NDDO fragment self-consistent field approximation for large electronic systems

A semi-empirical NDDO method, generalized from a similar scheme at the CNDO/2 level developed previously, is presented to treat very large molecules. The extended molecular system is divided into a relatively small subsystem where substantial chemical changes take place and an environment remaining more-or-less unperturbed during the process. Expanding the wave function on an atomic hybrid basis an SCF procedure is performed for the subsystem in the field of the iteratively determined electronic distribution of the environment. A computer program has been written for the IBM RISC System/6000 530 computer and several test calculations were done for a variety of large classical molecules, like substituted aliphatic hydrocarbons, water oligomers, and a heptapeptide. Protonation energies, proton transfer potential curves, rotational barriers, atomic net charges, and HOMO and LUMO energies, as computed by the exact version of the NDDO method, are fairly well reproduced by our approximation if the subsystem is appropriately defined. © 1992 by John Wiley & Sons, Inc.     

Quantum mechanical computations on very large molecular systems: The local self-consistent field method

Quantum chemical computations on a subset of a large molecule can be performed, at the neglect of diatomic differential overlap (NDDO) level, without further approximation provided that the atomic orbitals of the frontier atoms are replaced by parametrized orthogonal hybrid orbitals. The electrostatic interaction with the rest of the molecule, treated classically by the usual molecular mechanical approximations, is included into the self-consistent field (SCF) equations. The first and second derivatives of energy are obtained analytically, allowing the search for energy minima and transition states as well as the resolution of Newton equations in molecular dynamics simulations. The local self-consistent field (LSCF) method based on these approximations is tested by studying the intramolecular proton transfer in a Gly-Arg-Glu-Gly model tetrapeptide, which reveals an excellent agreement between a computation performed on the whole molecule and the results obtained by the present method, especially if the quantum subsystem includes the side chains and the peptidic unit in between. The merits of the LSCF method are examplified by a study of proton transfer in the Asp⁶⁹—Arg⁷¹ salt bridge in dihydrofolate reductase. Simulations of large systems, involving local changes of electronic structure, are therefore possible at a good degree of approximation by introducing a quantum chemical part in molecular dynamics studies. This methodology is expected to be very useful for reactivity studies in biomolecules or at the surface of covalent solids. © 1994 by John Wiley & Sons, Inc.     

An efficient local coupled cluster method for accurate thermochemistry of large systems

An efficient local coupled cluster method with single and double excitation operators and perturbative treatment of triple excitations [DF-LCCSD(T)] is described. All required two-electron integrals are evaluated using density fitting approximations. These have a negligible effect on the accuracy but reduce the computational effort by 1-2 orders of magnitude, as compared to standard integral-direct methods. Excitations are restricted to local subsets of non-orthogonal virtual orbitals (domain approximation). Depending on distance criteria, the correlated electron pairs are classified into strong, close, weak, and very distant pairs. Only strong pairs, which typically account for more than 90% of the correlation energy, are optimized in the LCCSD treatment. The remaining close and weak pairs are approximated by LMP2 (local second-order Mo?ller-Plesset perturbation theory); very distant pairs are neglected. It is demonstrated that the accuracy of this scheme can be significantly improved by including the close pair LMP2 amplitudes in the LCCSD equations, as well as in the perturbative treatment of the triples excitations. Using this ansatz for the wavefunction, the evaluation and transformation of the two-electron integrals scale cubically with molecular size. If local density fitting approximations are activated, this is reduced to linear scaling. The LCCSD iterations scale quadratically, but linear scaling can be achieved by neglecting some terms involving contractions of single excitations. The accuracy and efficiency of the method is systematically tested using various approximations, and calculations for molecules with up to 90 atoms and 2636 basis functions are presented.     

