SIESTA trunk-301用户指南：编译与执行详解

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Siesta trunk-301 用户指南是一份详细的文档，旨在帮助用户理解和使用Siesta这款先进的材料模拟软件。该软件由Emilio Artacho、José María Cela、Julian D. Gale等来自不同研究机构的专家共同开发，主要用于研究固态物质的电子结构和性质，特别是在纳米科学和材料科学领域。 1. **介绍** (INTRODUCTION) 本章首先简要介绍了Siesta的基本概念和其在科研中的重要性。它强调了软件在计算第一性原理方法中的应用，特别是密度泛函理论（DFT），以及其在理解复杂材料系统行为方面的潜力。用户可以从中了解到软件的历史、核心理念以及如何通过它来探索材料的电子结构和动力学特性。 2. **编译** (COMPILATION) 该部分详细说明了如何在计算机上编译Siesta程序，包括设置构建目录（The building directory）和配置编译选项。多目标编译（Multiple-target compilation）被提及，这意味着可以根据不同的硬件平台或优化需求定制编译。此外，还解释了如何使用arch.makefile进行配置，确保编译过程顺利进行。 3. **程序执行** (EXECUTION OF THE PROGRAM) 这一部分涵盖了如何启动和运行Siesta计算，包括输入文件的准备（如灵活数据格式FDF）、命令行参数的选择以及可能遇到的问题和解决策略。用户可以找到关于如何设置计算参数、选择合适的交换-correlation函数以及处理大型系统的方法。 4. **灵活数据格式(FDF)** (THE FLEXIBLE DATA FORMAT (FDF)) FDF是Siesta的核心输入文件格式，用于定义计算任务的详细设置。这部分深入解释了FDF文件的结构，如何组织各个参数，以及如何调整以适应不同的计算需求。它包括对基本参数、自旋极化、超精细结构、激发态计算等高级功能的指导。 5. **程序输出** (PROGRAM OUTPUT) Siesta的输出详细解析了计算结果，包括标准输出信息（Standard output），这通常包含重要的能量值、结构信息以及计算进度更新。此外，还有针对特定输出结果的详细说明，如电子密度、态密度图、能带结构以及振动模式分析等，以便用户解读和分析。总结来说，Siesta trunk-301用户指南为用户提供了一个全面的指南，帮助他们有效地使用Siesta进行精确且高效的材料科学计算。无论是初次接触的用户还是经验丰富的研究人员，都能从中找到所需的指导，以推进他们的科学研究工作。

%block Chemical_Species_label

1 201 ON-0.50000

%endblock Chemical_Species_label

%block SyntheticAtoms

1 # Species index

2 2 3 4 # n numbers for valence states with l=0,1,2,3

2.0 3.5 0.0 0.0 # occupations of valence states with l=0,1,2,3

%endblock SyntheticAtoms

Pseudopotentials for synthetic atoms can be created using the mixps and fractional

programs in the Util/VCA directory.

Use: This block is mandatory.

Default: There is no default. You must supply this block.

AtomicMass (data block): It allows the user to introduce the atomic masses of the diﬀerent

species used in the calculation, useful for the dynamics with isotopes, for example. If

a species index is not found within the block, the natural mass for the corresponding

atomic number is assumed. If the block is absent all masses are the natural ones. One

line per species with the species index (integer) and the desired mass (real). The order is

not important. If there is no integer and/or no real numbers within the line, the line is

disregarded.

%block AtomicMass

3 21.5

1 3.2

%endblock AtomicMass

Default: (Block absent or empty) Natural masses assumed. For ghost atoms (i.e. ﬂoating

orbitals), a default of 1.d30 a.u. is assigned.

6.2 Pseudopotentials

Siesta uses pseudopotentials to represent the electron-ion interaction (as do most plane-wave

codes and in contrast to so-called “all-electron” programs). In particular, the pseudopotentials

are of the “norm-conserving” kind, and can be generated by the Atom program, included

(with permission) in Pseudo/atom (see Pseudo/atom/README for more complete authorship and

tested before using them. We refer you to the standard literature on pseudopotentials and to

the ATOM manual siesta/Pseudo/atom/atom.tex for more information. A number of other

codes (such as Opium) can generate pseudopotentials that Siesta can use directly (typically in

the .psf format).

