Potential energy surface and molecular dynamics of MbNO: existence of an unsuspected FeON minimum

Ligands such as CO, O(2), or NO are involved in the biological function of myoglobin. Here we investigate the energetics and dynamics of NO interacting with the Fe(II) heme group in native myoglobin using ab initio and molecular dynamics simulations. At the global minimum of the ab initio potential energy surface (PES), the binding energy of 23.4 kcal/mol and the Fe-NO structure compare well with the experimental results. Interestingly, the PES is found to exhibit two minima: There exists a metastable, linear Fe-O-N minimum in addition to the known, bent Fe-N-O global minimum conformation. Moreover, the T-shaped configuration is found to be a saddle point, in contrast to the corresponding minimum for NO interacting with Fe(III). To use the ab initio results for finite temperature molecular dynamics simulations, an analytical function was fitted to represent the Fe-NO interaction. The simulations show that the secondary minimum is dynamically stable up to 250 K and has a lifetime of several hundred picoseconds at 300 K. The difference in the topology of the heme-NO PES from that assumed previously (one deep, single Fe-NO minimum) suggests that it is important to use the full PES for a quantitative understanding of this system. Why the metastable state has not been observed in the many spectroscopic studies of myoglobin interacting with NO is discussed, and possible approaches to finding it are outlined.     

Comparing search strategies for finding global optima on energy landscapes

We provide some tests of the convex global underestimator (CGU) algorithm, which aims to find global minima on funnel-shaped energy landscapes. We use two different potential functions—the reduced Lennard–Jones cluster potential, and the modified Sun protein folding potential, to compare the CGU algorithm with the simplest versions of the traditional trajectory-based search methods, simulated annealing (SA), and Monte Carlo (MC). For both potentials, the CGU reaches energies lower on the landscapes than both SA and MC, even when SA and MC are given the same number of starting points as in a full CGU run or when all methods are given the same amount of computer time. The CGU consistently finds the global minima of the Lennard–Jones potential for all cases with up to at least n=30 degrees of freedom. Finding the global or near-global minimum in the CGU method requires polynomial time [scaling between O(n³) and O(n⁴)], on average. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 1527–1532, 1999     

自动化势能面搜索方法新进展

本文简要介绍了势能面搜索的两个主要问题,即过渡态搜索和全局势能面搜索,并针对这两个问题介绍了本研究组最近发展的3种方法,即限制最小化双子算法、偏置势函数辅助限制性最小化双子算法以及势能面随机行走方法．这3种方法均只需计算一阶梯度,能够用于快速自动化的搜索过渡态以及势能面．通过几个典型例子分别说明了3种方法的特点及优势．     

Coarse-grained force field: general folding theory

We review the coarse-grained UNited RESidue (UNRES) force field for the simulations of protein structure and dynamics, which is being developed in our laboratory over the last several years. UNRES is a physics-based force field, the prototype of which is defined as a potential of mean force of polypeptide chains in water, where all the degrees of freedom except the coordinates of α-carbon atoms and side-chain centers have been integrated out. We describe the initial implementation of UNRES to protein-structure prediction formulated as a search for the global minimum of the potential-energy function and its subsequent molecular dynamics and extensions of molecular-dynamics implementation, which enabled us to study protein-folding pathways and thermodynamics, as well as to reformulate the protein-structure prediction problem as a search for the conformational ensemble with the lowest free energy at temperatures below the folding-transition temperature. Applications of UNRES to study biological problems are also described.     

Newton trajectories for finding stationary points on molecular potential energy surfaces

We present a new algorithm for computing Newton trajectories based on the Quadratic String Method (QSM) and explain how this can be used to find key stationary points on the molecular potential energy surface (PES). This method starts by using the intersections of Newton trajectories to locate stationary points on the PES. These points could then be used to determine the minimum energy path. The new method, called QSM-NT, is shown to be efficient and reliable for both analytical potential energy surfaces and potential energy surfaces computed from quantum chemistry calculations. The advantages and pitfalls of this method for exploring PES are discussed. In particular, the problem of discontinuous Newton trajectories is elucidated.     

