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Short Range Interactions

Short range interactions need to be given between some or all of the possible ion pairs. It is usual to have the short range interaction acting on the shells if a shell model ion is used. The short range interaction is designed to be as flexible as possible. Different ion pairs may have different short range interaction types. The short range interactions are given in one or more ranges for each ion pair, up to a maximum of MAXRNG ranges. For each ion pair, the ranges must be contiguous and there must be a range which starts at zero. Interactions which have a different analytic form in different ranges are permitted. In this case, overlapping ranges are not permitted. However it is permitted to split one of the interactions into two ranges so that a range is the sum of two potentials. A number of the potential keywords may only be applied to ellipsoidal shell model ions, the keyword BUCK may be applied to either. The keywords which may apply to ellipsoids only are DBUC, BVCK and DBVC. All other keywords apply to conventional shell model or rigid ion interactions only. Finally, potentials can be labelled to restrict them to apply to intramolecular interactions only. This option has been recently added and may not be available in all versions of the programs. The ranges, if more than one range is given, must be in ascending order. The maximum range is at present overriden by CUTPOT. (See section on cutoffs) A maximum of MAXPOT short range interactions may be given; this total includes also the core-shell interactions given by the HARM directive.

The general format of a short range interaction is given below. There are three types of input records. Species records indicate the start of a new two body interaction and give the two species involved. Species records begin with a 4 character keyword indicating the type of interaction involved. Species records are also used to indicate a different potential form in a new range. An interaction may have more than one species record. Range records give the parameters for the interaction in a given range. Finally an ENDS record terminates the input for this interaction. Interactions involving more than one species record should not be split up with more than one ENDS record. The format of a species record is:


A A A A A < F,I > < BOND > < A >
KEYW LABELA LABELB Additional Optional Optional
Parameters Keyword Label

Where

KEYW
is a 4 character keyword giving the potential type. These are described in detail below.
LABELA,LABELB
are species labels in the usual format. Note that as for species input, it is not necessary to distinguish between fixed species and free species. The labels CORE and SHEL should be used for both.
Additional Parameters
These are required for certain of the potential types only.
Optional keyword
The optional keyword BOND indicates to the program that the potential is to be used for intramolecular (bonded) interactions only. Note that this option is new and may not be available in all versions of the programs.
Optional label
Bonded interactions must be labelled with a four character keyword. The present intramolecular bonding setup makes no use of this keyword, but future versions may require it.

The format of a range record is:

F ... < F > F
Parameters Optional RMAX
RMIN

Where
Parameters
These are the parameters needed to define the short range potential. The number of parameters depends on the particular potential type, defined by KEYW on the species record.
RMIN and RMAX
define the minimum and maximum range for this potential. RMIN may be omitted; the program knows how many parameters there are on the record and can therefore determine whether an RMIN has been given. If RMIN is omitted, the program uses the following rules to decide which value it should have.
  • If it is the first range record after a species record, the minimum range is assumed to be zero.
  • If it is a subsequent range, the minimum range is taken as the maximum of the previous range.

If a second species record is given, the ranges must either coincide with ranges given after the first species record or must be new ranges, contiguous with the existing ranges but extending beyond the previous maximum. Overlapping ranges are not permitted. The limits of the ranges are given in Å so that no conversion needs to be done when the data is transferred to a different substance. (cf. the CUTPOT parameter, which is in lattice units (See sectionsm on REGI and CUTO )).


Printed output

POTENTIAL BETWEEN SPECIES Lab1 Typ1 AND Lab2 Typ2 WITH Nrange RANGES

LIST OF INTERACTIONS BETWEEN SPECIFIC SPECIES
The above message is printed before the potentials labelled with the optional keyword BOND.

BONDS LABELLED Blab
Blab is the bond label input on the species record.
LIST OF GENERAL INTERACTIONS
This indicates the end of the bonded interactions. This message is not yet produced by all versions of the programs.


