QM Methods Research Articles

The Importance of the MM Environment and the Selection of the QM Method in QM/MM Calculations: Applications to Enzymatic Reactions.

In this chapter, we discuss the influence of an anisotropic protein environment on the reaction mechanisms of saccharopine reductase and uroporphyrinogen decarboxylase, respectively, via the use of a quantum mechanical and molecular mechanical (QM/MM) approach. In addition, we discuss the importance of selecting a suitable DFT functional to be used in a QM/MM study of a key intermediate in the mechanism of 8R-lipoxygenase, a nonheme iron enzyme. In the case of saccharopine reductase, while the enzyme utilizes a substrate-assisted catalytic pathway, it was found that only through treating the polarizing effect of the active site, via the use of an electronic embedding formalism, was agreement with experimental kinetic data obtained. Similarly, in the case of uroporphyrinogen decarboxylase, the effect of the protein environment on the catalytic mechanism was found to be such that the calculated rate-limiting barrier is in good agreement with related experimentally determined values for the first decarboxylation of the substrate. For 8R-lipoxygenase, it was found that the geometries and energies of the multicentered open-shell intermediate complexes formed during the mechanism are quite sensitive to the choice of the density functional theory method. Thus, while density functional theory has become the method of choice in QM/MM studies, care must be taken in the selection of a particular high-level method.

Role of substrate dynamics in protein prenylation reactions.

ConspectusThe role dynamics plays in proteins is of intense contemporary interest. Fundamental insights into how dynamics affects reactivity and product distributions will facilitate the design of novel catalysts that can produce high quality compounds that can be employed, for example, as fuels and life saving drugs.We have used molecular dynamics (MD) methods and combined quantum mechanical/molecular mechanical (QM/MM) methods to study a series of proteins either whose substrates are too far away from the catalytic center or whose experimentally resolved substrate binding modes cannot explain the observed product distribution. In particular, we describe studies of farnesyl transferase (FTase) where the farnesyl pyrophosphate (FPP) substrate is ∼8 Å from the zinc-bound peptide in the active site of FTase. Using MD and QM/MM studies, we explain how the FPP substrate spans the gulf between it and the active site, and we have elucidated the nature of the transition state (TS) and offered an alternate explanation of experimentally observed kinetic isotope effects (KIEs). Our second story focuses on the nature of substrate dynamics in the aromatic prenyltransferase (APTase) protein NphB and how substrate dynamics affects the observed product distribution.Through the examples chosen we show the power of MD and QM/MM methods to provide unique insights into how protein substrate dynamics affects catalytic efficiency. We also illustrate how complex these reactions are and highlight the challenges faced when attempting to design de novo catalysts.While the methods used in our previous studies provided useful insights, several clear challenges still remain. In particular, we have utilized a semiempirical QM model (self-consistent charge density functional tight binding, SCC-DFTB) in our QM/MM studies since the problems we were addressing required extensive sampling. For the problems illustrated, this approach performed admirably (we estimate for these systems an uncertainty of ∼2 kcal/mol), but it is still a semiempirical model, and studies of this type would benefit greatly from more accurate ab initio or DFT models. However, the challenge with these methods is to reach the level of sampling needed to study systems where large conformational changes happen in the many nanoseconds to microsecond time regimes. Hence, how to couple expensive and accurate QM methods with sophisticated sampling algorithms is an important future challenge especially when large-scale studies of catalyst design become of interest.The use of MD and QM/MM models to elucidate enzyme catalytic pathways and to design novel catalytic agents is in its infancy but shows tremendous promise. While this Account summarizes where we have been, we also discuss briefly future directions that improve our fundamental ability to understand enzyme catalysis.

Intersystem Crossing Enables 4-Thiothymidine to Act as a Photosensitizer in Photodynamic Therapy: An Ab Initio QM/MM Study.