A comparative study of the simulated-annealing and Monte Carlo-with-minimization approaches to the minimum-energy structures of polypeptides: [Met]-enkephalin

A comparison of two methods for surmounting the multiple-minima problem, Simulated Annealing (SA) and Monte Carlo with Minimization (MCM), is presented with applications to [Met]-enkephalin in the absence and in the presence of water. SA explores a continuous space of internal variables, while MCM explores a discrete space consisting of the local energy minima on that space. Starting from random conformations chosen from the whole conformational space in both cases, it is found that, while SA converges to low-energy structures significantly faster than MCM, the former does not converge to a unique minimum whereas the latter does. Furthermore, the behavior of the RMS deviations with respect to the apparent global minimum (for enkephalin in the absence of water) shows no correlation with the observed overall energy decrease in the case of SA, whereas such a correlation is quite evident with MCM; this implies that, even though the potential energy decreases in the annealing process, the Monte Carlo SA trajectory does not proceed towards the global minimum. Possible reasons for these differences between the two methods are discussed. It is concluded that, while SA presents attractive prospects for possibly improving or refining given structures, it must be considered inferior to MCM, at least in problems where little or no structural information is available for the molecule of interest.     

Theoretical study of potential energy surface and vibrational spectra of ArF2 system

An ab initio potential energy surface (PES) of ArF2 system has been obtained by using MP4 calculation with a large basis set including bond functions. There are two local minimums on the PES: one is T-shaped and the other is L-shaped. The L-shaped minimum is the global minimum with a well depth of -119.62 cm- 1 at R = 0.3883nm. The T-shaped minimum has a well depth of -85.93cm -1 at R = 0.3486 nm. A saddle point is found at R = 0.3486 and θ = 61° with the well depth of -61.53 cm-1. The vibrational energy levels have been calculated by using VSCF-CI method. The results show that this PES supports 27 vibrational bound states, and the ground states are two degenerate states assigned to the L-type vibration.     

Structural variations and bonding in gold halides: a quantum chemical study of monomeric and dimeric gold monohalide and gold trihalide molecules, AuX, Au2X2, AuX3, and Au2X6 (X = F, Cl, Br, I)

The molecular structures of all gold mono- and trihalides and of their dimers have been calculated at the B3LYP, MP2, and CCSD(T) levels of theory by using relativistic pseudopotentials for all atoms except fluorine. Our computations support the experimental observation that the relative stability of the monohalides increases from the fluoride toward the iodide, while the stability trend of the trihalides is the opposite. The potential energy surface (PES) of all gold trihalides has been investigated. These molecules are typical Jahn-Teller systems; the trigonal planar D3h-symmetry geometry does not correspond to the minimum energy structure for any of them. At the same time, the amount and character of their Jahn-Teller distortion changes gradually from AuF3 to AuI3. The minimum energy geometry is a T-shaped structure for AuF3 and AuCl3, with a Y-shaped transition-state structure. For AuI3, the Y-shaped structure lies lower than the T-shaped structure on the PES. For AuBr3 and AuI3, neither of them is the global minimum but instead an L-shaped structure, which lies outside the Jahn-Teller PES. This structure can be considered to be a donor-acceptor system, or a closed-shell interaction, with I2 acting as donor and AuI as acceptor. The dimers of gold monohalides have very short gold-gold distances and demonstrate the aurophilic interaction. The dimers of the trihalides are planar molecules with two bridging halogen atoms.     

A global potential energy surface and time‐dependent quantum wave packet calculation of Au + H2 reaction

A global potential energy surface (PES) corresponding to the ground state of AuH₂ system has been constructed based on 22 853 ab initio energies calculated by the multireference configuration interaction method with a Davidson correction. The neural network method is used to fit the PES, and the root mean square error is only 1.87 meV. The topographical features of the novel global PES are compared with previous PES which is constructed by Zanchet et al. (Zanchet PES). The global minimum energy reaction paths on the two PESs both have a well and a barrier. Relative to the Au + H₂ reactants, the energy of well is 0.316 eV on the new PES, which is 0.421 eV deeper than Zanchet PES. The calculation of Au(²S) + H₂(X¹Σ_g⁺) → AuH(X¹Σ⁺) + H(²S) dynamical reaction is carried out on new PES, by the time‐dependent quantum wave packet method (TDWP) with second order split operator. The reaction probabilities, integral cross‐sections (ICSs) and differential cross‐sections are obtained from the dynamics calculation. The threshold in the reaction is about 1.46 eV, which is 0.07 eV smaller than Zanchet PES due to the different endothermic energies on the two PESs. At low collision energy (<2.3 eV), the total ICS is larger than the result obtained on Zanchet PES, which can be attributed to the difference of the wells and endothermic energies.     