The pseudopotentials will be read by Siesta from diﬀerent ﬁles, one for each deﬁned species

(species deﬁned either in block ChemicalSpeciesLabel). The name of the ﬁles should be:

Chemical label.vps (unformatted) or Chemical label.psf (ASCII)

where Chemical label corresponds to the label deﬁned in the ChemicalSpeciesLabel block.

Siesta can also handle pseudopotential ﬁles in the XML format designed by Junquera, Garcia,

and Verstraete (to be published), which enables interoperability with the ABINIT code. The

directory Util/pseudo-xml contains a program to translate the pseudo XML ﬁles to the .psf

form.

6.3 Basis set and KB projectors

6.3.1 Overview of atomic-orbital bases implemented in Siesta

The main advantage of atomic orbitals is their eﬃciency (fewer orbitals needed per electron for

similar precision) and their main disadvantage is the lack of systematics for optimal convergence,

an issue that quantum chemists have been working on for many years. They have also clearly

shown that there is no limitation on precision intrinsic to LCAO. This section provides some

information about how basis sets can be generated for Siesta.

It is important to stress at this point that neither the Siesta method nor the program are

bound to the use of any particular kind of atomic orbitals. The user can feed into Siesta

the atomic basis set he/she choses by means of radial tables (see User.Basis below), the only

limitations being: (i) the functions have to be atomic-like (radial functions mutiplied by spherical

harmonics), and (ii) they have to be of ﬁnite support, i.e., each orbital becomes strictly zero

beyond some cutoﬀ radius chosen by the user.

Most users, however, do not have their own basis sets. For these users we have devised some

schemes to generate basis sets within the program with a minimum input from the user. If

nothing is speciﬁed in the input ﬁle, Siesta generates a default basis set of a reasonable quality

that might constitute a good starting point. Of course, depending on the accuracy required in

the particular problem, the user has the degree of freedom to tune several parameters that can

be important for quality and eﬃciency. A description of these basis sets and some performance

tests can be found in the references quoted below.

“Numerical atomic orbitals for linear-scaling calculations”, J. Junquera, O. Paz, D. S´anchez-

Portal, and E. Artacho, Phys. Rev. B 64, 235111, (2001)

An important point here is that the basis set selection is a variational problem and, therefore,

minimizing the energy with respect to any parameters deﬁning the basis is an “ab initio” way

to deﬁne them.

We have also devised a quite simple and systematic way of generating basis sets based on

specifying only one main parameter (the energy shift) besides the basis size. It does not oﬀer

the best NAO results one can get for a given basis size but it has the important advantages

mentioned above. More about it in:

“Linear-scaling ab-initio calculations for large and complex systems”, E. Artacho, D. S´anchez-

Portal, P. Ordej´on, A. Garc´ıa and J. M. Soler, Phys. Stat. Sol. (b) 215, 809 (1999).

In addition to Siesta we provide the program Gen-basis, which reads Siesta’s input and

generates basis ﬁles for later use. Gen-basis can be found in Util/Gen-basis. It should be

run from the Tutorials/Bases directory, using the gen-basis.sh script. It is limited to a

single species.

Of course, as it happens for the pseudopotential, it is the responsibility of the user to check that

the physical results obtained are converged with respect to the basis set used before starting

any production run.

In the following we give some clues on the basics of the basis sets that Siesta generates. The

starting point is always the solution of Kohn-Sham’s Hamiltonian for the isolated pseudo-atoms,

solved in a radial grid, with the same approximations as for the solid or molecule (the same

exchange-correlation functional and pseudopotential), plus some way of conﬁnement (see below).

We describe in the following three main features of a basis set of atomic orbitals: size, range,

and radial shape.