Motivated by its potential use as a photosensitizer in photodynamic therapy, we report the first ab initio quantum mechanics/molecular mechanics (QM/MM) study of 4-thiothymidine in aqueous solution. The core chromophore 4-thiothymine was described using the multiconfigurational CASSCF and CASPT2 QM methods, while the ribose and the solvent water molecules were treated at the MM level (CHARMM and TIP3P, respectively). The minima of the five lowest electronic states (S0, S1, S2, T1, and T2) and six minimum-energy intersections were fully optimized at the QM(CASSCF)/MM level, and their energies were further refined by single-point QM(CASPT2)/MM and CASPT2 calculations. The relevant spin-orbit couplings were also computed. We find that (1) there are three efficient photophysical pathways that account for the experimentally observed ultrafast formation of the lowest triplet state with a quantum yield of nearly unity, (2) the striking qualitative differences in the photophysical behavior of 4-thiothymine and thymine originate from the different electronic structure of their S1 states, and (3) environmental effects play an important role. The present QM/MM calculations provide mechanistic insight that may guide the design of improved photosensitizers for photodynamic therapy.

Using quantum mechanical approaches to study biological systems.

ConspectusQuantum mechanics (QM) has revolutionized our understanding of the structure and reactivity of small molecular systems. Given the tremendous impact of QM in this research area, it is attractive to believe that this could also be brought into the biological realm where systems of a few thousand atoms and beyond are routine. Applying QM methods to biological problems brings an improved representation to these systems by the direct inclusion of inherently QM effects such as polarization and charge transfer. Because of the improved representation, novel insights can be gleaned from the application of QM tools to biomacromolecules in aqueous solution.To achieve this goal, the computational bottlenecks of QM methods had to be addressed. In semiempirical theory, matrix diagonalization is rate limiting, while in density functional theory or Hartree–Fock theory electron repulsion integral computation is rate-limiting. In this Account, we primarily focus on semiempirical models where the divide and conquer (D&C) approach linearizes the matrix diagonalization step with respect to the system size. Through the D&C approach, a number of applications to biological problems became tractable. Herein, we provide examples of QM studies on biological systems that focus on protein solvation as viewed by QM, QM enabled structure-based drug design, and NMR and X-ray biological structure refinement using QM derived restraints.Through the examples chosen, we show the power of QM to provide novel insights into biological systems, while also impacting practical applications such as structure refinement. While these methods can be more expensive than classical approaches, they make up for this deficiency by the more realistic modeling of the electronic nature of biological systems and in their ability to be broadly applied. Of the tools and applications discussed in this Account, X-ray structure refinement using QM models is now generally available to the community in the refinement package Phenix.While the power of this approach is manifest, challenges still remain. In particular, QM models are generally applied to static structures, so ways in which to include sampling is an ongoing challenge. Car–Parrinello or Born–Oppenheimer molecular dynamics approaches address the short time scale sampling issue, but how to effectively use QM to study phenomenon covering longer time scales will be the focus of future research. Finally, how to accurately and efficiently include electron correlation effects to facilitate the modeling of, for example, dispersive interactions, is also a major hurdle that a broad range of groups are addressingThe use of QM models in biology is in its infancy, leading to the expectation that the most significant use of these tools to address biological problems will be seen in the coming years. It is hoped that while this Account summarizes where we have been, it will also help set the stage for future research directions at the interface of quantum mechanics and biology.

Fireball/amber: An Efficient Local-Orbital DFT QM/MM Method for Biomolecular Systems.

In recent years, quantum mechanics/molecular mechanics (QM/MM) methods have become an important computational tool for the study of chemical reactions and other processes in biomolecular systems. In the QM/MM technique, the active region is described by means of QM calculations, while the remainder of the system is described using a MM approach. Because of the complexity of biomolecules and the desire to achieve converged sampling, it is important that the QM method presents a good balance between accuracy and computational efficiency. Here, we report on the implementation of a QM/MM technique that combines a DFT approach specially designed for the study of complex systems using first-principles molecular dynamics simulations (fireball) with the amber force fields and simulation programs. We also present examples of the application of this QM/MM approach to three representative biomolecular systems: the analysis of the effect of electrostatic embedding in the behavior of a salt bridge between an aspartic acid and a lysine residue, a study of the intermediate states for the triosephosphate isomerase catalyzed conversion of dihydroxyacetone phosphate into glyceraldehyde 3-phosphate, and the detailed description, using DFT QM/MM molecular dynamics, of the cleavage of a phosphodiester bond in RNA catalyzed by the enzyme RNase A.