New vibrational self-consistent field program for large molecules

A recently developed, general computer program that performs vibrational self-consistent field (VSCF) calculations for large molecules is described. The program, which we refer to as VSCF―95, requires as its only input a force field in mass-scaled normal coordinates. Currently, it is limited to a maximum of 200 normal modes, and the force field is limited to coupling terms involving a maximum of six normal modes, with a maximum order of six in any normal mode. As output the program returns VSCF energies for specified quantum states. We illustrate the code with two new applications. The first is to HCO, for which we use a full sixth-order force field. The second is to a model of the fullerene, C₆₀, for which we have calculated a 75,731-term force field, which includes all anharmonic terms up to fifth order, and all two-mode coupling terms up to fourth order. © 1996 by John Wiley & Sons, Inc.     

XO: An extended ONIOM method for accurate and efficient modeling of large systems

Calculation of large complex systems remains to be a great challenge, where there is always a trade‐off between accuracy and efficiency. Recently, we proposed the extended our own n‐layered integrated molecular orbital (ONIOM) method (XO) (Guo, Wu, Xu, Chem. Phys. Lett. 2010 , 498, 203) which surmounts some inherited limitations of the popular ONIOM method by introducing the inclusion‐exclusion principle used in the fragmentation methods. The present work sets up general guidelines for the construction of a good XO scheme. In particular, force‐error test is proposed to quantitatively validate the usefulness of an XO scheme, taking accuracy, efficiency and scalability all into account. Representative studies on zeolites, polypeptides and cyclodextrins have been carried out to demonstrate how to strive for high accuracy without sacrificing efficiency. As a natural extension, XO is applied to calculate the total energy, fully optimized geometry and vibrational spectra of the whole system, where ONIOM becomes inapplicable. © 2012 Wiley Periodicals, Inc.     

An efficient, fragment-based electronic structure method for molecular systems: self-consistent polarization with perturbative two-body exchange and dispersion

We report a fragment-based electronic structure method, intended for the study of clusters and molecular liquids, that incorporates electronic polarization (induction) in a self-consistent fashion but treats intermolecular exchange and dispersion interactions perturbatively, as post-self-consistent field corrections, using a form of pairwise symmetry-adapted perturbation theory. The computational cost of the method scales quadratically as a function of the number of fragments (monomers), but could be made to scale linearly by exploiting distance-dependent thresholds. Extensive benchmark calculations are reported using the S22 database of high-level ab initio binding energies for dimers, and we find that average errors can be reduced to <1 kcal/mol with a suitable choice of basis set. Comparison to ab initio benchmarks for water clusters as large as (H(2)O)(20) demonstrates that the method recovers ?90% of the binding energy in these systems, at a tiny fraction of the computational cost. As such, this approach represents a promising path toward accurate, systematically improvable, and parameter-free simulation of molecular liquids.     

Size-extensive vibrational self-consistent field method

The vibrational self-consistent field (VSCF) method is a mean-field approach to solve the vibrational Schro?dinger equation and serves as a basis of vibrational perturbation and coupled-cluster methods. Together they account for anharmonic effects on vibrational transition frequencies and vibrationally averaged properties. This article reports the definition, programmable equations, and corresponding initial implementation of a diagrammatically size-extensive modification of VSCF, from which numerous terms with nonphysical size dependence in the original VSCF equations have been eliminated. When combined with a quartic force field (QFF), this compact and strictly size-extensive VSCF (XVSCF) method requires only quartic force constants of the ?(4)V/?Q(i)(2)?Q(j)(2) type, where V is the electronic energy and Q(i) is the ith normal coordinate. Consequently, the cost of a XVSCF calculation with a QFF increases only quadratically with the number of modes, while that of a VSCF calculation grows quartically. The effective (mean-field) potential of XVSCF felt by each mode is shown to be harmonic, making the XVSCF equations subject to a self-consistent analytical solution without matrix diagonalization or a basis-set expansion, which are necessary in VSCF. Even when the same set of force constants is used, XVSCF is nearly three orders of magnitude faster than VSCF implemented similarly. Yet, the results of XVSCF and VSCF are shown to approach each other as the molecular size is increased, implicating the inclusion of unnecessary, nonphysical terms in VSCF. The diagrams of the XVSCF energy expression and their evaluation rules are also proposed, underscoring their connected structures.     

