Three-Body Interactions

BOHA

ILABEL is an integer label giving the index of the three-body bond type. The same label is used in the THBO directive. ILABEL must be 1 for the first three-body bond type, 2 for the second, and so on up to a maximum of MAXTHB. The analytic form of the potential is

where is the bond angle in the crystal. is in eV , is in degrees. is a user defined equilibrium angle and is not necessarily the same as the actual bond angle in the crystal. For example, in quartz, the exact tetrahedral angle can be can be chosen for for the oxygen-silicon-oxygen bonds.

However, the actual angles in the crystal deviate slightly from equilibrium. There is a restriction that none of the bond angles in the crystal can be 180 degrees (see QART). The cutoff chosen is cos() > - 0.999. Also the equilibrium angle supplied must be greater than acos(0.999) and less than acos(-0.999).

Printed output

THREE BODY FORCE CONSTANT WITH INDEX ILABEL

THE FORM OF THE THREE BODY POTENTIAL IS V = 1/2*K3* (THETA - THETA0)**2

K3 = K3 THETA0 = THETA0

Error messages

ERROR - A THREE BODY FORCE CONSTANT HAS BEEN DUPLICATED

ERROR - THE EQUILIBRIUM BOND ANGLE MUST BE GREATER THAN ARCCOS(0.999)

ILABEL is an integer label giving the index of the three-body bond type (see BOHA). The analytic form of the potential is

Where , and are the bond angles in the triangle of atoms i, j and k and , and are the bond lengths. is read in from the input record but not used. is in eV. There is no restriction on any of the bond angles being 180 degrees.

Printed output

THREE BODY FORCE CONSTANT WITH INDEX ILABEL

THE FORM OF THE THREE BODY POTENTIAL IS V = K3 * (1+3.0 * COS(THETAI) * COS(THETAJ) * COS(THETAK))/RIJ**3 * RIK**3 * RJK**3

K3 = K3 THETA0 = THETA0

Error messages

ERROR - A THREE BODY FORCE CONSTANT HAS BEEN DUPLICATED

The integer ILABEL has already been used for another three-body bond.

ILABEL is an integer label giving the index of the three-body bond type (see BOHA). The analytic form of the potential is

Where is the bond angle in the crystal. is in eV , is in degrees, and are in . is a user defined equilibrium angle and is not necessarily the same as the actual bond angle in the crystal. and are the bond lengths from the central atom i to the two peripheral atoms j and k, that is the angle .

Printed output

THREE BODY FORCE CONSTANT WITH INDEX ILABEL

THE FORM OF THE THREE BODY POTENTIAL IS V = 1/2*K3* (THETA - THETA0)**2 * EXP(-R/RHO1) * EXP(-R/RHO2)

K3 = K3 RHO1 = RHO1 RHO2 = RHO2

Error messages

ERROR - A THREE BODY FORCE CONSTANT HAS BEEN DUPLICATED

ERROR - THE EQUILIBRIUM BOND ANGLE MUST BE GREATER THAN ARCCOS(0.999)

 

ILABEL is an integer label giving the index of the three-body bond type (see BOHA). The analytic form of the potential is

Where is the bond angle in the crystal, is in eV , is in degrees. is a user defined equilibrium angle and is not necessarily the same as the actual bond angle in the crystal. This potential may be used when is 180 degrees, but not when is 180 degrees (see BOHZ). It is designed so that the second derivative of V with respect to is the same as for BOHA when . Also the first derivative of V with respect to tends to zero as tends to . This allows the derivative to be calculated using a power series approximation.

Printed output

THREE BODY FORCE CONSTANT WITH INDEX ILABEL

THE FORM OF THE THREE BODY POTENTIAL IS V = 0.5* K3*(0.25*(THETA0-PI)**2-0.5*(THETA-PI)**2+0.25*((THETA-PI)**4) /((THETA0-PI)**2))

K3 = K3 THETA0 = THETA0

Error messages

ERROR - A THREE BODY FORCE CONSTANT HAS BEEN DUPLICATED

ERROR - THE EQUILIBRIUM BOND ANGLE MUST BE GREATER THAN ARCCOS(0.999) AND LESS THAN ARCCOS(-0.999)

ILABEL is an integer label giving the index of the three-body bond type (see BOHA). The analytic form of the potential is very complex, it is given below for the sake of completeness.

Where

Printed output

THREE BODY FORCE CONSTANT WITH INDEX ILABEL

THE FORM OF THE THREE BODY POTENTIAL IS V = SIXTH ORDER POLYNOMIAL IN THETA WITH CORRECT LIMITS AT THETA = PI AND THETA = 0

K3 = K3 THETA0 = THETA0

Error message

ERROR - A THREE BODY FORCE CONSTANT HAS BEEN DUPLICATED

ILABEL is an integer label giving the index of the three-body bond type (see BOHA). The analytic form of the potential is

Where is the bond angle in the crystal, is in eV . The equilibrium angle is . This allows linear bonds to be treated. The derivatives are again calculated using a power series if is close to .

Printed output

THREE BODY FORCE CONSTANT WITH INDEX ILABEL

THE FORM OF THE THREE BODY POTENTIAL IS V = 1/2*K3* (THETA - PI)**2

K3 = K3 THETA0 = THETA0

Error messages

ERROR - A THREE BODY FORCE CONSTANT HAS BEEN DUPLICATED

THRH

ILABEL is an integer label giving the index of the three-body bond type (see BOHA). The analytic form of the potential is

Where is in eV . is the bond angle in the crystal. is in degrees. is a user defined equilibrium angle and is not necessarily the same as the actual bond angle in the crystal. r01 and r02 are in and are the equilibrium bond lengths of the ij and ik bonds respectively.

ILABEL is an integer label giving the index of the three-body bond type (see BOHA). The analytic form of the potential is

Where is in eV . r01 and r02 are in Å and are the equilibrium bond lengths of the ij and ik bonds respectively.