Applications of density functional theory to iron-containing molecules of bioinorganic interest.

The past decades have seen an explosive growth in the application of density functional theory (DFT) methods to molecular systems that are of interest in a variety of scientific fields. Owing to its balanced accuracy and efficiency, DFT plays particularly useful roles in the theoretical investigation of large molecules. Even for biological molecules such as proteins, DFT finds application in the form of, e.g., hybrid quantum mechanics and molecular mechanics (QM/MM), in which DFT may be used as a QM method to describe a higher prioritized region in the system, while a MM force field may be used to describe remaining atoms. Iron-containing molecules are particularly important targets of DFT calculations. From the viewpoint of chemistry, this is mainly because iron is abundant on earth, iron plays powerful (and often enigmatic) roles in enzyme catalysis, and iron thus has the great potential for biomimetic catalysis of chemically difficult transformations. In this paper, we present a brief overview of several recent applications of DFT to iron-containing non-heme synthetic complexes, heme-type cytochrome P450 enzymes, and non-heme iron enzymes, all of which are of particular interest in the field of bioinorganic chemistry. Emphasis will be placed on our own work.

In Depth Analysis on the Binding Sites of Adamantane Derivatives in HCV (Hepatitis C Virus) p7 Channel Based on the NMR Structure

BackgroundThe recently solved solution structure of HCV (hepatitis C virus) p7 ion channel provides a solid structure basis for drug design against HCV infection. In the p7 channel the ligand amantadine (or rimantadine) was determined in a hydrophobic pocket. However the pharmocophore (−NH2) of the ligand was not assigned a specific binding site.ResultsThe possible binding sites for amino group of adamantane derivatives is studied based on the NMR structure of p7 channel using QM calculation and molecular modeling. In the hydrophobic cavity and nearby three possible binding sites are proposed: His17, Phe20, and Trp21. The ligand binding energies at the three binding sites are studied using high level QM method CCSD(T)/6–311+G(d,p) and AutoDock calculations, and the interaction details are analyzed. The potential application of the binding sites for rational inhibitor design are discussed.ConclusionsSome useful viewpoints are concluded as follows. (1) The amino group (−NH2) of adamantane derivatives is protonated (−NH3 +), and the positively charged cation may form cation-π interactions with aromatic amino acids. (2) The aromatic amino acids (His17, Phe20, and Trp21) are the possible binding sites for the protonated amino group (−NH3 +) of adamantane derivatives, and the cation-π bond energies are 3 to 5 times stronger than the energies of common hydrogen bonds. (3) The higher inhibition potent of rimantadine than amantadine probably because of its higher pKa value (pKa = 10.40) and the higher positive charge in the amino group. The potential application of p7 channel structure for inhibitor design is discussed.

