请教下使用vasp计算了个体系，怎么能查看各个原子的电荷转移情况呢，如何看一下某个原子在这个化合物中是几价的。
看了网上有人用BADER CHARGE ANALYSIS 来做布局分析，不用这个能看吗？大家有知道的吗？麻烦指点一下

化合物里面原子的价态并不是一个well-defined的量。价态的分析一般都是要借助于某种电荷布局分析的。你提到的Bader charge analysis是其中的一种。像castep里面有Mulliken charge population, PWSCF里面有Lowdin population analysis。各种布局分析给出的原子周围的电荷量的值会存在一定的偏差，这个是可可能的，也是可理解的。

调整RWIGS值，使总电荷收敛，比较各原子上电荷变化

前面的帖子，可能你自己的问题就提到了。采用Bader charge analysis是一种方法，这个Bader charge analysis，你可以在http://theory.cm.utexas.edu/vtsttools/bader/
上面找找相关的文献读读，看它算例子的。了解这种方法对价态分析或电荷转移的准确性。

    bader chargefile

    bader [ -c bader | voronoi ]
          [ -n bader | voronoi ]
          [ -b neargrid | ongrid ]
          [ -r refine_edge_method ]
          [ -ref reference_charge ]
          [ -vac off | auto | vacuum_density ]
          [ -p all_atom | all_bader ]
          [ -p sel_atom | sel_bader ] [volume list or range ]
          [ -p sum_atom | sum_bader ] [ volume list or range ]
          [ -p atom_index | bader_index ]
          [ -i cube | chgcar ]
          [ -h ] [ -v ]
          chargefile

    bader [ -p all_atom | all_bader ] chargefile
    bader [ -p sel_atom | sel_bader ] [ volume list or range ] chargefile
    bader [ -p sum_atom | sum_bader ] [ volume list or range ] chargefile
    bader [ -p atom_index | bader_index ] chargefile

Mulliken population analysis

Mulliken charges and bond populations are calculated according to the formalism described by Segall et al. (1996a and 1996b).

Introduction

A disadvantage of the use of a plane wave (PW) basis set is that, due to the delocalized nature of the basis states, it provides no information regarding the localization of the electrons in the system. In contrast, a Linear Combination of Atomic Orbitals (LCAO) basis set provides a natural way of specifying quantities such as atomic charge, bond population, charge transfer etc.

Population analysis in CASTEP is performed using a projection of the PW states onto a localized basis using a technique described by Sanchez-Portal et al. (1995). Population analysis of the resulting projected states is then performed using the Mulliken formalism (Mulliken, 1955). This technique is widely used in the analysis of electronic structure calculations performed with LCAO basis sets.

Formalism

The eigenstates |ψ_α(k)>, obtained from the PW calculation when sampling at a given wavevector k, are projected onto Bloch functions formed from a LCAO basis set |f_μ(k)>. In general, such a localized basis set will be neither orthonormal nor complete. Therefore, care must be taken when performing the projection.

The overlap matrix of the localized basis set, S(k), is defined as:

Eq. CASTEP 63

http://www.tcm.phy.cam.ac.uk/castep/documentation/WebHelp/Html/Graphics/anc22.gif

The quality of the projection may be assessed by calculating a spilling parameter:

Eq. CASTEP 64

http://www.tcm.phy.cam.ac.uk/castep/documentation/WebHelp/Html/Graphics/anc23.gif

where N_α is the number of PW states, w_k are the weights associated with the calculated k-points in the Brillouin zone and p(k) is the projection operator of Bloch functions with wavevector k generated by the atomic basis set:

Eq. CASTEP 65

http://www.tcm.phy.cam.ac.uk/castep/documentation/WebHelp/Html/Graphics/anc24.gif

where |f_μ(k)>are the duals of the LCAO basis, such that:

Eq. CASTEP 66

http://www.tcm.phy.cam.ac.uk/castep/documentation/WebHelp/Html/Graphics/anc25.gif

The spilling parameter varies between one, when the LCAO basis is orthogonal to the PW states and zero when the projected wavefunctions perfectly represent the PW states.

The density operator may be defined:

Eq. CASTEP 67

http://www.tcm.phy.cam.ac.uk/castep/documentation/WebHelp/Html/Graphics/anc26.gif

where n_α are the occupancies of the PW states, |Χ_α(k)> are the projected PW states p(k)|ψ_α(k)> and |Χ^α(k)> are the duals of these states. From this operator the density matrix for the atomic states may be calculated as follows:

Eq. CASTEP 68

http://www.tcm.phy.cam.ac.uk/castep/documentation/WebHelp/Html/Graphics/anc27.gif

The density matrix P(k) and the overlap matrix S(k) are sufficient to perform population analysis of the electronic distribution. In Mulliken analysis (Mulliken, 1955) the charge associated with a given atom, A, is determined by:

Eq. CASTEP 69

http://www.tcm.phy.cam.ac.uk/castep/documentation/WebHelp/Html/Graphics/anc28.gif

and the overlap population between two atoms, A and B, is:

Eq. CASTEP 70

http://www.tcm.phy.cam.ac.uk/castep/documentation/WebHelp/Html/Graphics/anc29.gif

The weight of a band on a given orbital may be calculated by simply projecting the band onto the selected orbital. So, the weight of band α on orbital μ is given by:

Eq. CASTEP 71

http://www.tcm.phy.cam.ac.uk/castep/documentation/WebHelp/Html/Graphics/anc30.gif

The contribution of each band α to the density of states is multiplied by the weight W_αμ(k) to get the projected density of states for orbital μ.

