偏分势能面及其应用(I):概念、构造方法及几个简例

提出了偏分势能面的概念,偏分势能面可由完全势能面抽取出来,也可采用abinitio方法进行构造.作为范例,给出了F+H2→FH+H,H+H2→H2+H,I+HI→IH+I及Na+I2→Na++I-等体系中几种偏分势能面的构造和应用.2可以看到,应用偏分势能面对于分析反应机理及散射共振态的生成方面显示突出优点.     

用神经网络方法拟合的反应体系H＋CH4←→H2＋CH3的一个全域势能面

利用神经网络力法,基于47783个高精度从头算能量点构建了反应体系H＋CH4←→H2＋CH3的一个全域势能面．通过大最的准经典轨线以及量子散射计算测试了势能面的收敛性质．这个势能面对于拟合过程以及从头算点的数目都已经完全收敛,拟合误差很小县比Shepard插值的势能面计算速度更快,代表了此标志性多原子反应体系最好的势能面．     

H与ClF生成HF反应机理的量子化学研究

用从头算分子轨道法对H与ClF生成HF反应的势能面进行了系统的计算 .优选了与生成HF有关的各种可能的过渡态 .通过从以F原子为中心的线状过渡态出发作IRC的计算 ,并结合偏离线状构型后势能面的扫描数据确定了生成HF的直接型反应途径 ;通过从以H原子为中心的过渡态出发作IRC的计算确定了生成HF的迁移型反应途径 .从理论上证实了Polanyi提出的关于H与ClF生成HF的反应过程包含直接型与迁移型两种机理的假设 .     

多原子反应体系的高精度拟合势能面

本文介绍了近几年来我们组构建多原子反应体系的高精度拟合势能面的进展。我们基于神经网络(NN)方法,成功构建了多原子气相分子体系和气相分子在金属表面解离的一系列势能面。这些势能面的拟合精度相当高,并且经过了严格的量子动力学测试,能广泛应用到动力学研究中。我们还提出了一种新的置换不变势能面的拟合方法,即基本不变量神经网络方法(FI-NN)。基本不变量的使用极大地减少了神经网络输入层多项式的个数,有效提高了势能面的计算速度。     

偏分势能面及其应用(Ⅰ):概念、构造方法及几个简例

提出了偏分势能面的概念,偏分势能面可由完全势能面抽取出来,也可采用ab initio方法进行构造．作为范例。给出了F H2→FH H,H H2→H2 H,I HI→IH I及Na I2→Na^ I2^-等体系中几种偏分势能面的构造和应用．可以看到,应用偏分势能面对于分析反应机理及散射共振态的生成方面显示突出优点．     

精确固定节面量子Monte Carlo差值法

提出了精确固定节面量子Monte Carlo差值法, 这个新算法能够在精确固定节面量子Monte Carlo方法的基础上直接计算两个体系之间的能量差, 且使计算结果的统计误差达到10-5 hartree 数量级, 获得电子相关能90%以上. 我们把这个新算法应用于分子势能面的研究中, 使用一个“刚性移动”模型, 利用Jacobi变换使分子两个几何构型的能量计算具有很好的正相关性, 因而能得到准确的能量差值, 由此就可以得到精确的分子势能面.     

化学反应的高精度从头算势能面

势能面是化学反应动力学研究的基础。近年来随着理论方法的发展与计算技术的进步,不但含三、四个原子反应体系的电子基态势能面的构建精度进一步提高,一些反应体系的多电子态耦合势能面的构建和含六个原子以上反应体系的高维从头算势能面的构建也取得了重要进展。本文结合若干典型体系势能面的构建工作,主要介绍了高精度电子基态势能面,包括Renner-Teller、旋轨耦合等非绝热效应的耦合势能面以及高维势能面方面的研究进展。     

构造SO~2分子势能面的李代数方法

把李代数方法得到的SO~2分子的代数Hamiltonian,利用相干态基经典化并找到一个新的变换,将分子的键角引入,而得到SO~2分子的势能面。由该势能面计算的解离能,所给出的势能面的立体图和相应的等高线以及力常数与其他方法给出的相一致。该方法可以推广到多原子分子及反应体系。     

势能面特征与过渡态熵及A因子

反应体系的势能面,对了解反应的微观过程起着重要的作用,它的特征决定了化学反应的机理.原则上,由反应体系的Schrodinger方程的解,可得到体系能量随核间距变化的函数,从而获得势能面.除少数简单反应外,几乎无法精确求得复杂反应体系的势能面.因而,除从头算法外,人们先后发展了计算势能面的一些半经验方法.对某一反应,文献中可能记载好几个势能面,因此,在分析反应或计算反应的各物理量时,应当说明所应用的是何种势能面.我们曾指出,过渡态熵的可靠性,有赖于提供过渡态参数的势能面.本文从下述基元反应     

