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Short
Range Interactions
|
A | A A | A A | < F,I > | < BOND > | < A > |
KEYW | LABELA | LABELB | Additional | Optional | Optional |
Parameters | Keyword | Label |
F ... | < F > | F |
Parameters | Optional | RMAX |
RMIN |
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
)).
POTENTIAL BETWEEN SPECIES Lab1 Typ1 AND Lab2 Typ2 WITH Nrange RANGES
LIST OF INTERACTIONS BETWEEN SPECIFIC SPECIESThe above message is printed before the potentials labelled with the optional keyword BOND.
BONDS LABELLED BlabBlab is the bond label input on the species record.
LIST OF GENERAL INTERACTIONSThis indicates the end of the bonded interactions. This message is not yet produced by all versions of the programs.
ERROR - INVALID POTENTIAL GIVEN IN ABOVE LINEThis 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 RANGESA 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 DIRECTIVEThe 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 MISSINGA 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 INCLUDEDA 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 POTENTIALSA 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 TYPEThe 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 RANGESA 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 POTENTIALAny species records with the optional BOND keyword for intramolecular interactions must be given before species records with no BOND keyword.
ERROR IN CHECKING MKNBP LISTAn 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 ORDERA range record has a RMAX value which is less than the previous record.
ERROR - THE MAXIMUM OF MAXRNG RANGES HAS BEEN EXCEEDEDIncrease the value of MAXRNG in all PARAMETER statements in the program and recompile it.
The individual keywords
will now be described.
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
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
BUCK NA+ SHEL NA+ SHEL
7895.4 0.1709 29.06 20.0
ENDS
BUCKINGHAM POTENTIAL V(R) = A * EXP(-R/RHO) - C/R**6
A | RHO | C | RMIN | RMAX |
A | rho | C | RMIN | RMAX |
. . . |
. . . |
. . . |
. . . |
. . . |
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
MODI NA+ SHEL NA+ SHEL 8
7895.4 0.1709 29.06 20.0
ENDS
MODIFIED BUCKINGHAM POTENTIAL V(R) = A * EXP(-R/RHO) - C/R**N.
A | RHO | C | N | RMIN | RMAX |
A | rho | C | N | RMIN | RMAX |
. . . |
. . . |
. . . |
. . . |
. . . |
. . . |
LENN CL- SHEL CL- SHEL 12 6
8560.7 30.67 5.78 20.0
ENDS
LENNARD-JONES POTENTIAL V(R)= A/R**N - B/R**M
A | B | N | M | RMIN | RMAX |
A | B | N | M | RMIN | RMAX |
. . . |
. . . |
. . . |
. . . |
. . . |
. . . |
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
C is in Å
The ranges are terminated with an ENDS record or a new species record between the same species.
MORSE POTENTIAL V(R) = A *(1.0-EXP(-B*(R-C)))**2-A
A | B | C | RMIN | RMAX |
A | B | C | RMIN | RMAX |
. . . |
. . . |
. . . |
. . . |
. . . |
There are no additional parameters read in from the species record. The analytic form of the potential is
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
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.
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 - 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
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.ERROR - THE RANGES ON THE FOUR RANGE BUCKINGHAM CARD ARE NOT GIVEN IN ASCENDING ORDER
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.
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 |
. . . |
. . . |
. . . |
. . . |
. . . |
. . . |
. . . |
ERROR - A MINIMUM RANGE MUST NOT BE GIVEN ON A CUBIC SPLINE PARAMETERS CARDOne 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 POTENTIALEither 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.
B is in
C is in Å
D is dimensionless
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 |
. . . |
. . . |
. . . |
. . . |
. . . |
. . . |
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
B is in Å
C is dimensionless
The ranges are terminated with an ENDS record or a new species record between the same species.
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 |
. . . |
. . . |
. . . |
. . . |
. . . |
COULOMB POTENTIAL V(R) = A*Q1*Q2/R
A*Q1*Q2 | RMIN | RMAX |
A*Q1*Q2 | RMIN | RMAX |
. . . |
. . . |
. . . |
VAN DER WAALS INTERACTION V(R) = A/R**N
A | N | RMIN | RMAX |
A | N | RMIN | RMAX |
. . . |
. . . |
. . . |
. . . |
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
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 | ||
. . . |
. . . |
. . . |
. . . |
. . . |
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.
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 - 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
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.
B-SPLINE POTENTIAL. ORDER 5
SEPARATION | SPLINE PARAMETER | ENERGY, 1ST AND 2ND DERIVATIVES | ||
R | A | E | G | W |
. . . |
. . . |
. . . |
. . . |
. . . |
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 iThe number of quintic spline points input was too large.
ERROR - SMOOT ERROR CODE i
User error - probably too few points.
Where
= Effective distance between shells
= Radius of ion i
= Distance of ellipsoid surface from centre
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 | ||||
. . . |
. . . |
. . . |
. . . |
. . . |
. . . |
Where
= Effective distance between shells
= Radius of ion i
= Distance of ellipsoid surface from centre
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.
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.
Next: Job Steps In DMAREL - Short Range Potential Input: Core Shell Interactions Previous: Job Steps In DMAREL - Short Range Potential Input: Species Data Input Contents: Contents Page