新手指南：掌握高斯计算的基石

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《高斯使用指南》是由郭勇编著，专为初学者设计的教程，旨在帮助读者掌握高斯这一强大的量子化学计算软件。作者在新疆大学化学化工学院攻读硕士学位期间，通过对高斯软件的学习和实际操作，积累了丰富的经验，并在此基础上编写了这份指南。该书主要覆盖了以下几个关键知识点： 1. **入门基础**：书中详细介绍了高斯软件的基础操作，包括安装、界面介绍以及基本的分子结构输入设置。这将使读者能够快速上手并理解软件的工作原理。 2. **计算原理与应用**：虽然作者强调自己学习时间较短，但书中还是分享了一定的理论背景，如优化、频率分析、能量计算、光谱解析以及组态相关的计算方法。这部分内容对于理解和使用高斯进行精确的分子力学和量子力学计算至关重要。 3. **特定领域的应用**：针对金属配合物、多核配合物、块体材料（如周期性体系）和纳米材料的分子建模，以及QM/MM（量子力学/分子力学）和ONIOM（多层多体方法）计算，书中提供了一些实际建模和计算策略。对于CASSCF（完全配置状态选择性单电子重排法）这样的高级计算技术，虽然未深入探讨，但读者可从中获取基础线索。 4. **比较与拓展**：虽然本书重点在于高斯，但也提到了其他量化软件如ADF和Sybyl的使用，这有助于读者了解不同软件之间的差异和互补性。 5. **不足与补充**：由于作者的学习历程有限，书中存在一些内容的空白，如分子模拟和相关软件介绍，这部分鼓励熟悉这些内容的朋友进行补充。作者希望这些补充内容可以作为附录添加，以不断完善和丰富该指南。 6. **资源来源与合作**：作者感谢贾殿赠教授、刘浪讲师等人在学习过程中的指导，以及大话西游论坛、厦门大学量化论坛、北京大学量化论坛等平台提供的帮助，以及高斯公司和相关技术支持部门的技术支持。《高斯使用指南》是一本实用且互动性强的教材，适合那些希望系统学习和实践高斯软件的化学和物理研究人员，通过作者的亲身体验和网络社区的交流，读者不仅能掌握高斯的使用，还能了解其在实际科研中的应用与挑战。

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5. The values produced may be random and not bounded within any upper or

lower limits.

Which type of non-linear behavior is seen depends upon several

things; the equation being used, the constants in the equation and the

initial value of the variables.

It stands to reason that the total energy may follow any of

these patterns during SCF iterations. We have encountered oscillating

and random behavior in the convergence of open shell transition metal

compounds but have never tried to determine if the random values were

bounded or not.

HOW TO CONTROL NONLINEAR BEHAVIOR

Changing the constants in a non-linear equation would be roughly

equivalent to switching the basis set used for an SCF calculation. Since

a particular basis set is often chosen for a desired accuracy and speed,

this is not generally the most practical solution to a convergence problem.

Plots of behavior vs constant values are the bifurcation diagrams which

are found in many explanations of chaos theory.

Another way of changing the constants in an SCF calculation is

to change the geometry a bit. Often pulling a bond length a bit shorter

than expected is effective (say making the length 90% of the expected

value). lengthening bond lengths a bit and avoiding eclipsed or gauche

conformations are second and third best. Once you have a converged

wave function move the geometry back where you want it and use the

converged function as the initial guess.

Changing the initial value of variables is equivalent to using

a different initial guess in an SCF calculation. The best initial guess

is usually a converged SCF calculation for a different state of the

same molecule or a slightly different geometry of the same molecule.

This can be a very effective way to circumvent convergence problems.

In the worst case it may be necessary to construct an initial guess by hand

in order to ensure that the nodal properties of all of the orbitals are

correct for the desired electronic state of the molecule. The construction

of the virtual orbitals as well as the occupied orbitals can have a

significant effect on convergence. Chaos theorists will try many

starting points and color code a plot by which solution is obtained

for each starting point, this is called fractal geometry (i.e. the

famous Mandelbrot diagram).

There are quite a number of ways to effectively change the

equation in an SCF calculation. These include switching computation

methods, using level shifting and using forced convergence methods.

Switching between Hartree-Fock (HF), semiempirical, generalized

valence bond (GVB), multi-configuration self consistent field (MCSCF),

complete active space self consistent field (CASSCF) and

Moller-Plesset calculations (MPn) will change the convergence properties.

Configuration interaction (CI) and coupled cluster (CC) calculations

usually start with an SCF calculation, thus will not circumvent problems

with an SCF. In general higher levels of theory tend to be harder to

converge. Ease of convergence as well as calculation speed are why lower

level calculations are usually used to generate the initial guess for

higher level calculations.