HNCS与CX(X=H,F,Cl)自由基反应的理论研究

用量子化学密度泛函理论的UB3LYP方法,在6-31 G^*水平上按BERNY能量梯度解析法全参数优化了HNCS与CX(X=H,F,Cl)反应势能面上各驻点的几何构型,通过同一水平的振动频率分析确认了中问体和过渡态,并得到各驻点的零点能校正(Ezpc)．通过内禀反应坐标(IRC)计算确认了反应物、中间体、过渡态和产物的相关性并得到最小能量途径(MEP)．为了得到体系势能面的更准确信息,在各驻点的UB3LYP／6-31 G^*构型基础上,又进行了UQCISD(T)／6-311 G^**水平上的单点能计算,得到体系的势能面信息和可能的反应机理．应用变分过渡态理论及最小能量途径半经典绝热基态(MEPSAG)、小曲率半经典绝热基态(SCSAG)隧道效应校正的方法计算了标题反应在250～1500K温度范围内的速率常数．研究结果表明,HNCS与CX自由基反应是通过分子间H原子迁移及N—C键的断裂,生成产物CS NCXH．反应均为放热反应．     

Generic implementation of semi-analytical CI gradients for NDDO-type methods

Generic semi-analytical energy gradients are derived and implemented for NDDO-type methods, by using numerical integral and Fock matrix derivatives in the context of an otherwise analytical approach for configuration interaction (CI) and other non-variational treatments. The correctness, numerical precision, and performance of this hybrid approach are established through comparisons with fully numerical and fully analytical calculations. The semi-analytical evaluation of the CI gradient is generally much faster than the fully numerical computation, but somewhat slower than a fully analytical calculation, which however shows the same scaling behavior. It is the method of choice whenever a fully analytical CI gradient is not available due to the lack of analytical integral derivatives. The implementation is generic in the sense that it can easily be extended to any new NDDO-type Hamiltonian. The present development of a semi-analytical CI gradient will facilitate studies of electronically excited states with recently proposed NDDO methods that include orthogonalization corrections. Dedicated to Professor Karl Jug on the occasion of his 65th birthday     

Energy-optimized GTO basis sets for LCAO Calculations. A Gradient Approach

The use of gradient techniques for the development of energy-optimized basis sets has been investigated. The region where the energy surface is approximately quadratic with a positive definite Hessian is found to be very small for large basis sets. However, scaled Newton-Raphson methods prove quite effective even when the starting point is outside this region. The analytic calculation of the Hessian is found to be most efficient in terms of computing time.     

Analytical energy gradient evaluation in relativistic and nonrelativistic density functional calculations

The expressions of analytical energy gradients in density functional theory and their implementation in programs are reported. The evaluation of analytical energy gradients can be carried out in the fully 4-component relativistic, approximate relativistic, and nonrelativistic density functional calculations under local density approximation or general gradient approximation with or without frozen core approximation using different basis sets in our programs. The translational invariance condition and the fact that the one-center terms do not contribute to the energy gradients are utilized to improve the calculation accuracy and to reduce the computational effort. The calculated results of energy gradients and optimized geometry as well as atomization energies of some molecules by the analytical gradient method are in very good agreement with results obtained by the numerical derivative method.     

B-spline method for energy minimization in grid-based molecular mechanics calculations

A method is described for molecular mechanics calculations based on a cubic B-spline approximation of the potential energy. This method is useful when parts of the system are allowed to remain fixed in position so that a potential energy grid can be precalculated and used to approximate the interaction energy between parts of a molecule or between molecules. We adapted and modified the conventional B-spline method to provide an approximation of the Empirical Conformational Energy Program for Peptides (ECEPP) potential energy function. The advantage of the B-spline method over simpler approximations is that the resulting B-spline function is C2 continuous, which allows minimization of the potential energy by any local minimization algorithm. The standard B-spline method provides a good approximation of the electrostatic energy; but in order to reproduce the Lennard–Jones and hydrogen-bonding functional forms accurately, it was necessary to modify the standard B-spline method. This modification of the B-spline method can also be used to improve the accuracy of trilinear interpolation for simulations that do not require continuous derivatives. As an example, we apply the B-spline method to rigid-body docking energy calculations using the ECEPP potential energy function. Energies are calculated for the complex of Phe-Pro-Arg with thrombin. For this system, we compare the performance of the B-spline method to that of the standard pairwise summation in terms of speed, accuracy, and overhead costs for a variety of grid spacings. In our rigid-body docking calculations, the B-spline method provided an accurate approximation of the total energy of the system, and it resulted in an 180-fold reduction in the time required for a single energy and gradient calculation for this system. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 71–85, 1998     