Error messages

A number of error messages will be given here as they do not depend on the keyword given on the species record.
ERROR - INVALID POTENTIAL GIVEN IN ABOVE LINE
This error message arises immediately after range records have been read in. The program expects either an ENDS record, or a new species record with a different potential type between the same two species. Neither of these two was found. Check that an ENDS record has not been omitted.
ERROR - POTENTIAL TYPE GIVEN WITH NO RANGES
A species record was input with no range records before an ENDS record or another species record.
ERROR - IN ABOVE LINE AN INVALID SPECIES LABEL WAS GIVEN ON A POTENTIAL DIRECTIVE
The labels do not match anything given after the SPEC directive.
ERROR - EACH POTENTIAL MUST BE MADE UP OF INTERACTIONS BETWEEN THE SAME TWO SPECIES. CHECK THAT AN ENDS DIRECTIVE IS NOT MISSING
A species record immediately after a range record was found, with no intervening ENDS. The species labels must be the same as on the previous species record. Most probably a new interaction was intended and an ENDS record was omitted. If a second species record between the same species was intended, check that the species labels have been put in correctly.
ERROR - THE POTENTIAL BETWEEN THE ABOVE TWO SPECIES IS DUPLICATED. CHECK THAT AN UNNECESSARY ENDS DIRECTIVE HAS NOT BEEN INCLUDED
A species record has just been read between two species for which a previous interaction has been read in. If you want to have an interaction with two different potential types, there must not be an ENDS record after the ranges of the first potential.
ERROR - A POTENTIAL HAS ALREADY BEEN SUPPLIED BETWEEN THESE TWO SPECIES. HARMONIC CORE-SHELL INTERACTIONS CANNOT HAVE ADDITIONAL POTENTIALS
A HARM directive between two species does not permit any additional potentials.
ERROR IN ABOVE POTENTIAL DIRECTIVE, KEYWORD EXPECTED WAS BOND, KEYWORD FOUND WAS Keyw.
The program found enough parameters on the species record to expect to need to read in the optional keyword BOND, but the keyword found in this place was not BOND but Keyw.
ERROR - IN ABOVE LINE A MINIMUM RANGE IS SUPPLIED WHICH MUST BE ZERO FOR FIRST RANGE OF FIRST POTENTIAL VALUE READ IN IS F CHECK THE NUMBER OF PARAMETERS NEEDED FOR THIS POTENTIAL TYPE
The program found enough parameters on a range record to expect to have an RMIN parameter, but the value read in was not zero for the first range. Check that you have got the correct number of parameters for this potential type.
ERROR - IF MINIMUM OF RANGE IS GIVEN IT MUST BE THE SAME AS AN EXISTING MAXIMUM, VALUE IS F.
An RMIN parameter has been read in from the current range record. This was not the first range, and the value of RMIN read in was different from any of the previously read in values of RMAX. This makes the ranges overlapping. Split the appropriate previous range into two.
ERROR - POTENTIALS WHOSE RANGES OVERLAP MUST HAVE IDENTICAL RANGES
A second species record has been read in followed by a range record. The RMAX value on this record is less than the current maximum from the previous potential. There may also have been an RMIN read in. In either case, the next highest RMAX value read in from the previous potential does not match the current RMAX. This makes an overlapping range.
ERROR - AN INTERACTION BETWEEN SPECIFIC SPECIES MUST BE GIVEN BEFORE GENERAL INTERACTIONS IN ANY POTENTIAL
Any species records with the optional BOND keyword for intramolecular interactions must be given before species records with no BOND keyword.
ERROR IN CHECKING MKNBP LIST
An internal consistency error has been detected. This is probably due to a bug in the program.
ERROR - TOO MANY POTENTIALS READ IN, MAXIMUM NUMBER OF POTENTIALS IS MAXPOT.
Increase the value of MAXPOT in all PARAMETER statements in the program and recompile it.
ERROR - RANGES MUST BE GIVEN IN ASCENDING ORDER
A range record has a RMAX value which is less than the previous record.
ERROR - THE MAXIMUM OF MAXRNG RANGES HAS BEEN EXCEEDED
Increase the value of MAXRNG in all PARAMETER statements in the program and recompile it.

The individual keywords will now be described.