회로 최소화를 위한 개선된 Quine-McCluskey 알고리즘

본 논문은 회로 최소화 문제에 대한 Quine-McCluskey 법을 개선한 알고리즘을 제안하였다. Quine-McCluskey 법은 주 내포 항을 반복적인 방법으로 찾고, 회로 최소화 방법으로 시행착오법, 분기한정법 또는 Petrick 법을 적용한다. 반면에 제안된 알고리즘은 사전에 항표를 생성하여 주 내포 항을 간단히 찾는 방법을 제안하였으며, 집합피복을 결정하는 방법을 적용하여 1차와 2차 필수 주 내포 항을 간단히 찾는 방법을 제안하였다. 3-변수와 4-변수 실험 데이터에 적용한 결과 제안된 알고리즘이 Quine-McCluskey 법에 비해 보다 간단하면서도 정확히 해를 구할 수 있었다. This paper revises the Quine-McCluskey Algorithm to circuit minimization problems. Quine-McCluskey method repeatedly finds the prime implicant and employs additional procedures such as trial-and-error, branch-and-bound, and Petrick's method as a means of circuit minimization. The proposed algorithm, on the contrary, produces an implicant chart beforehand to simplify the search for the prime implicant. In addition, it determines a set cover to streamline the search for <TEX>$1^{st}$</TEX> and <TEX>$2^{nd}$</TEX> essential prime implicants. When applied to 3-variable and 4-variable experimental data, the proposed algorithm has indeed proved to obtain the optimal solutions much more simply and accurately than the Quine-McCluskey method.

Parameterization of DFTB3/3OB for Sulfur and Phosphorus for Chemical and Biological Applications.

We report the parametrization of the approximate density functional tight binding method, DFTB3, for sulfur and phosphorus. The parametrization is done in a framework consistent with our previous 3OB set established for O, N, C, and H, thus the resulting parameters can be used to describe a broad set of organic and biologically relevant molecules. The 3d orbitals are included in the parametrization, and the electronic parameters are chosen to minimize errors in the atomization energies. The parameters are tested using a fairly diverse set of molecules of biological relevance, focusing on the geometries, reaction energies, proton affinities, and hydrogen bonding interactions of these molecules; vibrational frequencies are also examined, although less systematically. The results of DFTB3/3OB are compared to those from DFT (B3LYP and PBE), ab initio (MP2, G3B3), and several popular semiempirical methods (PM6 and PDDG), as well as predictions of DFTB3 with the older parametrization (the MIO set). In general, DFTB3/3OB is a major improvement over the previous parametrization (DFTB3/MIO), and for the majority cases tested here, it also outperforms PM6 and PDDG, especially for structural properties, vibrational frequencies, hydrogen bonding interactions, and proton affinities. For reaction energies, DFTB3/3OB exhibits major improvement over DFTB3/MIO, due mainly to significant reduction of errors in atomization energies; compared to PM6 and PDDG, DFTB3/3OB also generally performs better, although the magnitude of improvement is more modest. Compared to high-level calculations, DFTB3/3OB is most successful at predicting geometries; larger errors are found in the energies, although the results can be greatly improved by computing single point energies at a high level with DFTB3 geometries. There are several remaining issues with the DFTB3/3OB approach, most notably its difficulty in describing phosphate hydrolysis reactions involving a change in the coordination number of the phosphorus, for which a specific parametrization (3OB/OPhyd) is developed as a temporary solution; this suggests that the current DFTB3 methodology has limited transferability for complex phosphorus chemistry at the level of accuracy required for detailed mechanistic investigations. Therefore, fundamental improvements in the DFTB3 methodology are needed for a reliable method that describes phosphorus chemistry without ad hoc parameters. Nevertheless, DFTB3/3OB is expected to be a competitive QM method in QM/MM calculations for studying phosphorus/sulfur chemistry in condensed phase systems, especially as a low-level method that drives the sampling in a dual-level QM/MM framework.

DPT tautomerisation of the wobble guanine·thymine DNA base mispair is not mutagenic: QM and QTAIM arguments

We have shown for the first time, connecting QM methods with QTAIM analysis and using the methodology of the sweeps of the energetical, electron-topological and geometrical parameters, that the tautomerisation of the wobble guanine·thymine (wG·T) DNA base mispair into the wG*·T* base mispair induced by the double proton transfer (DPT), which undergoes a concerted asynchronous pathway, is not mutagenic. The wG·T → wG*·T* DPT tautomerisation does not result in the transition of the G base into its mutagenic tautomeric form G* able to mispair with the T base within the Watson–Crick base pairing scheme. This observation is explained by the so-called quantum protection of the wG·T DNA base mispair from its mutagenic tautomerisation – the dynamical non-stability of the tautomerised wG*·T* base mispair and significantly negative value of the Gibbs free energy of activation for the reverse reaction of the wG·T → wG*·T* DPT tautomerisation.