Ab initio crystal structure prediction-I. Rigid molecules

A new methodology for the prediction of molecular crystal structures using only the atomic connectivity of the molecule under consideration is presented. The approach is based on the global minimization of the lattice enthalpy of the crystal. The modeling of the electrostatic interactions is accomplished through a set of distributed charges that are optimally and automatically selected and positioned based on results of quantum mechanical calculations. A four-step global optimization algorithm is used for the identification of the local minima of the lattice enthalpy surface. A parallelized implementation of the algorithm permits a much more extensive search of the solution space than has hitherto been possible, allowing the identification of crystal structures in less frequently occurring space groups and with more than one molecule in the asymmetric unit. The algorithm has been applied successfully to the prediction of the crystal structures of 3-aza-bicyclo(3.3.1)nonane-2,4-dione (P2(1)/a, Z' = 1), allopurinol (P2(1)/c, Z' = 1), 1,3,4,6,7,9-hexa-azacycl(3.3.3)azine (Pbca, Z' = 2), and triethylenediamine (P6(3)/m, Z' = 1). In all cases, the experimentally known structure is among the most stable predicted structures, but not necessarily the global minimum.     

Theoretical study of potential energy surface and vibrational spectra of ArF2 system

Anab initio potential energy surface (PES) of ArF₂ system has been obtained by using MP4 calculation with a large basis set including bond functions. There are two local minimums on the PES: one is T-shaped and the other is L-shaped. The L-shaped minimum is the global minimum with a well depth of -119.62 cm^-1 atR = 0.3883nm. The T-shaped minimum has a well depth of -85.93cm^-1 atR = 0.3486 nm. A saddle point is found atR = 0.3486 and τ = 61° with the well depth of -61.53 cm^-1. The vibrational energy levels have been calculated by using VSCF-CI method. The results show that this PES supports 27 vibrational bound states, and the ground states are two degenerate states assigned to the L-type vibration.     

Using swarm intelligence for finding transition states and reaction paths

We describe an algorithm that explores potential energy surfaces (PES) and finds approximate reaction paths and transition states. A few (≈6) evolving atomic configurations ("climbers") start near a local minimum M1 of the PES. The climbers seek a shallow ascent, low energy, path toward a saddle point S12, cross over to another valley of the PES, and climb down to a new minimum M2 that was not known beforehand. Climbers use both energy and energy derivatives to make individual decisions, and they use relative fitness to make team-based decisions. In sufficiently long runs, they keep exploring and may go through a sequence M1-S12-M2-S23-M3 ... of minima and saddle points without revisiting any of the critical points. We report results on eight small test systems that highlight advantages and disadvantages of the method. We also investigated the PES of Li(8), Al(7)(+), Ag(7), and Ag(2)NH(3) to illustrate potential applications of this new method.     

Energy landscape study of water splitting and H2 evolution at a ruthenium(II) pincer complex

A bird's-eye view of the water splitting and H₂ generation at a ruthenium(II) pincer complex is presented. Using a combination of density functional theory and efficient algorithms for exploration of potential energy hypersurface (PES), a total of 197 local minima and 186 transition states are identified, and a new mechanism for water splitting and H₂ evolution via hydroxycarbonyl intermediates is presented. Furthermore, a global feature of the reaction PES, so-called potential energy landscape, is discussed on analyzing the obtained structures. As a result, the landscape is characterized by hierarchical structure, namely, PES consists of many “superbasins (SBs)” that are separated by relatively high energy barriers corresponding to bond breaking around Ru(II) center. Each SB involves a set of conformational isomers that can be interchanged with each other through relatively small barriers. To the best of our best knowledge, this is the first report on the quantum chemical computation of the hierarchical structure of PES for a realistic, catalytic reaction system.     

Adsorption and diffusion on a stepped surface: atomic hydrogen on Pt(211)

We present density functional theory calculations for atomic hydrogen interacting with a stepped surface, the Pt(211) surface. The calculations have been performed at the generalized gradient approximation level, using a slab representation of the surface. This is the state-of-the-art method for calculating the interaction of atoms or molecules with metal surfaces, nevertheless only few studies have used it to study atoms or molecules interacting with stepped surfaces, and none, to the best of our knowledge, have considered hydrogen interacting with stepped platinum surfaces. Our goal has been to initiate a systematic study of this topic. We have calculated the full three-dimensional potential energy surface (PES) for the H/Pt(211) system together with the vibrational band structure and vibrational eigenfunctions of H. A deep global minimum of the PES is found for bridge-bonded hydrogen on the step edge, in agreement with experimental results for the similar H/Pt(533) system. All the local vibrational excitations at the global minimum have been identified, and this will serve as a helpful guide to the interpretation of future experiments on this (or similar) system(s). Furthermore, from the calculated PES and vibrational band structure, we identify a number of consequences for the interpretation or modelling of diffusion experiments studying the coverage and directional dependence of atomic hydrogen diffusion on stepped platinum surfaces.     