An efficient method for large scale configuration interaction calculations

An efficient method of handling large scale configuration interaction calculations is developed and applied to the H₂O molecule as a test case. The method, which is based upon matrix partitioning, is shown to be capable of calculating the ¹B₁ spectrum of H₂O to an accuracy level of 0.1 eV for each state with very moderate computational effort.     

A new method analyzing large and strongly interacting reaction systems

A new method is presented to analyze the various interactions in reaction systems. The method is especially suited for large and strongly interacting systems where other analyzing methods are not practical. The method could isolate the particular interaction from the whole interaction by a procedure termed the partial diagonalization of the bond order matrix. The usefulness of the method is exemplified by the adsorption of CO on Pt and W surfaces. The interactions on the W surface are much stronger than those on the Pt surface, which is consistent with the experimental data. The role of individual interactions for the weakening of the C-O bond and the formation of the Pt-C and W-C bonds is discussed separately.     

Pre-processing two-electron integrals for efficient utilization in many-electron self-consistent field calculations

A procedure for pre-processing a random list of two-electron integrals is described. Construction of Fock-matrices with the resulting PK-file is shown to be three times faster than use of a file containing the random two-electron integrals, indices, and a branching code.     

An elongation method for large systems toward bio-systems

The elongation method, proposed in the early 1990s, originally for theoretical synthesis of aperiodic polymers, has been reviewed. The details of derivation of the localization scheme adopted by the elongation method are described along with the elongation processes. The reliability and efficiency of the elongation method have been proven by applying it to various models of bio-systems, such as gramicidin A, collagen, DNA, etc. By means of orbital shift, the elongation method has been successfully applied to delocalized π-conjugated systems. The so-called orbital shift works in such a way that during the elongation process, some strongly delocalized frozen orbitals are assigned as active orbitals and joined with the interaction of the attacking monomer. By this treatment, it has been demonstrated that the total energies and non-linear optical properties determined by the elongation method are more accurate even for bio-systems and delocalized systems like fused porphyrin wires. The elongation method has been further developed for treating any three-dimensional (3D) systems and its applicability is confirmed by applying it to entangled insulin models whose terminal is capped by both neutral and zwitterionic sequences.     

Applications of self-consistent field theory in polymer systems

1Introduction Owing to the specificity of the long chain,polymers present complexity and versatility.These molecules in the system can be various in their topological struc-tures,such as linear,star,comb or circle structures;meanwhile they can be polymeri…     

An algorithm for self-consistent field MO LCAO computations on conjugated systems with allowance for configuration interaction

The Pariser-Parr-Pople method is described briefly. An algorithm is presented for quantum-mechanical computation of molecular structures. A program for the BESM-2M computer is presented.     

An efficient molecular orbital approach for self-consistent calculations of molecular junctions

To model electron transport through a molecular junction, we propose an efficient method using an ab initio self-consistent nonequilibrium Green's function theory combined with density functional theory. We have adopted a model close to the extended molecule approach, due to its flexibility, but have improved on the problems relating to molecule-surface couplings and the long-range potential via a systematic procedure for the same ab initio level as that of Green's function. The resulting algorithm involves three main steps: (i) construction of the embedding potential; (ii) perturbation expansion of Green's function in the molecular orbital basis; and (iii) truncation of the molecular orbital space by separating it into inactive, active, and virtual spaces. The above procedures directly reduce the matrix size of Green's function for the self-consistent calculation step, and thus, the algorithm is suitable for application to large molecular systems.     

A force field for some weakly coupled conjugated systems

A force field developed in a series of overlay calculations for some weakly coupled conjugated systems is discussed. The force fieid is compared with other, mainly overlay force fields of related molecules, as this gives further evidence for the transferability of the force constants. In order to be of any use for large molecules the force field must be easy to transfer to related, more complicated molecules. The disadvantages of using individual force fields are also discussed.     