Perturbative approximation to hybrid equation of motion coupled cluster/effective fragment potential method

Hybrid quantum mechanics/molecular mechanics (QM/MM) methods provide an attractive way to closely retain the accuracy of the QM method with the favorable computational scaling of the MM method. Therefore, it is not surprising that QM/MM methods are being increasingly used for large chemical/biological systems. Hybrid equation of motion coupled cluster singles doubles/effective fragment potential (EOM-CCSD/EFP) methods have been developed over the last few years to understand the effect of solvents and other condensed phases on the electronic spectra of chromophores. However, the computational cost of this approach is still dominated by the steep scaling of the EOM-CCSD method. In this work, we propose and implement perturbative approximations to the EOM-CCSD method in this hybrid scheme to reduce the cost of EOM-CCSD/EFP. The timings and accuracy of this hybrid approach is tested for calculation of ionization energies, excitation energies, and electron affinities of microsolvated nucleic acid bases (thymine and cytosine), phenol, and phenolate.

Quantum and Molecular Mechanical (QM/MM) Monte Carlo Techniques for Modeling Condensed-Phase Reactions.

A recent review (Acc. Chem. Res. 2010, 43:142-151) examined our use and development of a combined quantum and molecular mechanical (QM/MM) technique for modelling organic and enzymatic reactions. Advances included the PDDG/PM3 semiempirical QM (SQM) method, computation of multi-dimensional potentials of mean force (PMF), incorporation of on-the-fly QM in Monte Carlo simulations, and a polynomial quadrature method for rapidly treating proton-transfer reactions. The current article serves as a follow up on our progress. Highlights include new reactions, alternative SQM methods, a polarizable OPLS force field, and novel solvent environments, e.g., "on water" and room temperature ionic liquids. The methodology is strikingly accurate across a wide range of condensed-phase and antibody-catalyzed reactions including substitution, decarboxylation, elimination, isomerization, and pericyclic classes. Comparisons are made to systems treated with continuum-based solvents and ab initio or density functional theory (DFT) methods. Overall, the QM/MM methodology provides detailed characterization of reaction paths, proper configurational sampling, several advantages over implicit solvent models, and a reasonable computational cost.

Minimization of Switching Functions using Quine-McCluskey Method

The minimization of switching functions is important to reduce the original number of logic gates required to implement digital logic circuits. Quine-McCluskey algorithm is classical method for simplifying these functions which can handle any number of variables. This paper presents Quine-McCluskey algorithm for minimizing switching functions, with additional specific elements, such as starting part (that is decoding DNF form) and cost of circuit. An example of implementation of the algorithm is given too.

Toward Reliable Prediction of the Energy Ladder in Multichromophoric Systems: A Benchmark Study on the FMO Light-Harvesting Complex.

We present an evaluation of the performance of various single-reference QM methods for the prediction of the relative site energies and transition moments of the Q bands in the bacteriochlorophyll a (BChl a) pigments of the Fenna-Matthew-Olson (FMO) complex. We examine the relative merits of ZINDO, CIS, TD-DFT (with the functionals PBE, BLYP, PBE0, B3LYP, and CAM-B3LYP) and RI-CC2 in reproducing the variations across the pigments that occur as a consequence of geometrical and electrostatic effects of the FMO complex by comparison to DFT-BHLYP/MRCI. We find that these pigments are near-multiconfigurational in nature and, thus, constitute critical cases for the RI-CC2 method. The commonly used ZINDO method is fairly reliable for the site energies of the isolated pigments; however, it overestimates the coupling to the environment, thereby leading to variations across the embedded pigments that are too drastic. The overall best performance is provided by the investigated TD-DFT methods, where PBE0 is found to be slightly superior to the other functionals tested.

