VaList- Bond Valence Calculation and Listing by Andrew S. Wills University College London, Department of Chemistry, 20 Gordon Street, London, WC1H 0AJ VaList is available from : www.ccp14.ac.uk www.ucl.ac.uk/chemistry/staff/academic_pages/andrew_wills

VaList and all parts therein are under the copyright of UCL and is available from the above addresses or from the author at [email protected]. The licence for academic institutions is free. VaList-3 and 4 include automatic updates and it is recommended that it be allowed to check for these through your firewall.

Please reference the use of VaList as: A.S. Wills, VaList, Program available from www.ccp14.ac.uk VaList is a bond valence calculation and analysis program. Using the technique of bond valence analysis the user can quickly analyse coordination geometries and oxidation states. Input files containing bond lengths are accepted from a number of standard crystallographic formats and refinement packages: CIF, GSAS (*.LST), ICSD (*.CGI) Fullprof (*.DIS), TOPAS (*.INP). VaList uses a compiled list of over 1 300 bond valence parameters. I hope that you find this program and the bond valence technique useful. Please email me with any problems (attach appropriate files) and suggestions. -ASW (2010)

Technical Details • •

VaList will run on any Windows pc, though I haven’t checked it under VISTA! Up to 300 bonds can be read in. Please ensure that all atom names are unique, e.g. use ‘O1’ rather than ‘O’

•

GSAS (*.LST) files must contain only one set of bond length output from the program DISANG. This section can be copied and pasted from the EXPGUI window

•

ICSD (*.CGI) files are the bond length files created from ICSD for WWW.

•

Fullprof (.DIS) files are those created from the programs BONDS for PC, or Distances and Angles (SGI version used at the ILL).

•

CIFs may contain user defined atom type aliases.

The example CIF for CaCrF5 and Pb3.58 Sb4.42 Se10 (the alias M = Pb and Sb is used) are included. VaList is written in Visual Basic 6. Only one version may be installed at a time. Before reinstallation, the old version should be removed with the Add/Remove programs utility.

Program Overview 1. Main Window (Initial state)

Upon starting VaList the user is presented with the main working screen. Click on to start loading a file. After opening the bond-distance file Alias definition, Delete unknown Bonds, and Inconsistent valence states windows may open automatically depending on the details of the structure file.

Open the file containing the bond lengths..

2. Alias Definitions

If the bond-distance file contains atom labels for which parameters are not found in VALPAR.DAT, VaList will prompt the user to identify the atoms. This allows for the use of dummy element symbols. If the unidentified atom is a dummy element or an alias (e.g. M as representing either Na or Ca) then these can be defined here. Automatic identification tries to truncate the atom label down to a known element symbol. (Note in this feature the deuterium symbol is automatically changed to hydrogen.) If the alias corresponds to two or more elements, they will all be used in further VaList calculations: if the alias is defined as Pb,Sb both Pb and Sb atoms will be generated to replace the M label. To aid identification, the same atom numbers (identifiers) will be assigned to all substituted atoms. Atoms for which no bond valence parameters are found will NOT subsequently be displayed in the main summary list box, but will appear in the full printed or saved listings.

In the case of real elements for which bond valence parameters are not given in Valpar.dat, the user should accept the atom alias list and enter the bond valence parameters as described in Section 9.

Automatically truncates the symbol to a known element symbol



Adds an atom alias definition to the list box.



Accepts atom alias list.



Clears all atom aliases.

3. Delete unidentified bonds

If bonds are present that cannot be found in VALPAR.DAT they are displayed and an option given to delete them. This is recommended for a first analysis of a structure as it will simplify the calculations and prevent unexpected results. In later analyses it is recommended that these bonds be left in so that their contribution to the local coordination can be examined.

Delete or leave in the unidentified bonds

4. Inconsistent valence states

The valence states of all the coordinations are searched. Any states that cannot be consistently defined are automatically identified and removed from subsequent calculations.