BUCK

There are no additional parameters to be read from the species record. Three parameters plus RMIN (optional) and RMAX must be read from the range records. The analytic form is

The parameters A, B and C must be read from the range record. Their units are given below
A is in eV
B is in Å
C is in eV

The ranges are terminated with an ENDS record or a new species record between the same species. This keyword may be used with rigid ions, conventional shells or ellipsoidal shells. If ellipsoidal shells are present, the energy expression is

where

= Effective distance between shells

= Radius of ion i

= Distance of ellipsoid surface from centre in the direction of ion j

Example

BUCK NA+ SHEL NA+ SHEL

7895.4 0.1709 29.06 20.0

ENDS

Printed output

BUCKINGHAM POTENTIAL V(R) = A * EXP(-R/RHO) - C/R**6

A RHO C RMIN RMAX
A rho C RMIN RMAX

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MODI

There is one additional parameter read in from the species record. It has format I and operand name N. The analytic form of the potential is

The exponent N is read in from the MODI record. It is assumed that N remains the same for all ranges, if there is more than one. The parameters A, B and C must be read from the range record. The units of C are given below
C is in eV
The ranges are terminated with an ENDS record or a new species record between the same species.

Example

MODI NA+ SHEL NA+ SHEL 8

7895.4 0.1709 29.06 20.0

ENDS

Printed output

MODIFIED BUCKINGHAM POTENTIAL V(R) = A * EXP(-R/RHO) - C/R**N.

A RHO C N RMIN RMAX
A rho C N RMIN RMAX

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LENN

There are two additional parameters read in from the species record. They have format I and operand names N and M. The analytic form of the potential is

The exponents N and M are read in on the LENN record. It is assumed that N and M remain the same for all ranges, if there is more than one. The parameters A and B must be read from the range record. The units of A and B are given below
A is in eV
B is in eV
The ranges are terminated with an ENDS record or a new species record between the same species.

Example

LENN CL- SHEL CL- SHEL 12 6

8560.7 30.67 5.78 20.0

ENDS

Printed output

LENNARD-JONES POTENTIAL V(R)= A/R**N - B/R**M


A B N M RMIN RMAX
A B N M RMIN RMAX

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MORS

There are no additional parameters read in from the species record. The analytic form of the potential is

This has the energy zero offset from the conventional spectroscopic definition, which defines the energy zero at the minimum. The new definition is consistent with the other potentials, which have the energy zero at infinity. The parameters A, B and C must be read from the range record. The units of A, B and C are given below

A is in eV
B is in

C is in Å

 

The ranges are terminated with an ENDS record or a new species record between the same species.

Printed output

MORSE POTENTIAL V(R) = A *(1.0-EXP(-B*(R-C)))**2-A


A B C RMIN RMAX
A B C RMIN RMAX

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BUC4

There are no additional parameters read in from the species record. The analytic form of the potential is

 5mm
 5mm

There are 6 parameters read in from the range record. These are A, B, C, , and . Their units are given below

A is in eV

B is in Å

C is in

r are given in Å

 
The ranges are terminated with an ENDS record. On input, the ranges must satisfy the condition

If ra is less than CUTPOT, the term will be calculated out to CUTPOT.

The polynomials are fitted so that the functions, first derivatives and second derivatives match at , and . At the potential has a minimum so that the first derivatives of both polynomials are zero. Only one ranges record is permitted for this interaction, since all of the ranges are given on the first record. Also, this potential must not overlap an existing potential.

Printed output

4 RANGE MODIFIED BUCKINGHAM POTENTIAL

RANGE 1 V(R)= A * EXP(-R/RHO),

RANGE 2 V(R) = A5*R**5+ B5*R**4 + C5*R**3 + D5*R**2 + E5*R + F5

RANGE 3 V(R) = A3*R**3 + B3*R**2 + C3*R + D3,

RANGE 4 V(R)= -C/R**6

            RMIN RMAX
A = A RHO = RHO     RMIN
A5 = A5 B5 = B5 C5 = C5    
D5 = D5 E5 = E5 F5 = F5
A3 = A3 B3 = B3        
C3 = C3 D3 = D3 E3 = E3
C = C         RMAX

Error messages

ERROR - THE FOUR RANGE BUCKINGHAM POTENTIAL AND CUBIC SPLINE MUST NOT OVERLAP AN EXISTING POTENTIAL

ERROR - ONLY ONE PARAMETERS DIRECTIVE MUST BE GIVEN WITH THE FOUR RANGE BUCKINGHAM FORM

ERROR - THE RANGES ON THE FOUR RANGE BUCKINGHAM CARD ARE NOT GIVEN IN ASCENDING ORDER


SPLI

There are two additional parameters on the species record, but they are both optional. They have format F, with operand names SMIN and SMAX. If only one F format number is given , the program interprets it as SMAX. If both are given, the program interprets them in the order SMIN then SMAX.