Differential diffusion quantum Monte Carlo method: determination of potential energy surfaces of molecules

A differential approach for self-optimizing diffusion Monte Carlo calculation was proposed in this paper, which is a new algorithm combining three techniques such as optimizing, diffusion and correlation sampling. This method can be used to directly compute the energy differential between two systems in the diffusion process, making the statistical error of calculation be reduced to order of 10-5 hartree, and recover about more than 80% of the correlation energy. We employed this approach to set up a potential energy surface of a molecule, used a "rigid move" model, and utilized Jacobi transformation to make energy calculation for two configurations of a molecule having good positive correlation. So, an accurate energy differential could be obtained, and the potential energy surface with good quality can be depicted. In calculation, a technique called "post-equilibrium remaining sample was set up firstly, which can save about 50% of computation expense. This novel algorithm was used to study the potenti     

Protein calculations on parallel processors. I. Parallel algorithm for the potential energy

We investigate and test an algorithm suitable for the parallel calculation of the potential energy of a protein, or its spatial gradient, when the protein atoms interact via pair potentials. This algorithm is similar to one previously proposed, but it is more efficient, having half the interprocessor communications costs. For a given protein, we show that there is an optimal number of processors that gives a maximum speedup of the potential energy calculation compared to a sequential machine. (Using more than the optimum number of processors actually increases the computation time). With the optimum number the computation time is proportional to the protein size N. This is a considerable improvement in performance compared to sequential machines, where the computation time is proportional to N². We also show that the dependence of the maximum speedup on the message latency time is relatively weak.     

Calculation of exchange-correlation potentials with auxiliary function densities

The use of Hermite Gaussian auxiliary function densities from the variational fitting of the Coulomb potential for the calculation of exchange-correlation potentials is discussed. The basic working equations for the energy and gradient calculation are derived. The accuracy of this approximation for optimized structure parameters and bond energies are analyzed. It is shown that the quality of the approximation can be systematically improved by enlarging the auxiliary function set. Average errors of 0.5 kcal/mol are obtained with auxiliary function sets including f and g functions. The timings for a series of alkenes demonstrate a substantial performance improvement.     

Minimization of empirical energy functions in proteins including hydrophobic surface area effects

We present analytical expressions to calculate the gradient of the water-accessible surface area of proteins with respect to Cartesian coordinates and dihedral angles. A detailed mathematical analysis leads to corrected equations for the gradient calculation used previously in the ANAREA program. To study the hydrophobic effect of solvent-protein interactions, our expressions have been implemented to further improve the program package FANTOM. We used this version of FANTOM to minimize the ECEPP/2 and the hydrophobic energy of tendamistat. © 1993 John Wiley & Sons, Inc.     

On the quadratic reaction path evaluated in a reduced potential energy surface model and the problem to locate transition states*

Knowledge of the location of saddle points is crucial to the study the chemical reactivity. Using a path following method defined in a reduced potential energy surface, and starting at either the reactant or product region, we propose an algorithm that locates the corresponding saddle point. The reduced potential energy surface is defined by the set of molecular geometry parameters, namely bond distances, bond angles, and dihedral angles that undergo the largest change for the reaction under consideration; the rest of the coordinates are forced to have a null gradient. Consequently, the proposed method can be seen as a new formulation of the distinguished coordinate method. The method is based on a quadratic model; consequently, it only requires the calculation of the energy and the gradient. The Hessian matrix is normally updated except in the first step and the steps where the resulting updated Hessian matrix is not adequate. Some examples are presented and analyzed. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 387–406, 2001     

Dynamics of (H(-), H(2)) collisions: a time-dependent quantum mechanical investigation on a new ab initio potential energy surface

A global analytical potential energy surface for the ground state of H(3)(-) has been constructed by fitting an analytic function to the ab initio potential energy values computed using coupled cluster singles and doubles with perturbative triples [CCSD(T)] method and Dunning's augmented correlation consistent polarized valence triple zeta basis set. Using this potential energy surface, time-dependent quantum mechanical wave packet calculations were carried out to calculate the reaction probabilities (P(R)) for the exchange reaction H(-)+H(2)(v, j)-->H(2)+H(-), for different initial vibrational (v) and rotational (j) states of H(2), for total angular momentum equal to zero. With increase in v, the number of oscillations in the P(R)(E) plot increases and the oscillations become more pronounced. While P(R) increases with increase in rotational excitation from j=0 to 1, it decreases with further increase in j to 2 over a wide range of energies. In addition, rotational excitation quenches the oscillations in P(R)(E) plots.