5. Main Window (Completed)

The calculated bond valence sums for each central atom are displayed in a scrolling list box (the central atom is the first atom listed in the bond). Those atoms for

which no bond valence parameters are found will NOT be displayed in this summary list box, but will appear in the full printed or saved listings If the central atom can exist in different oxidation states (as determined from the VALPAR.DAT file) then bond valence sums are presented for each set of oxidation states. (These are defined as the 1st set of valence parameters listed in the, View Bond Valences/Delete Bonds window; then the 2nd set etc. To help these calculations the default for VaList is to simplify the valence parameters so that only one definition is used for a given valence state. See 11 below.) If the oxidation states of the coordinating atoms are not uniquely defined in VALPAR.DAT for the different models, the bond valence sum and other parameters are represented by (---). The percentage deviation of the bond valence sum from the input oxidation state of the principal atom is displayed with the most consistent, and so likely, oxidation state (based on the bond valence sum) indicated by an asterisk (*). If a number of identical oxidation states are displayed then their order corresponds to the order in which the bond valence parameters appear in VALPAR.DAT and the View Bond Valences/Delete Bonds window (see 12 below). The saved and printed output of VaList are the only places that bond valence data for ALL the atoms are listed. To ensure that calculations are correct, the user is urged to check these outputs against the input bond-distance file.

Open the file containing the bond lengths..



Recalculate bond valence sums after changes to Bond Valence Parameters (see 7) or to Define Oxidation States (see 8).



Prints

a

document

which

contains

detailed

which

contains

detailed

information for all bonds

Saves

a

text

file

information for all bonds.

See Section 8.



See Section 9.

See Section 7.



See Section 10.

6. Define Oxidation States

The number of possible valence states or parameter sets exist for the central atom are shown. Those to be used in subsequent calculations may be chosen by selecting or unselecting them. The calculations will be carried out for each change and the main window updated automatically. To simplify first examinations of the bond valences the simplify box should be checked. Only the first valence parameters for a given valence state will be selected. This is the default option.

If checked, only the first set of parameters for a given valence state are checked



Return to main window

7. View Bond Valences/Delete Bonds

By selecting a particular principal atom (double click on the atom, or click and press ) a window appears which displays the individual bond valences and the parameters that were used to calculate them. This is the most important window for a bond valence analysis as all the individual bond valences are displayed. The coordinated atoms are scrolled vertically and oxidation states horizontally. Bonds for which no bond valence parameters are given in VALPAR.DAT are indicated with a hyphen (-). The individual bond valences are useful for examining any special bonding configurations. The number of coordinating atoms whose bond valences have been calculated is displayed at the bottom of the window.. Bond lengths are displayed to 3 decimal places. The different bond types for the selected central atom are shown in a separate menu and can be deleted as required, e.g. if they correspond to anion-anion bond lengths or the bond valence parameters are unknown.

Delete the selected bond from the calculations



Return to main window.

8. Analyse oxidation states

In the case of sites that contain more than one element or the same element in two oxidation states or in a non-integral oxidation state, a bond valence anaylsis can be used to calculate the proportions of each element or oxidation state. This is of particular use in minerals and other non-stoichiometric crystals. Those central atoms with defined bond valences are displayed in the first list box. When two of these atoms or oxidation states are selected, they appear in the second box with the percentage occupancy of each displayed to the right of the box. The average site valence is also presented (in bold), along with the details of the equation used to calculate them.

Return to main window.

9. Edit bond valence parameters

All the input bond valence parameters retrieved from VALPAR.DAT are displayed in the list box and can be edited. Values for expected oxidation states that do not appear on the list can be added (by extrapolation, interpolation or by fitting to other known structures). This window can also be used in systems with partial oxidation states, such as superconductors. Parameters for oxidation states that are not found in the compound can be deleted from this list as an alternative to defining the oxidation states in Section 11.

Accept

changes

to

selected

bond

valence

parameters.

Add new bond valance parameters.



Delete selected bond valence parameters.



Return to main window with no changes made.



Reset all Bond Valence Parameters to those found in VALPAR.DAT.



Accept changes and return to main window.

Introduction to Bond Valence Analysis -I.D. Brown 1

Brockhouse Institute for Materials Research, McMaster University, Hamilton, Ontario, Canada, L8S 4M1.

1. Theory The valence of a bond, S, is a quantity whose sum around each atom is equal to the oxidation state of the atom, V: Vj =ΣiSij

(1)

It correlates inversely with bond length, which allows it to be calculated if the bond length has been measured. Newly determined crystal structures can therefore be checked by comparing oxidation states (formal ionic charges) with bond valence sums. The agreement is generally good if the structure is correct, but when the agreement is poor the structure or its determination should be carefully examined. Some of the causes of poor agreement and the uses to which bond valences can be put are described below. Reviews of the bond valence model are given by Brown (1992) and O'Keeffe (1989).