Size: number of orbitals per atom

Following the nomenclature of Quantum Chemistry, we establish a hierarchy of basis sets, from

single-ζ to multiple-ζ with polarization and diﬀuse orbitals, covering from quick calculations of

low quality to high precision, as high as the ﬁnest obtained in Quantum Chemistry. A single-ζ

(also called minimal) basis set (SZ in the following) has one single radial function per angular

momentum channel, and only for those angular momenta with substantial electronic population

in the valence of the free atom. It oﬀers quick calculations and some insight on qualitative

trends in the chemical bonding and other properties. It remains too rigid, however, for more

quantitative calculations requiring both radial and angular ﬂexibilization.

Starting by the radial ﬂexibilization of SZ, a better basis is obtained by adding a second function

per channel: double-ζ (DZ). In Quantum Chemistry, the split valence scheme is widely used:

starting from the expansion in Gaussians of one atomic orbital, the most contracted Gaussians

are used to deﬁne the ﬁrst orbital of the double-ζ and the most extended ones for the second. For

strictly localized functions there was a ﬁrst proposal of using the excited states of the conﬁned

atoms, but it would work only for tight conﬁnement (see PAO.BasisType nodes below). This

construction was proposed and tested in D. S´anchez-Portal et al., J. Phys.: Condens. Matter 8,

3859-3880 (1996).

We found that the basis set convergence is slow, requiring high levels of multiple-ζ to achieve

what other schemes do at the double-ζ level. This scheme is related with the basis sets used in

the OpenMX project [see T. Ozaki, Phys. Rev. B 67, 155108 (2003); T. Ozaki and H. Kino,

Phys. Rev. B 69, 195113 (2004)].

We then proposed an extension of the split valence idea of Quantum Chemistry to strictly

localized NAO which has become the standard and has been used quite successfully in many

systems (see PAO.BasisType split below). It is based on the idea of suplementing the ﬁrst

ζ with, instead of a gaussian, a numerical orbital that reproduces the tail of the original PAO

outside a matching radius r

, and continues smoothly towards the origin as r

(a − br

), with

a and b ensuring continuity and diﬀerentiability at r

. Within exactly the same Hilbert space,

the second orbital can be chosen to be the diﬀerence between the smooth one and the original

PAO, which gives a basis orbital strictly conﬁned within the matching radius r

(smaller than

the original PAO!) continuously diﬀerentiable throughout.

Extra parameters have thus appeared: one r

per orbital to be doubled. The user can again

introduce them by hand (see PAO.Basis below). Alternatively, all the r

’s can be deﬁned

at once by specifying the value of the tail of the original PAO beyond r

, the so-called split

norm. Variational optimization of this split norm performed on diﬀerent systems shows a very

general and stable performance for values around 15% (except for the ∼ 50% for hydrogen). It

generalizes to multiple-ζ trivially by adding an additional matching radius per new zeta.

Note: What is actually used is the norm of the tail plus the norm of the parabola-like inner

function.

Angular ﬂexibility is obtained by adding shells of higher angular momentum. Ways to generate

these so-called polarization orbitals have been described in the literature for Gaussians. For

NAOs there are two ways for Siesta and Gen-basis to generate them: (i) Use atomic PAO’s

of higher angular momentum with suitable conﬁnement, and (ii) solve the pseudoatom in the

presence of an electric ﬁeld and obtain the l + 1 orbitals from the perturbation of the l orbitals

by the ﬁeld.

So-called diﬀuse orbitals, that might be important in the description of open systems such as

surfaces, can be simply added by specifying extra “n” shells. [See S. Garcia-Gil, A. Garcia, N.

Lorente, P. Ordejon, Phys. Rev. B 79, 075441 (2009)]

Finally, the method allows the inclusion of oﬀ-site (ghost) orbitals (not centered around any

speciﬁc atom), useful for example in the calculation of the counterpoise correction for basis-set

superposition errors. Bessel functions for any radius and any excitation level can also be added

anywhere to the basis set.

Range: cutoﬀ radii of orbitals.

Strictly localized orbitals (zero beyond a cutoﬀ radius) are used in order to obtain sparse Hamil-

tonian and overlap matrices for linear scaling. One cutoﬀ radius per angular momentum channel

has to be given for each species.