Counterpoise-corrected potential energy surfaces of simple H-bonded systems

Geometries and stabilization energies of various simple H-bonded complexes (water dimer, hydrogen fluoride dimer, formamide dimer, formic acid dimer) have been determined by a gradient optimization that eliminates the basis set superposition error (BSSE) by the counterpoise (CP) method in each gradient cycle as well as by the standard gradient optimization. Both optimization methods lead to different potential energy surfaces (PES). The difference depends on the theoretical level used and is larger if correlation energy is considered. Intermolecular distances from the CP-corrected PES are consistently longer, and this difference might be significant (∼0.1 ?); also angular characteristics determined from both surfaces differ significantly. Different geometries were obtained even when passing to larger basis sets (aug-cc-pVDZ). The standard optimization procedure can result in a completely wrong structure. For example, the “quasi-linear” structure of the (HF)₂ (global minimum) does not exist at the standard MP2/ 6-31G** PES (where only cyclic structure was detected) and is found only at the CP-corrected PES. Stabilization energies obtained from the CP-corrected PES are always larger than these from the standard PES where the BSSE is added only a posteriori for the final optimized structure; both energies converge only when passing to a larger basis set (aug-cc-pVDZ). Received: 11 March 1998 / Accepted: 19 June 1998 / Published online: 4 September 1998 RID=" ID=" <E6>Acknowledgements.</E6> The project was supported by the Grant Agency of the Czech Republic (Grant No. 203/98/1166). RID=" ID=" <E5>Correspondence to</E5>: P. Hobza     

Structural,spectroscopic aspects,and electronic properties of (TiO2)n clusters: A study based on the use of natural algorithms in association with quantum chemical methods

In this article, we propose a stochastic search‐based method, namely genetic algorithm (GA) and simulated annealing (SA) in conjunction with density functional theory (DFT) to evaluate global and local minimum structures of (TiO₂)_n clusters with n = 1–12. Once the structures are established, we evaluate the infrared spectroscopic modes, cluster formation energy, vertical excitation energy, vertical ionization potential, vertical electron affinity, highest occupied molecular orbital (HOMO)‐lowest unoccupied molecular orbital (LUMO) gaps, and so forth. We show that an initial determination of structure using stochastic techniques (GA/SA), also popularly known as natural algorithms as their working principle mimics certain natural processes, and following it up with density functional calculations lead to high‐quality structures for these systems. We have shown that the clusters tend to form three‐dimensional networks. We compare our results with the available experimental and theoretical results. The results obtained from SA/GA‐DFT technique agree well with available theoretical and experimental data of literature. © 2013 Wiley Periodicals, Inc.     

Rg—HX(Rg=He,Ne;X=F,Cl,Br)分子间势的精确量子化学从头计算研究III.He—HBr

在用非迭代的三重激发项来校正CCSD的CCSD（T）理论水平下，采用aug-cc- pVQZ基函数对He—HBr的分子间势进行了系统的研究。结果表明：He—HBr以线型结 构存在。在极限基的情况下，复合物两种线型极小点结构He—H—Br和He—Br—H势 阱深分别为28.792 cm~(-1)和35.707 cm~(-1)，对应He原子到HBr分子质心的距离 R分别为0.407 nm和0.343 nm。讨论了不同的基函数和理论方法在研究此类弱束缚 态复合物的分子间势时的可靠性及其对结果的影响，同时也给出了热函数的解析形 式。     

Do intelligent configuration search techniques outperform random search for large molecules?

We compare three global configuration search methods on a scalable model problem to measure relative performance over a range of molecule sizes. Our model problem is a 2-D polymer composed of atoms connected by rigid rods in which all pairs of atoms interact via Lennard–Jones potentials. The global minimum energy can be calculated analytically. The search methods are all hybrids combining a global sampling algorithm with a local refinement technique. The sampling methods are simulated annealing (SA ), genetic algorithms (GA ), and random search. Each of these uses a conjugate gradient (CG ) routine to perform the local refinement. Both GA and SA perform progressively better relative to random search as the molecule size increases. We also test two other local refinement techniques in addition to CG , coupled to random search as the global method. These are simplex followed by CG and simplex followed by block-truncated Newton. For small problems, the addition of the intermediate simplex step improved the performance of the overall hybrid method. © 1992 John Wiley & Sons, Inc.