QuanPol: A full spectrum and seamless QM/MM program

The quantum chemistry polarizable force field program (QuanPol) is implemented to perform combined quantum mechanical and molecular mechanical (QM/MM) calculations with induced dipole polarizable force fields and induced surface charge continuum solvation models. The QM methods include Hartree-Fock method, density functional theory method (DFT), generalized valence bond theory method, multiconfiguration self-consistent field method, Møller-Plesset perturbation theory method, and time-dependent DFT method. The induced dipoles of the MM atoms and the induced surface charges of the continuum solvation model are self-consistently and variationally determined together with the QM wavefunction. The MM force field methods can be user specified, or a standard force field such as MMFF94, Chemistry at Harvard Molecular Mechanics (CHARMM), Assisted Model Building with Energy Refinement (AMBER), and Optimized Potentials for Liquid Simulations-All Atom (OPLS-AA). Analytic gradients for all of these methods are implemented so geometry optimization and molecular dynamics (MD) simulation can be performed. MD free energy perturbation and umbrella sampling methods are also implemented.

Tests of an Adaptive QM/MM Calculation on Free Energy Profiles of Chemical Reactions in Solution

We present reaction free energy calculations using the adaptive buffered force mixing quantum mechanics/molecular mechanics (bf-QM/MM) method. The bf-QM/MM method combines nonadaptive electrostatic embedding QM/MM calculations with extended and reduced QM regions to calculate accurate forces on all atoms, which can be used in free energy calculation methods that require only the forces and not the energy. We calculate the free energy profiles of two reactions in aqueous solution: the nucleophilic substitution reaction of methyl chloride with a chloride anion and the deprotonation reaction of the tyrosine side chain. We validate the bf-QM/MM method against a full QM simulation, and show that it correctly reproduces both geometrical properties and free energy profiles of the QM model, while the electrostatic embedding QM/MM method using a static QM region comprising only the solute is unable to do so. The bf-QM/MM method is not explicitly dependent on the details of the QM and MM methods, so long as it is possible to compute QM forces in a small region and MM forces in the rest of the system, as in a conventional QM/MM calculation. It is simple, with only a few parameters needed to control the QM calculation sizes, and allows (but does not require) a varying and adapting QM region which is necessary for simulating solutions.

On the Nature of the Hydrogen Bonds to Neutral Ubiquinone in the QABinding Site in Purple Bacterial Photosynthetic Reaction Centers

The nature of hydrogen bonding to pigments in protein complexes is currently a topic of some debate. The debate centers on whether hydrogen bonds can be understood on purely electrostatic grounds or whether they need to be considered quantum mechanically. This distinction is of current relevance primarily because of the application of QM/MM computational methods to the study of biological problems. To address this problem we have used QM/MM methods to study the neutral state of the hydrogen bonded ubiquinone molecule termed QA that functions as an electron transfer cofactor in purple bacterial photosynthetic reaction centers. In these calculations we have treated the hydrogen bonding amino acids either quantum mechanically or using molecular mechanics methods. As a specific metric for comparing the different computational methods isotope edited FTIR difference spectra are calculated. The calculated spectra are in remarkable agreement with experimental spectra, and it is found that the calculated spectra are very similar when hydrogen bonding amino acids are treated using either QM or MM methods. The latter result suggests that hydrogen bonding to neutral ubiquinone in purple bacterial reaction centers can be considered in purely electrostatic terms, which is contrary to the widely held belief that the hydrogen bonding amino acids should be treated quantum mechanically. Natural bond orbital analysis is used to further verify that the hydrogen bonds are predominantly electrostatic in nature. Calculated bond lengths and vibrational frequencies of the N-H groups involved in hydrogen bonding are used to estimate the relative strengths of the hydrogen bonds to either ubiquinone carbonyl group.

