Siesta 3.0-rc2 用户手册：非平衡输运计算

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"TranSIESTA-3.0-rc2手册是SIESTA软件的一个版本，专注于非平衡输运计算。该手册由多个研究人员合作编写，包括来自University of Cambridge、Barcelona Supercomputing Center、Curtin University of Technology等机构的专家。" SIESTA（Simulation of Electronic Structure: A First-Principles Package）是一款基于密度泛函理论（Density Functional Theory，DFT）的开源软件，用于模拟固体材料的电子结构和性质。TranSIESTA是SIESTA的一个扩展模块，专门用于研究电子输运现象，例如在纳米器件中的电流流动，这是理解和设计新型电子设备的关键。手册的主要内容可能包括以下方面： 1. **介绍**： - 提供了对TranSIESTA-3.0-rc2的基本概述，强调它是用于非平衡输运计算的工具。 - 强调该手册不是初学者教程，而是包含输入、输出和执行特性的详细描述。 2. **输入参数**： - 详细解释了设置计算任务所需的输入文件和参数，这可能涉及原子结构、电荷密度、基组选择、交换相关泛函等。 3. **输出解析**： - 描述了程序运行后生成的输出文件格式和内容，如能量结构、密度矩阵、电子态分布等。 4. **执行流程**： - 说明了如何启动和运行TranSIESTA计算，包括并行化选项和性能优化策略。 5. **电子输运理论**： - 深入讨论非平衡格林函数方法（Non-Equilibrium Green's Function, NEGF）在TranSIESTA中的应用，这是处理电子输运的基础理论。 6. **实例分析**： - 可能包含一些实际计算案例，帮助用户理解如何应用TranSIESTA解决具体问题。 7. **开发团队的计划**： - 开发团队计划改进文档，提供更全面的教程和指导，以弥补现有手册的不足。 8. **版权信息**： - 提到了软件的版权和作者，强调了软件的开放源代码性质和使用条款。对于想要使用TranSIESTA进行计算的科研人员或学生来说，这个手册是一个重要的参考资料，它可以帮助他们理解和掌握如何使用该软件进行复杂的电子输运模拟。然而，由于手册并不是一个入门教程，初学者可能需要额外的学习资源来辅助理解。

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):

The kind of basis to be generated is chosen. All are based on ﬁnite-range pseudo-atomic

orbitals [PAO’s of Sankey and Niklewsky, PRB 40, 3979 (1989)]. The original PAO’s

were described only for minimal bases. Siesta generates extended bases (multiple-ζ,

polarization, and diﬀuse orbitals) applying diﬀerent schemes of choice:

- Generalization of the PAO’s: uses the excited orbitals of the ﬁnite-range pseudo-

atomic problem, both for multiple-ζ and for polarization [see S´anchez-Portal, Artacho,

and Soler, JPCM 8, 3859 (1996)]. Adequate for short-range orbitals.

- Multiple-ζ in the spirit of split valence, decomposing the original PAO in several pieces

of diﬀerent range, either deﬁning more (and smaller) conﬁning radii, or introducing

Gaussians from known bases (Huzinaga’s book).

All the remaining options give the same minimal basis. The diﬀerent options and their

FDF descriptors are the following:

• split: Split-valence scheme for multiple-zeta. The split is based on diﬀerent radii.

• splitgauss: Same as split but using gaussian functions e

−(x/α

)

. The gaussian

widths α

are read instead of the scale factors (see below). There is no cutting

algorithm, so that a large enough r

should be deﬁned for the gaussian to have

decayed suﬃciently.

• nodes: Generalized PAO’s.

• nonodes: The original PAO’s are used, multiple-zeta is generated by changing the

scale-factors, instead of using the excited orbitals.

Note that, for the split and nodes cases the whole basis can be generated by Siesta with

no further information required. Siesta will use default values as deﬁned in the following

(PAO.BasisSize, PAO.EnergyShift, and PAO.SplitNorm, see below).

Default value: split

6.3.3 Size of the basis set

PAO.BasisSize (string): It deﬁnes usual basis sizes. It has eﬀect only if there is no block

PAO.Basis present.

• SZ or MINIMAL: minimal or single-ζ basis.

• DZ: Double zeta basis, in the scheme deﬁned by PAO.BasisType.

• SZP: Single-zeta basis plus polarization orbitals.

• DZP or STANDARD: Like DZ plus polarization orbitals. Polarization orbitals are con-

structed from perturbation theory, and they are deﬁned so they have the minimum

angular momentum l such that there are not occupied orbitals with the same l in the

If an old-style (tail+parabola) calculation is being done, perform a scan of the

tail+parabola norm in the whole range of the 1st-zeta orbital, and store that in a ta-

ble. The construction of the 2nd-zeta orbital involves simply scanning the table to ﬁnd

the appropriate place. Due to the idiosyncracies of the old algorithm, the new one is not

guaranteed to produce exactly the same results, as it might settle on a neighboring grid

point for the matching.

Default value: .false.

PAO.FixSplitTable (boolean):

After the scan of the allowable split-norm values, apply a damping function to the tail to

make sure that the table goes to zero at the radius of the ﬁrst-zeta orbital.

Default value: .false.

PAO.SplitTailNorm (boolean):

Use the norm of the tail instead of the full tail+parabola norm. This is the behavior

described in the JPC paper. (But note that, for numerical reasons, the square root of the

tail norm is used in the algorithm.) This is the preferred mode of operation for automatic

operation, as in non-supervised basis-optimization runs.

Default value: .false.

As a summary of the above options:

• For complete backwards compatibility, do nothing.

• To exercise the new code, set PAO.NewSplitCode.

• To maintain the old split-norm heuristic, but making sure that the program ﬁnds a

solution (even if not optimal, in the sense of producing a second-ζ r

very close to the

ﬁrst-ζ one), set PAO.FixSplitTable (this will automatically set PAO.NewSplitCode).

• If the old heuristic is of no interest (for example, if only a robust way of mapping split-

norms to radii is needed), set PAO.SplitTailNorm (this will set PAO.NewSplitCode

automatically).

6.3.6 Soft-conﬁnement options

PAO.SoftDefault (boolean): If set to true then this option causes soft conﬁnement to be the

default form of potential during orbital generation. The default potential and inner radius

are set by the commands given below.

Default value: .false.

PAO.SoftInnerRadius (real): For default soft conﬁnement, the inner radius is set at a

fraction of the outer conﬁnement radius determined by the energy shift. This option

controls the fraction of the conﬁnement radius to be used.

Default value: 0.9

PAO.SoftPotential (real): For default soft conﬁnement, this option controls the value of the

potential used for all orbitals.

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