A cubic spline is defined in the following way. The energies at n points are given. The points need not be equally spaced. A cubic polynomial is then defined, polynomial being between points i and i + 1. There are thus n - 1 cubic polynomials. These are defined to be equal to and at and respectively. Also and will have the same first and second derivatives at . A quick count of the number of parameters and equations shows that two more equations are required. These are taken to be that the second derivatives of and are zero at and respectively. It is also possible to define two more polynomials, which are in fact linear equations, and , to be extensions of the spline beyond the points and .

There are two parameters read in from the range record, and . is in eV and is in Å. The interpretation of the range records for the cubic spline potential is somewhat different to the other potentials. Usually this would be interpreted as the maximum of the range RMAX. For the cubic spline, it should be the value of r at which the energy is E. A value of RMIN is not permitted on the range record for a cubic spline. The program rearranges the input data so that it defines n - 1 ranges each with an RMIN and RMAX. The usual convention that the potential must start at zero also applies to the cubic spline. There are two ways of doing this. Firstly, the energy at zero may be given on the first range card. The program will define n - 1 ranges. If the energy at zero is not known, then input SMIN = 0.0 on the species record and input a value for SMAX. The program will define n + 1 ranges, with range 1 and n + 1 being the linear functions and defined above. A third format is permitted, in which SMAX only is supplied. The cubic spline potential cannot have other potentials defined in the same range for the same species. It may, however, have different potential types defined in other ranges. A minimum of 3 and a maximum of MAXRNG - 1 records defining the energy points must be given. The RMAX parameters must be in ascending order as usual. Care is needed if the ranges do not extend as far as CUTPOT. In this case the program will extend the last range out to CUTPOT. In general, however, the energy will not tend to zero as the range is extended. This may be overcome by adding extra ranges with zero energy.

Printed output

CUBIC SPLINE POTENTIAL V(R)= A*R**3 + B*R**2 + C*R + D*R

A B C D RMIN RMAX E(RMIN)
A B C D RMIN RMAX E

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Error messages

ERROR - A MINIMUM RANGE MUST NOT BE GIVEN ON A CUBIC SPLINE PARAMETERS CARD
One of the range records has three parameters on it; the program assumes that an RMIN has been given.
ERROR - FOR CUBIC SPLINE THE FIRST PARAMETER CARD HAS A MINIMUM RANGE ON IT. THIS MUST BE ZERO FOR FIRST RANGE OF FIRST POTENTIAL
Either no SMIN has been given on the species record and the value of r on the first range record is not zero, or SMIN has been given but is not zero.
ERROR - THE CUBIC SPLINE MUST NOT EXCEED THE MAXIMUM NUMBER OF RANGES -1, MAXIMUM NUMBER OF RANGES IS MAXRNG

ERROR - THE FOUR RANGE BUCKINGHAM POTENTIAL AND CUBIC SPLINE MUST NOT OVERLAP AN EXISTING POTENTIAL

ERROR - THE CUBIC SPLINE MUST HAVE AT LEAST 3 RANGES, THE NUMBER INPUT IS N

ERROR - THE MAXIMUM FOR THE LINEAR EXTENSION OF THE CUBIC SPLINE IS LESS THAN THE LAST RANGE

This error message occurs when SMAX is given on the species record, but the value is less than the last RMAX given on the range records.


MORQ

There are no additional parameters read in from the species record. The analytic form of the potential is

The parameters A, B, C and D must be read from the range record. and are the charges on the species 1 and 2. This potential is intended to permit a Morse function for nearest neighbour interactions with no Coulomb term. To achieve this the parameter D must be set equal to 1.0 The effect of this additional term is to remove the Coulomb interaction between the species 1 and 2. Note however that if either species is a shell model ion, the total Coulomb interaction between both components of the ion is not removed. The units of A, B, C and D are given below
A is in eV

B is in

C is in Å

D is dimensionless

 
The ranges are terminated with an ENDS record or a new species record between the same species.