QM/MM kinetic isotope effects for chloromethane hydrolysis in water

Computational simulations for chloromethane hydrolysis have been performed using hybrid quantum‐mechanical/molecular‐mechanical methods with explicit solvation by large numbers of water molecules. In the first part of the paper, we present results for 2° 2H3, 1° 14C, and 1° 37Cl kinetic isotope effects (KIEs) at 298 K with both the AM1/TIP3P and B3LYP/6‐31G* QM methods for the nucleophile H2O and electrophile CH3Cl surrounded by 496 solvating TIP3P water molecules. An initial Hessian computed for a subset of this system including up to 104 MM water molecules was reduced in size by successive deletion of rows and columns, and KIEs were evaluated for each. We suggest that accurate calculations of KIEs in solvated systems should involve a subset Hessian including the substrate together with any solvent atoms making specific interactions with any isotopically substituted atom. In the second part of the paper, the ensemble‐averaged 2° α‐2H3 KIE calculated with the B3LYP/6‐31+G(d,p)/TIP3P method is shown to be in good agreement with experiment. This comparison is meaningful because it includes consideration of uncertainties owing to sampling of a range of representative thermally accessible solvent configurations. We also present ensemble‐averaged 14C and 37Cl KIEs which have not as yet been determined experimentally. Copyright © 2013 John Wiley &amp; Sons, Ltd.

Theoretical study on the polar hydrogen-π (Hp-π) interactions between protein side chains.

BackgroundIn the study of biomolecular structures and interactions the polar hydrogen-π bonds (Hp-π) are an extensive molecular interaction type. In proteins 11 of 20 natural amino acids and in DNA (or RNA) all four nucleic acids are involved in this type interaction.ResultsThe Hp-π in proteins are studied using high level QM method CCSD/6-311 + G(d,p) + H-Bq (ghost hydrogen basis functions) in vacuum and in solutions (water, acetonitrile, and cyclohexane). Three quantum chemical methods (B3LYP, CCSD, and CCSD(T)) and three basis sets (6-311 + G(d,p), TZVP, and cc-pVTZ) are compared. The Hp-π donors include R2NH, RNH2, ROH, and C6H5OH; and the acceptors are aromatic amino acids, peptide bond unit, and small conjugate π-groups. The Hp-π interaction energies of four amino acid pairs (Ser-Phe, Lys-Phe, His-Phe, and Tyr-Phe) are quantitatively calculated.ConclusionsFive conclusion points are abstracted from the calculation results. (1) The common DFT method B3LYP fails in describing the Hp-π interactions. On the other hand, CCSD/6-311 + G(d,p) plus ghost atom H-Bq can yield better results, very close to the state-of-the-art method CCSD(T)/cc-pVTZ. (2) The Hp-π interactions are point to π-plane interactions, possessing much more interaction conformations and broader energy range than other interaction types, such as common hydrogen bond and electrostatic interactions. (3) In proteins the Hp-π interaction energies are in the range 10 to 30 kJ/mol, comparable or even larger than common hydrogen bond interactions. (4) The bond length of Hp-π interactions are in the region from 2.30 to 3.00 Å at the perpendicular direction to the π-plane, much longer than the common hydrogen bonds (~1.9 Å). (5) Like common hydrogen bond interactions, the Hp-π interactions are less affected by solvation effects.

Derivations of Single Hypothetical Don't-Care Minterms Using the Quasi Quine-McCluskey Method

Automatically deriving only individual dont-care minterms that can effectively reduce a Boolean logic expressions are being investigated. Dont-care conditions play an important role in optimizing logic design. The type of unknown dont-care minterms that can always reduce the number of product terms in Boolean expression are referred as single hypothetical dont-care (S-HDC) minterms. This paper describes the Quasi Quine-McCluskey method that systematically derives S-HDC minterms. For the most part, this method is similar to the original Quine-McCluskey method in deriving the prime implicants. However, the Quasi Quine-McCluskey method further derives S-HDC minterms by applying so-called a combinatorial comparison operation. Upon completion of the procedure, the designer can review generated S-HDC minterms to test its appropriateness for a particular application.