2. Restrictions on the model The model is restricted to compounds which can, in a formal sense, be described as ionic, i.e. all atoms can be labelled as anions or cations in such a way that the compound contains no cation-cation or anion-anion bonds. It thus applies to most salts, minerals and ceramic compounds as well as to many of the environments of metal atoms in coordination complexes and metal ions in organic salts. The method cannot normally be used for metallic solids or organic molecules.

3. Applications of bond valences Bond valences have a number of uses. In addition to providing a quantitative measure of bond strength, indicating which bonds are the most important in defining the structure, bond valences can be used for detecting errors in a structure determination, for assigning oxidation states, for determining partial occupancies of atomic sites, for locating hydrogen bonds and for detecting the presence of the lattice induced strains that give rise to displacive phase transitions and the unusual properties shown, for example, by perovskite related crystals.

3.1. Detecting errors in the structure determination By checking the bond valence sums against the oxidation states of each atom it is possible to tell if a proposed structure obeys the normal rules of structural chemistry. Bond valence sums should be calculated and checked around both anions and cations. If the deviation between the bond valence sum and the oxidation state of any atom differs by more than 0.1 valence units (v.u.) the reason for the discrepancy should be investigated. One possible cause of large deviations is that the structure is incorrectly or poorly determined. For the method to be useful, the bond lengths must be accurate to better than 0.05 Å. If the bond valence sums differ significantly from the oxidation state in well determined structures, the discrepancy may caused by: •

use of an incorrect space group (e.g, a non-centrosymmetric space group when the crystal possesses a center of symmetry),

•

use of the correct space group but with the wrong choice of origin,

•

missing bonds (indicated by the two terminal atoms having low bond valence sums, particularly useful for identifying hydrogen bonded atoms when the positions of the hydrogen atoms have not been determined, see 3.5 below),

•

missing atoms (e.g. water of crystallisation) indicated by the valence sums around all the atoms bonded to the missing atom being too low.

3.2. Determining the oxidation state of an atom The bond valence sum will give an indication of the correct oxidation state in cases where this is not known or has been wrongly assigned. VaList initially displays several bond valence sums, each calculated assuming a different oxidation state, providing the bondvalence − bond-length correlation is given in the file VALPAR.DAT. From these results it is usually apparent which is the correct oxidation state, even when, as is sometimes the case, the oxidation state is non-integral. When the correct oxidation state has been chosen, the bond valence sums around both the cations and the anions should be close to the assumed oxidation states, and the formal ionic charges summed over all atoms should be zero (the electroneutrality condition). A special feature in VaList is the calculation of the site occupation of 2 different oxidation states or atoms: (see 3.3 below and VaList Section 8).

3.3. Determining the occupation numbers of occupationally disordered sites When a site is occupied by two different atoms, a comparison of the bond valence sums calculated for each of the disordered atoms can be used to determine the relative occupation numbers of the two atoms (see 9 below). This can be done using the same feature of VaList used for estimating partial oxidation numbers (see 3.2 above). In cases where the atoms have similar scattering factors, bond valence calculations may be the only way to determine the relative amounts of each atom on the site (Skowron and Brown, 1990).

3.4. Analysing the strain in lattice mismatched structures The bonds in some compounds, e.g. perovskites, are strained as a result of the geometric constraints imposed by the 3-dimensional geometry and the space group symmetry. Because of these constraints some bonds are stretched and others compressed, a condition indicated by some cations having bond valence sums that are too large (cation under compression) and others having bond valence sums that are too small (cation under tension). In such cases a careful examination of the structure usually reveals the origin of the strain. Strains will tend to relax, resulting in lower crystallographic symmetry, distorted cation environments, nonstoichiometry, structure modulations or unusual oxidation states. A bond valence analysis is helpful in identifying the mode of relaxation.

A useful measure of the degree of strain is the Global Instability Index, GII, which is the root mean square deviation of the bond valence sums from the oxidation state averaged over all the atoms (both cations and anions) in the formula unit (Salinas-Sanchez et al., 1992). GII = 1/2

(2)

If this index exceeds 0.2, the reported structure is likely to be wrong since the real structure will probably have relaxed, often to a lower symmetry space group. The model used for the structure refinement should be carefully examined for a possible loss of symmetry. GII is calculated by VaList only when all the atomic valences are uniquely defined and each atom has one or more bonds for which the bond valence parameters are known. The user MUST verify that all bonds in the formula unit are included in the summations; for this reason, the value of GII is only written to the file or printout.