The LCAO Basis Set

In this case, the natural choice of basis set is that of pseudo-atomic orbitals, generated from the pseudopotentials used in the electronic structure calculation. These are generated automatically when population analysis is performed. The orbitals are calculated by solving for the lowest energy eigenstates of the pseudopotential in a sphere, using a spherical Bessel basis set.

By default, the basis set used on an atom of a given species is that of the orbitals in the closed valence shell of that species. This is usually a sufficiently good basis set for the purposes of population analysis and partial density of states projection. If the spilling parameter indicates that the basis set does not represent the PW states with sufficient accuracy, the number of orbitals in the atomic basis set may be increased. A spilling parameter in the region of a few percent or less is sufficiently good for population analysis and partial density of states projection. Care should be exercised when increasing the basis set dramatically, as this can lead to artificial transfers of charge.

Implementation details

The elements of the overlap matrix S(k) are computed in reciprocal space, as the imposition of periodic boundary conditions implies that the orbitals need only be evaluated on a discrete reciprocal space grid. The overlaps between orbitals on different atomic sites are calculated on the same grid with the application of a phase factor. The overlaps between the plane wave states and the basis functions:

Eq. CASTEP 72

http://www.tcm.phy.cam.ac.uk/castep/documentation/WebHelp/Html/Graphics/anc31.gif

are also calculated in reciprocal space as this is the natural representation of the plane wave states.

The duals of the orbitals are constructed as follows:

Eq. CASTEP 73

http://www.tcm.phy.cam.ac.uk/castep/documentation/WebHelp/Html/Graphics/anc32.gif

The duals of the projected wavefunctions are generated in a similar manner:

Eq. CASTEP 74

http://www.tcm.phy.cam.ac.uk/castep/documentation/WebHelp/Html/Graphics/anc33.gif

where R(k) is the overlap matrix between projected states:

Eq. CASTEP 75

http://www.tcm.phy.cam.ac.uk/castep/documentation/WebHelp/Html/Graphics/anc34.gif

Two auxiliary matrices can be defined for efficiency, namely:

Eq. CASTEP 76

http://www.tcm.phy.cam.ac.uk/castep/documentation/WebHelp/Html/Graphics/anc35.gif

and

Eq. CASTEP 77

http://www.tcm.phy.cam.ac.uk/castep/documentation/WebHelp/Html/Graphics/anc36.gif

These matrices are used to calculate the spilling parameter:

Eq. CASTEP 78

http://www.tcm.phy.cam.ac.uk/castep/documentation/WebHelp/Html/Graphics/anc37.gif

Similarly, the density matrix may be straightforwardly calculated as:

Eq. CASTEP 79

http://www.tcm.phy.cam.ac.uk/castep/documentation/WebHelp/Html/Graphics/anc38.gif

In the case of spin dependent systems, the populations of the two spin components are calculated separately and the sum and difference of the atomic and overlap populations are calculated to find the net charge and spin, respectively.

Interpreting the results

It is widely accepted that the absolute magnitude of the atomic charges yielded by population analysis have little physical meaning, since they display a high degree of sensitivity to the atomic basis set with which they were calculated (Davidson and Chakravorty, 1992). However, consideration of their relative values can yield useful information (Segall et al., 1996a; Segall et al., 1996b; Winkler et al., 2001), provided a consistent basis set is used for their calculation.

The spilling parameter should be in the region of a few percent or less in order to ensure that the results are reliable. If this is not the case, the number of orbitals in the basis set should be increased with care. If this does not significantly improve the spilling parameter, it may be that atomic orbitals do not provide a good representation of some of the states in the system.

In addition to providing an objective criterion for bonding between atoms, the overlap population may be used to assess the covalent or ionic nature of a bond. A high value of the bond population indicates a covalent bond, while a low value indicates an ionic interaction. A further measure of ionic character may be obtained from the effective ionic valence, which is defined as the difference between the formal ionic charge and the Mulliken charge on the anion species. A value of zero indicates a perfectly ionic bond, while values greater than zero indicate increasing levels of covalency. See Segall et al. (1996b) for more details.

Care should be taken when interpreting the bond order values for small unit cells. The results will be incorrect whenever an atom is bonded to a number of periodic images of itself. For example, bond orders for the primitive cell of silicon are reported as 3.0, while the same calculation for the conventional cell gives 0.75. The factor of four appears because CASTEP sums up the bond orders for the four bonds that link the Si atom at the origin with the periodic images of itself, in the primitive cell. A manual analysis of the multiplicities is required in such cases, specifically: determine the number of bonds to periodic images of the same atom and divide the bond order by that number.

Note. The physical meaning of Mulliken charges or bond populations for metallic systems is unclear. This calculation is allowed, but the scientific interpretation of the results will be left to the user.