacking‐c), and dimer IV (b‐dimer, π‐stacking‐p). The interaction energies of the four dimers are along the sequence of II>I>III>IV. The intermolecular distance of the interactions follows the order: I (O···H? N)II>III>IV, and the electrostatic character decreases along the sequence: I>II>III>IV.     

Potassium cation affinities of matrix assisted laser desorption ionization matrices determined by threshold collision-induced dissociation: application to benzoic acid derivatives

Threshold collision-induced dissociation of K+(xBA) complexes with xenon is studied using guided ion beam mass spectrometry. The xBA ligands studied include benzoic acid and all of the mono- and dihydroxy-substituted benzoic acids: 2-, 3-, and 4-hydroxybenzoic acid and 2,3-, 2,4-, 2,5-, 2,6-, 3,4-, and 3,5-dihydroxybenzoic acid. In all cases, the primary product corresponds to endothermic loss of the intact xBA ligand. The cross section thresholds are interpreted to yield 0 and 298 K bond dissociation energies (BDEs) for K+-xBA after accounting for the effects of multiple ion-neutral collisions, the kinetic and internal energy distributions of the reactants, and dissociation lifetimes. Density functional theory calculations at the B3LYP/6-31G* level of theory are used to determine the structures of the xBA ligands and their complexes with K+. Theoretical BDEs are determined from single-point energy calculations at the B3LYP/6-311+G(2d,2p) and MP2(full)/6-311+G(2d,2p) levels using B3LYP/6-31G* optimized geometries. Four favorable binding modes for the K+(xBA) complexes are found. In all complexes to an xBA ligand that does not have a 2-hydroxyl substituent, the most favorable binding mode corresponds to a single interaction with the carbonyl oxygen atom. Formation of a 4-membered ring via chelation interactions with both oxygen atoms of the carboxylic acid group is found to be the most favorable binding mode for all of the 2-hydroxy-substituted systems except K+(2,3-dihydroxybenzoic acid). In these complexes, a hydrogen-bonding interaction between the hydrogen atom of the carboxylic acid moiety and the oxygen atom of the 2-hydroxy substituent provides additional stabilization. Formation of a 5-membered chelation ring via interaction of K+ with the oxygen atoms of adjacent hydroxyl substituents is also favorable and corresponds to the ground-state geometry for the K+(23DHBA) complex. Formation of a 6-membered chelation ring via interaction of K+ with the carbonyl and 2-hydroxyl oxygen atoms is also quite favorable but does not correspond to the ground-state geometry for any of the systems examined here. The experimental BDEs determined here are in very good agreement with the calculated values.     

Lennard-Jones parameters for the combined QM/MM method using the B3LYP/6-31G*/AMBER potential

A combined DFT quantum mechanical and AMBER molecular mechanical potential (QM/MM) is presented for use in molecular modeling and molecular simulations of large biological systems. In our approach we evaluate Lennard-Jones parameters describing the interaction between the quantum mechanical (QM) part of a system, which is described at the B3LYP/6-31+G* level of theory, and the molecular mechanical (MM) part of the system, described by the AMBER force field. The Lennard-Jones parameters for this potential are obtained by calculating hydrogen bond energies and hydrogen bond geometries for a large set of bimolecular systems, in which one hydrogen bond monomer is described quantum mechanically and the other is treated molecular mechanically. We have investigated more than 100 different bimolecular systems, finding very good agreement between hydrogen bond energies and geometries obtained from the combined QM/MM calculations and results obtained at the QM level of theory, especially with respect to geometry. Therefore, based on the Lennard-Jones parameters obtained in our study, we anticipate that the B3LYP/6-31+G*/AMBER potential will be a precise tool to explore intermolecular interactions inside a protein environment.     

2-羟基吡啶与水氢键作用的理论研究

本文采用量子化学的Hatree-Fock方法和密度泛函理论(DFT)的B3LYP方法,在6-31G(d)水平上,研究了2-羟基吡啶分子(Hy)及其酮式互变异构体2(1H)-吡啶酮(Py)与水的相互作用。考察它们之间在形成Hy…H2O,Py…H2O,Hy…Hy,Py…Py和Hy…Py等复合物前后的能量变化和分子结构参数变化特点。计算结果表明,在这些复合物中都形成了较强的氢键作用,在水合物中,Py与水形成复合物时能量降低较多,与实验结果一致。经过零点振动能(ZPVE)和基组叠加误差(BSSE)校正后的复合物离解能分别为38.3,40.8,73.0,82.7和71.1 kJ/mol(B3LYP/6-31G(d)),水合物的离解能远小于二聚体复合物,而酮式结构的二聚体的离解能最大。     

Intermolecular Interaction of HMX： an Application of ONIOM Methodology

IntroductionExtensive studies on intermolecular interac-tions have been made in the past decades due totheir importance in a wide range of physical,chem-ical and biological fields.Researches on the weakintermolecular interactions began with hydrogenbonds.Scheiner summarized the ab initio investiga-tions on hydrogen bonding in detail[1] .With the abinitio method supermolecular structures and bind-ing energies can be predicted notonly for H- bondedsystems but also for other systems[2 _ 5] when …