3.5. Hydrogen bonding The bond valence model works well with the bonds formed by hydrogen. However, there are a number problems in analysing structures containing hydrogen atoms. The hydrogen atom positions are often not reported, since hydrogen has too low a scattering power to be easily detected by x-rays. If H atoms are detected, their positions may be poorly determined and, in any case, the centre of the electron density is usually systematically displaced from the nuclear position (which can be accurately determined by neutron diffraction). Finally, the range of bond lengths observed is so large that the simple two parameter expression used for determining the bond valences from the bond lengths (Equation (3) below) is a poor approximation. All of these problems mean that bonds to hydrogen require special treatment in a bond valence analysis. Firstly, the location of hydrogen bonds can be inferred from the bond valence sums of the anions. If the valences of the bonds to H are not included in the valence sums, a hydrogen-bond donor anion will typically have a bond valence sum that is 0.8 v.u. too low, while an acceptor anion will have a bond valence sum that is 0.2 to 0.4 v.u. too low.

Combining this information with the geometrical arrangement of acceptor anions around a donor usually allows hydrogen bonds to be identified. Once the hydrogen bonds have been located, their bond valences can be assigned in the following manner. If the H atom positions have been accurately assigned, the valences of the long H...X (X = anion) bonds can be determined from their length using Fig. 1 of Brown and Altermatt (1985). If the H positions have not been determined, the valences of the same bonds can be found (for O-H...O hydrogen bonds) from the O...O distance using Fig. 2 of Brown and Altermatt (1985). When valences have been assigned to all the acceptor bonds, the valence of the donor O-H bond is found by assuming a bond valence sum around H of 1.0. If the assignment of bond valences is correct, the bond valence sums around the anions should be close to the anion oxidation state.

4. Source of bond valence parameters Bond valences, S, are calculated from the bond lengths, R, using the function: S = exp((Ro - R)/B)

(3)

where Ro, the length of a bond of unit valence, and B, the slope of the correlation curve, are fitted parameters stored in the file VALPAR.DAT. Brown and Altermatt (1985) showed that B has a value not significantly different from 0.37 Å for most bonds. Because B cannot be precisely determined, most subsequent workers have found it convenient to adopted the same value. The value used for Ro can be determined accurately but it depends quite critically on the value chosen for B. Once B is chosen, it is possible to determine Ro for each cation surrounded by ligands of the same chemical species, by assuming that the valence sum around the cation is equal to the cation oxidation state, V. Combining (1) and (3) gives: V = Σiexp((Ro - Ri)/B) = exp(Ro/B)Σiexp(-Ri/B)

(4)

where the index i is summed over all the bonds in the cation coordination sphere. (4) can be solved for Ro for each coordination sphere whose bond lengths have been determined. For each pair of ions, e.g. Si-O, Brown and Altermatt (1985) averaged the values of Ro obtained for all accurately measured cation coordination spheres to give the values listed under reference (a) in VALPAR.DAT. This list covers the majority of commonly found bonds. Brese and O'Keeffe (1991) showed that there are simple relations between the bond valence parameters for different anions around the same cation, e.g., there is a simple relation between the parameters for Si-O and for Si-F bonds. They used these relations to predict values of Ro for many further bonds, particularly those for anions other than O2-. These values are listed under reference (b) in VALPAR.DAT. Other parameters have been subsequently determined for the same or different pairs of ions and these are all referenced in VALPAR.DAT. Generally only one set of parameters is given for a given bond type, but where significantly different values have been determined by different authors, additional values are included. Thus when reading a new file, VaList may calculate bond valence sums around a given ion for several different bond valence parameters for the same oxidation state. In general, the first-listed parameters are recommended, but the user is free to choose any of the others or to provide different parameters. An atomic valence of 9 indicates parameters considered to be valid for all oxidation states. In this case the % deviation calculated will be in error unless the oxidation state is redefined. VALPAR.DAT is installed by default in C:\Program Files\Valist for Windows and may be edited by the user to add or change bond valence parameters.

5. References N.E.Brese and M.O'Keeffe, (1991) Acta Cryst. B47, 192-197. I.D.Brown, (1995) Acta Cryst. B48, 553-572. I.D.Brown and D.Altermatt, (1985) Acta Cryst. B41, 244-247. M.O'Keeffe, (1989) Structure and Bonding 71, 161-190.

A.Salinas-Sanchez, J.L.Garcia-Monoz, J.Rodrigues-Carvajal, and R.Saez-Puche, (1992) J. Solid State Chem. 100, 201-211. A.Skowron and I.D.Brown, (1990) Acta Cryst. C46, 527-531.