Printed output

COULOMB SUBTRACTED OFFSET MORSE POTENTIAL

V(R)=A*(1.0-EXP(-B(R-C)))**2 - A -D*Q1*Q2/R


A B C D*Q1*Q2 RMIN RMAX
A B C D*Q1 *Q2 RMIN RMAX

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SPRI

There are no additional parameters to be read in from the species record. The analytic form of the potential is

and are the charges on the species 1 and 2. This potential is intended to permit a harmonic spring function for nearest neighbour interactions with no Coulomb term. The parameter B should be set equal to the bond length, and A to the spring constant. To achieve this the parameter C must be set equal to 1.0 Setting C equal to 0.0 will leave the Coulomb term in. The effect of this additional term is to remove the Coulomb interaction between the species 1 and 2. Note however that if either species is a shell model ion, the total Coulomb interaction between both components of the ion is not removed. The units of A, B and C are given below

A is in eV

B is in Å

C is dimensionless

 

The ranges are terminated with an ENDS record or a new species record between the same species.

Printed output

HARMONIC SPRING CONSTANT BETWEEN DIFFERENT BASIS ATOMS WITH COULOMB TERM SUBTRACTED

V(R) = 1/2*K*(R-R0)**2 - A*Q1*Q2/R


K R0 D*Q1*Q2 RMIN RMAX
K R0 D*Q1 *Q2 RMIN RMAX

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COUL

There are no additional parameters to be read in from the species record. The analytic form of the potential is

and are the charges on the species 1 and 2. This potential is intended to permit Coulomb subtraction between nearest neighbours. To achieve this the parameter A must be set equal to -1.0 Note however that if either species is a shell model ion, the total Coulomb interaction between both components of the ion is not removed. The units of A are given below
A is dimensionless
The ranges are terminated with an ENDS record or a new species record between the same species.

Printed output

COULOMB POTENTIAL V(R) = A*Q1*Q2/R


A*Q1*Q2 RMIN RMAX
A*Q1*Q2 RMIN RMAX

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VDWA

There is one additional parameter read in from the species record. It has format I and operand name N. The analytic form of the potential is

The exponent N is read in on the VDWA record. It is assumed that N remains the same for all ranges, if there is more than one. The parameter A must be read from the range record. The units of A is given below
A is in eV
The ranges are terminated with an ENDS record or a new species record between the same species.

Printed output

VAN DER WAALS INTERACTION V(R) = A/R**N


A N RMIN RMAX
A N RMIN RMAX

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HULB

There are no additional parameters to be read in from the species record. The analytic form of the potential is


Where


The parameters A, B, C, D, E and F must be read from the range record. The units of A, B, C, D, E and F are given below
A is in eV
B is in
C is in Å
D is dimensionless
E is dimensionless
 
F is in eV
The ranges are terminated with an ENDS record or a new species record between the same species.

Printed output

COULOMB SUBTRACTED OFFSET HULBURT-HIRCHFELDER INTERACTION

V(R) = A * ((1.0-EXP (-B*(R-C)))**2 + (D*(B**3) * ((R-C)**3) * EXP (-2.0 * B * (R-C)) * (1.0 + E * B * (R-C))))-F-QI*QJ/R


A B C RMIN RMAX
D E F    
A B C RMIN RMAX
D E F    

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BUC7

There are no additional parameters read in from the species record. The analytic form of the potential is

 5mm
 5mm

There are 6 parameters read in from the range record. These are A, B, C, , and . Their units are given below
A is in eV
B is in Å
C is in eV
r are given in Å
The ranges are terminated with an ENDS record. On input, the ranges must satisfy the condition

If is less than CUTPOT, the term will be calculated out to CUTPOT (see section on cutoffs).

The polynomials are fitted so that the functions, first derivatives, second derivatives and third derivatives match at , and . At the potential has a minimum so that the first derivatives of both polynomials are zero. Only one ranges record is permitted for this interaction, since all of the ranges are given on the first record. Also, this potential must not overlap an existing potential.

Printed output

4 RANGE MODIFIED BUCKINGHAM POTENTIAL WITH 7/4 SPLINE

RANGE 1 V(R) = A * EXP(-R/RHO)

RANGE 2 V(R) = A7*R**7 + B7*R**6 + C7*R**5 + D7*R**4 + E7*R**3 + F7*R**2 + G7*R + H7

RANGE 3 V(R) = A4*R**4 + B4*R**3 + C4*R**2 + D4*R + E4

RANGE 4 V(R) = -C/R**6


            RMIN RMAX
A = A RHO = RHO     RMIN
A7 = A7 B7 = B7 C7 = C7    
D7 = D7 E7 = E7 F7 = F7    
G7 = G7 H7 = H7    
A4 = A4 B4 = B4 C4 = C4    
D4 = D4 E4 = E4    
C = C         RMAX