A balanced and systematic starting point for deﬁning all the diﬀerent radii is achieved by giving

one single parameter, the energy shift, i.e., the energy increase experienced by the orbital when

conﬁned. Allowing for system and physical-quantity variablity, as a rule of thumb ∆E

PAO

≈ 100

meV gives typical precisions within the accuracy of current GGA functionals. The user can,

nevertheless, change the cutoﬀ radii at will.

Shape

Within the pseudopotential framework it is important to keep the consistency between the

pseudopotential and the form of the pseudoatomic orbitals in the core region. The shape of the

orbitals at larger radii depends on the cutoﬀ radius (see above) and on the way the localization

is enforced.

The ﬁrst proposal (and quite a standard among Siesta users) uses an inﬁnite square-well poten-

tial. It was originally proposed and has been widely and successfully used by Otto Sankey and

collaborators, for minimal bases within the ab initio tight-binding scheme, using the Fireball

program, but also for more ﬂexible bases using the methodology of Siesta. This scheme has

the disadavantage, however, of generating orbitals with a discontinuous derivative at r

. This

discontinuity is more pronounced for smaller r

’s and tends to disappear for long enough values

of this cutoﬀ. It does remain, however, appreciable for sensible values of r

for those orbitals that

would be very wide in the free atom. It is surprising how small an eﬀect such a kink produces

in the total energy of condensed systems. It is, on the other hand, a problem for forces and

stresses, especially if they are calculated using a (coarse) ﬁnite three-dimensional grid.

Another problem of this scheme is related to its deﬁning the basis starting from the free atoms.

Free atoms can present extremely extended orbitals, their extension being, besides problematic,

of no practical use for the calculation in condensed systems: the electrons far away from the

atom can be described by the basis functions of other atoms.

A traditional scheme to deal with this is one based on the radial scaling of the orbitals by suitable

scale factors. In addition to very basic bonding arguments, it is soundly based on restoring the

virial’s theorem for ﬁnite bases, in the case of Coulombic potentials (all-electron calculations).

The use of pseudopotentials limits its applicability, allowing only for extremely small deviations

from unity (∼ 1%) in the scale factors obtained variationally (with the exception of hydrogen

that can contract up to 25%). This possiblity is available to the user.

Another way of dealing with the above problem and that of the kink at the same time is adding

a soft conﬁnement potential to the atomic Hamiltonian used to generate the basis orbitals:

it smoothens the kink and contracts the orbital as suited. Two additional parameters are

introduced for the purpose, which can be deﬁned again variationally. The conﬁning potential is

ﬂat (zero) in the core region, starts oﬀ at some internal radius r

with all derivatives continuous

and diverges at r

ensuring the strict localization there. It is

V (r) = V

−

−r

r−r

− r

(1)

and both r

and V

can be given to Siesta together with r

in the input (see PAO.Basis below).

Finally, the shape of an orbital is also changed by the ionic character of the atom. Orbitals

in cations tend to shrink, and they swell in anions. Introducing a δQ in the basis-generating

free-atom calculations gives orbitals better adapted to ionic situations in the condensed systems.

More information about basis sets can be found in the proposed literature.

There are quite a number of options for the input of the basis-set and KB projector speciﬁca-

tion, and they are all optional! By default, Siesta will use a DZP basis set with appropriate

choices for the determination of the range, etc. Of course, the more you experiment with

the diﬀerent options, the better your basis set can get. To aid in this process we oﬀer an

auxiliary program for optimization which can be used in particular to obtain variationally op-

timal basis sets (within a chosen basis size). SeeUtil/Optimizer for general information, and

Util/Optimizer/Examples/Basis Optim for an example. The directory Tutorials/Bases in

the main Siesta distribution contains some tutorial material for the generation of basis sets

and KB projectors.

Finally, some optimized basis sets for particular elements are available at the Siesta web page.

Again, it is the responsability of the users to test the transferability of the basis set to their

problem under consideration.

6.3.2 Type of basis sets

PAO.BasisType (string):

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