An efficient newton-like method for molecular mechanics energy minimization of large molecules

Techniques from numerical analysis and crystallographic refinement have been combined to produce a variant of the Truncated Newton nonlinear optimization procedure. The new algorithm shows particular promise for potential energy minimization of large molecular systems. Usual implementations of Newton's method require storage space proportional to the number of atoms squared (i.e., O(N²)) and computer time of O(N³). Our suggested implementation of the Truncated Newton technique requires storage of less than O(N^1.5) and CPU time of less than O(N²) for structures containing several hundred to a few thousand atoms. The algorithm exhibits quadratic convergence near the minimum and is also very tolerant of poor initial structures. A comparison with existing optimization procedures is detailed for cyclohexane, arachidonic acid, and the small protein crambin. In particular, a structure for crambin (662 atoms) has been refined to an RMS gradient of 3.6 × 10^?6 kcal/mol/Å per atom on the MM2 potential energy surface. Several suggestions are made which may lead to further improvement of the new method.     

An efficient self-optimized sampling method for rare events in nonequilibrium systems

Rare events such as nucleation processes are of ubiquitous importance in real systems.The most popular method for nonequilibrium systems,forward flux sampling(FFS),samples rare events by using interfaces to partition the whole transition process into sequence of steps along an order parameter connecting the initial and final states.FFS usually suffers from two main difficulties:low computational efficiency due to bad interface locations and even being not applicable when trapping into unknown intermediate metastable states.In the present work,we propose an approach to overcome these difficulties,by self-adaptively locating the interfaces on the fly in an optimized manner.Contrary to the conventional FFS which set the interfaces with equal distance of the order parameter,our approach determines the interfaces with equal transition probability which is shown to satisfy the optimization condition.This is done by firstly running long local trajectories starting from the current interface i to get the conditional probability distribution Pc(>i|i),and then determining i+1by equaling Pc(i+1|i)to a give value p0.With these optimized interfaces,FFS can be run in a much more efficient way.In addition,our approach can conveniently find the intermediate metastable states by monitoring some special long trajectories that neither end at the initial state nor reach the next interface,the number of which will increase sharply from zero if such metastable states are encountered.We apply our approach to a two-state model system and a two-dimensional lattice gas Ising model.Our approach is shown to be much more efficient than the conventional FFS method without losing accuracy,and it can also well reproduce the two-step nucleation scenario of the Ising model with easy identification of the intermediate metastable state.     

Continuous configuration time-dependent self-consistent field method for polyatomic quantum dynamical problems

A new continuous configuration time-dependent self-consistent field method has been developed to study polyatomic dynamical problems by using the discrete variable representation for the reaction system, and applied to a reaction system coupled to a bath. The method is very efficient because the equations involved are as simple as those in the traditional single configuration approach, and can account for the correlations between the reaction system and bath modes rather well.     

An open-ended self-consistent field method. A simulation of a molecular orbital technique for small memory computers

The steps in a nonconventional algorithm for self-consistent field calculations are outlined, and calculations on cumulenes are given to demonstrate the convergence properties of the method. The approach is essentially open ended and is likely to be cost effective on computer systems with minimal core.     

The trust-region self-consistent field method in Kohn-Sham density-functional theory

The trust-region self-consistent field (TRSCF) method is extended to the optimization of the Kohn-Sham energy. In the TRSCF method, both the Roothaan-Hall step and the density-subspace minimization step are replaced by trust-region optimizations of local approximations to the Kohn-Sham energy, leading to a controlled, monotonic convergence towards the optimized energy. Previously the TRSCF method has been developed for optimization of the Hartree-Fock energy, which is a simple quadratic function in the density matrix. However, since the Kohn-Sham energy is a nonquadratic function of the density matrix, the local energy functions must be generalized for use with the Kohn-Sham model. Such a generalization, which contains the Hartree-Fock model as a special case, is presented here. For comparison, a rederivation of the popular direct inversion in the iterative subspace (DIIS) algorithm is performed, demonstrating that the DIIS method may be viewed as a quasi-Newton method, explaining its fast local convergence. In the global region the convergence behavior of DIIS is less predictable. The related energy DIIS technique is also discussed and shown to be inappropriate for the optimization of the Kohn-Sham energy.