Error messages

ERROR - THE FOUR RANGE BUCKINGHAM POTENTIAL AND CUBIC SPLINE MUST NOT OVERLAP AN EXISTING POTENTIAL

ERROR - ONLY ONE PARAMETERS DIRECTIVE MUST BE GIVEN WITH THE FOUR RANGE BUCKINGHAM FORM

ERROR - THE RANGES ON THE FOUR RANGE BUCKINGHAM CARD ARE NOT GIVEN IN ASCENDING ORDER

NONE

There are no additional parameters to be read from the species record. This is a dummy two-body potential which does nothing. It may be used where the true range of a potential is less than CUTPOT, and where a range needs to be put in so that the potential extends out as far as CUTPOT. This will most commonly occur for intramolecular potentials. The range record should contain the value of RMAX and (optionally) the value of RMIN.


BSPL

There are no additional parameters on the species record. The program will fit a 5th. order spline between the points using the method of ???. There are two parameters read in from the range record, and . is in eV and is in Å. The interpretation of the range records for the quintic spline potential is somewhat different to the other potentials. Usually this would be interpreted as the maximum of the range RMAX. For the quintic spline, it should be the value of r at which the energy is E. A value of RMIN is not permitted on the range record for a quintic spline. The program rearranges the input data. In doing this ranges are redefined and extra ranges may be added. The quintic spline should not therefore be used with any other potential functions. The usual convention that the potential must start at zero also applies to the quintic spline.

Printed output

B-SPLINE POTENTIAL. ORDER 5

SEPARATION SPLINE PARAMETER ENERGY, 1ST AND 2ND DERIVATIVES
R A E G W

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Error messages

ERROR - FOR QUINTIC SPLINE THE NUMBER OF RANGES INPUT IS i AND MUST BE LESS THAN MAXRNG -6 WHERE MAXRNG = maxrng

ERROR - THE NUMBER OF QUINTIC SPLINE KNOTS WHICH IS SET INTERNALLY IS TOO LARGE RESET MAXRNG TO i
The number of quintic spline points input was too large.
ERROR - SMOOT ERROR CODE i

User error - probably too few points.


DBUC

There are no additional parameters to be read from the species record. Six parameters plus RMIN (optional) and RMAX must be read from the range records. This potential is currently only available for the ellipsoidal shell model. It provides a Buckingham potential with the Van der Waals term damped. The analytic form is

 

Where

= Effective distance between shells

= Radius of ion i

= Distance of ellipsoid surface from centre


The parameters A, B, C, D, E, and F must be read from the range record. Their units are given below
A is in eV
B is in Å
C is in eV
D is in
E is in eV
F is in

Printed output

BUCKINGHAM WITH DAMPED VAN DER WAALS V(R) = A * EXP(-R/RHO) - C * (1-EXP(-ALPHA6*R))**2/R**6 - D * (1-EXP(-ALPHA8*R))**2/R**8

A RHO C ALPHA6 RMIN RMAX
D ALPHA8        
A rho C alpha6 RMIN RMAX
D alpha8        

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BVCK

There are no additional parameters to be read from the species record. Three parameters plus RMIN (optional) and RMAX must be read from the range records. This potential may only be used by ellipsoidal shell models. It is the same as the ellipsoidal Buckingham model, except that the effective radius is used for the Van der Waals term instead of the actual radius. The energy equation is

 

Where

= Effective distance between shells

= Radius of ion i

= Distance of ellipsoid surface from centre


The parameters A, B and C must be read from the range record. Their units are given below
A is in eV
B is in Å
C is in eV

The ranges are terminated with an ENDS record or a new species record between the same species. The printed output is the same as for the Buckingham potential.


DBVC

There are no additional parameters to be read from the species record. Six parameters plus RMIN (optional) and RMAX must be read from the range records. This potential is currently only available for the ellipsoidal shell model. It provides a Buckingham potential with the Van der Waals term damped. The potential is the same as DBUC except that the effective radius is used for the Van der Waals terms. The analytic form is

 

Where

= Effective distance between shells

The parameters A, B, C, D, E, and F must be read from the range record. Their units are as for the DBUC potential.


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