Oscillating convergence in an SCF calculation is usually an

oscillation between wave functions that are close to different states

or a mixing of states. Thus oscillating convergence can often be helped

by level shifting, which artificially raises the energies of the

virtual orbitals. Level shifting may or may not help in cases of

random convergence.

Most programs will stop trying to converge a problem after a

certain number of iterations. In a few rare cases the wave function will

converge if given more than the default number of iterations.

Most SCF programs do not actually compute orbitals from the

previous iteration orbitals in the way that is described in introductory

descriptions of the SCF method. Most programs use a convergence

excelleration method which is designed to reduce the number of iterations

necessary to converge to a solution. The method of choice is usually

Pulay's DIIS method (Direct Inversion of the Iterative Subspace).

Some programs also give the user the capability to modify the DIIS method,

such as putting in a dampening factor. These modifications can be

useful for fixing convergence problems but they usually require a

significant amount of experience to know how best to modify the procedure.

Turning off the DIIS extrapolation can help a calculation converge, but

usually requires more iterations.

Some programs contain alternative convergence methods that are

designed to force even the most difficult problems to converge. These

methods are often called direct covergence or quadratic convergence

methods. While these methods almost always work, they often require

a very large number of iterations and thus a very large amount of CPU time.

WHAT TO TRY FIRST

If you have an SCF calculation that failed to converge, which of

these tricks should you try first? Here are my suggestions with number

one being the first thing I try and etc.

1. Try a different initial guess (using the "guess" keyword in Gaussian).

2. Try level shifting ( "SCF=Vshift" in Gaussian).

3. Try changing the geometry. First slightly shortening a bond length

then slightly lengthening a bond length then shifting the conformation

a bit.

4. Consider trying a different basis set.

5. Consider doing the calculation at a different level of theory. This

isn't always practical, but beyond this point the increased number of

iterations may make the computation time as much as using a higher level

of theory anyway.

6. Turn off the DIIS extrapolation ( "SCF=NoDIIS" in Gaussian ). You

should probably give the calculation more iterations along with this.

7. Give the calculation more SCF iterations ( "SCF(MaxCyc=N)" where N is

the number of iterations in Gaussian ). This seldom helps but the next

option often uses so many iterations that its worth a try.

8. Use a forced convergence method. (In Gaussian "SCF=QC" is usually

the best but on rare occasions "SCF=DM" will be faster). Don't forget

to give the calculation an extra thousand iterations or so. The wave

function obtained by these methods should be tested to make sure

it is a minimum and not just a stable point ( see the "stable" keyword

in Gaussian ).

9. See if the software documentation suggests any other ways to change

the DIIS method. You may well have to run hundreds of calculations to

get enough experience with this to know what works when and how much

to change it by.

FURTHER INFORMATION

The manuals accompanying many software packages contain discussions of

how to handle convergence difficulties.

There is a very small discussion of handling convergence problems in

T. Clark "A Handbook of Computational Chemistry" Wiley-Interscience (1985)

A good introduction to chaos theory is

J. Gleick "Chaos: Making a New Science" Viking (1987)

A more mathematical treatment of chaos theory is

S. H. Strogatz "Nonlinear Dynamics and Chaos With Applications to Physics,

Biology, Chemistry and Engineering" Addison Wesley (1994)

3.6 请问薛定谔方程的数值解法的原理哪里可以找到

Re: 请问薛定谔方程的数值解法的原理哪里可以找到

发信人: valenhou (AAA), 信区: Gaussian

标题: Re: 请问薛定谔方程的数值解法的原理哪里可以找到

发信站: BBS 大话西游站 (Fri Aug 16 10:07:19 2002)

http://www.giss.nasa.gov/molscat/

MOLSCAT is a code for quantum mechanical (coupled channel) solution of the n

onreactive molecular scattering problem. Code is implemented for various typ

es of collision partners. In addition to the essentially exact close couplin

g method several approximate methods, including the Coupled States and Infin

ite Order Sudden approximations, are provided. The code is in near standard

FORTRAN 77 and has been ported to a large number of platforms. The source co

de supplied was run at this site on an IBM RS/6000 and also on IBM and compa

tible mainframes. It should work on most other machines; for the Cray, howev

er, modifications to run in single precision should be made.

MOLSCAT is an evolving computer program designed for use in a research envir

onment. Although the authors made every attempt to ensure that it works corr

ectly, it is the responsibility of the user to determine whether the code is

suitable for a given application and to determine accuracy of any results.

No warranties of any kind are made.

上面有一个程序可以下载。

3.7 Gaussian FAQ 系列

发信人: Elizerbeth (小小鸟~~~幸福的蔡鸟), 信区: Gaussian

标题: Gaussian FAQ(7)

发信站: BBS 大话西游站 (Mon Aug 12 08:14:28 2002)

In the BHandH methods, is Beckes non-local correction to exchange included

in the functional?

ANSWER

It depends. The functionals actually employed by these keywords to Gaussian

92/DFT are:

BHandH: 0.5*Ex(LSDA) + 0.5*Ex(HF) + Ec(LYP)

BHandHLYP: 0.5*Ex(LSDA) + 0.5*Ex(HF) + 0.5*Delta-Ex(B88) + Ec(LYP)

Unfortunately, neither of these is actually the formulation proposed by Beck

e in his January 1993 paper (reference given below). Note that we recommend

Becke3LYP over this earlier hybrid method as it seems to give uniformly bett

er results.

A careful reading of Beckes paper reveals the need for a factor of 0.5 on a

non-gradient-corrected correlation functional (it uses a 1992 functional of

Perdew and Wang not available in Gaussian 92/DFT). The paper also proposes a

second formulation involving slightly different coefficients (p. 1375), sel

ected by fitting to the G1 molecule set atomization energies.

In general, a functional specified with these IOp options is given by this e

xpression:

P2*Ex(HF) + P1*(P4*Ex(local) + P3*Ex(non-local)) + P6*Ec(local) + P5*Ec(non-

local)

For example, this route section produces a "half-and-half" type functional r

esembling Becke's:

# LSDA IOp(5/45=10000500) P1 and P2

# IOp(5/46=00000500) P3 and P4

# IOp(5/47=00000500) P5 and P6

Within the IOp keywords, parameters are given as two concatenated four-digit

numbers, interpreted as numerators over 1000 (i.e., 500 yields 0.5); for ex

ample, the first line sets P1 to 1.0 and P2 to 0.5.

The reference for Beckes "half-and-half" methods is:

A. D. Becke, "A new mixing of Hartree-Fock and local density-functional theo

ries," J. Chem. Phys. 98, 1372 (1993).

Gaussian FAQ(6)

发信人: Elizerbeth (小小鸟~~~幸福的蔡鸟), 信区: Gaussian

标题: Gaussian FAQ(6)

发信站: BBS 大话西游站 (Mon Aug 12 08:13:33 2002)

What is the reference for the Becke3LYP method in Gaussian 92/DFT?

ANSWER

Becke3LYP implements a slight variation of Becke's three-parameter hybrid fu

nctional. The reference for Becke's functional is:

A. D. Becke, J. Chem. Phys. 98 (1993) 5648.

Papers using Gaussian 92/DFT's Becke3 methods should cite at least this pape

r in addition to the program itself.

Form of the Functional

Becke's three-parameter hybrid functional has the following form:

Ex(LSDA) + Ec(LSDA) + a0*(Ex(HF) - Ex(LSDA)) + ax*Delta-Ex(B88) + ac*Delta-E

c(P91)

The functional used in Gaussian 92/DFT is slightly different and has this fo

rm:

(1-a0)*Ex(LSDA) + a0*Ex(HF) + ax*Delta-Ex(B88) + ac*Ec(LYP) + (1-ac)*Ec(VWN)

where the energy terms are the Slater exchange, the Hartree-Fock exchange, B

eckes 1988 exchange functional correction, the gradient-corrected correlatio

n functional of Lee, Yang and Parr, and the local correlation functional of

Vosko, Wilk and Nusair, respectively. Note that the correlation functional i

s constructed from LYP, which includes both local (equivalent to VWN) and no

n-local terms, and VWN. The factor of (1-aC) on the latter puts a coefficien

t of 1.0 on the local part, as called for by Becke's formulation.

The values of the coefficients determined by Becke are:

a0 = 0.20

ax = 0.72

ac = 0.81

When presenting Becke3LYP results, you may also wish to cite the papers desc

ribing the component functionals. Here are the relevant references:

A. D. Becke, Phys. Rev. A 38 (1988) 3098.

C. Lee, W. Yang, and R. G. Parr, Phys. Rev. B 37 (1988) 785.

S. H. Vosko, L. Wilk, and M. Nusair, Can. J. Phys. 58 (1980) 1200.

The Gaussian 92/DFT implementation of this method is briefly described in P.

J. Stevens, F. J. Devlin, C. F. Chablowski and M. J. Frisch, J. Chem. Phys.

, submitted, which presents applications of Becke3LYP to vibrational spectra

Gaussian FAQ(5)

发信人: Elizerbeth (小小鸟~~~幸福的蔡鸟), 信区: Gaussian

标题: Gaussian FAQ(5)

发信站: BBS 大话西游站 (Mon Aug 12 08:12:13 2002)

In order to request a tighter convergence criteria, Conv=7 for 10-7 converg

ence doesn't work in our version of Gaussian , but IOP(5/6=7) will produce t

he desired result. Why is this?

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