V0_REAL
Note
Some versions of TensErLEED currently do not support arbitrary definitions of V0_REAL, instead always using the “Rundgren form” (see below) with parameters from the PHASESHIFTS file.
TODO: Update documentation to match TensErLEED 2.0
V0_REAL is used to provide the real part of the inner potential of the solid. (V0_IMAG is the imaginary part, instead)
Default: V0_REAL = RUNDGREN c0 c1 c2 c3, where the c* values are
taken from the first line in PHASESHIFTS, as derived from the output of the
phase shifts calculation.
Syntax
V0_REAL = -1*max(-10.17, -0.08 - 74.19/sqrt(EE+19.18))
V0_REAL = RUNDGREN -10.17 -0.08 -74.19 19.18
Acceptable values: The right-hand side should be any real-valued function
of the electron energy (in electronvolts). Use only EE, ee, eE, or
Ee to represent the electron energy. The expression will be interpreted by
Fortran, so follow Fortran syntax. Acceptable arithmetic/mathematic functions
are listed below. The special command RUNDGREN can be used to choose the
following functional form for the real part of the inner potential
V(EE) = FILAMENT_WF - max(c0,c1+c2/sqrt(EE+c3)),
as per Eq. (A8) in Rundgren’s paper, Ref. 24.
The same result can be obtained by the input
V0_REAL = -1*max(c0,c1+c2/sqrt(EE+c3))
Notice that, in this case, it’s necessary that c0<0 and c1<0.
It is advisable to stick to the Default (i.e., do not define
V0_REAL), unless you have provided an externally generated
PHASESHIFTS file. In this case, it is best to
define the parameter with the RUNDGREN command and copying the
c0–c3 constants from the first line of any of the PS.r.* output
files of the phase-shift calculation tool (c0 is the second number,
c1 the third, and so on).
In all cases, the program will replace EE with
E+:ref:FILWF, since the relevant
electron energy is the one in vacuum, with respect to Fermi.
Acceptable math expressions: all names are case insensitive, all angles are in RADIANS, use parentheses ‘()’ to indicate precedence of operation, as well as for surrounding function arguments.
Operation |
Symbol |
Syntax example |
|---|---|---|
Exponentiation |
** |
a**b (a to the power of b) |
Multiplication |
* |
a*b (a times b) |
Division |
/ |
a/b (a divided by b) |
Sum |
+ |
a+b (a plus b) |
Subtraction, Negation |
- |
a-b (a minus b), -a (negative of a) |
Absolute value |
abs() |
abs(a) = |a| |
Arc-cosine |
acos() |
acos(a), result in radians |
Arc-sine |
asin() |
asin(a), result in radians |
Arc-tangent |
atan() |
atan(a), result in radians |
Complex conjugate |
conjg() |
conjg(a+bi)=a-bi |
Cosine |
cos() |
cos(a), a in radians |
Hyperbolic cosine |
cosh() |
cosh(a) |
Error function |
erf() |
erf(a) |
Exponential |
exp() |
exp(a) = e to the power of a |
Imaginary part |
imag() |
imag(a+bi)=a (real) |
Natural logarithm |
log() |
log(a) |
Maximum |
max() |
max(a,b,c,..) |
Minimum |
min() |
min(a,b,c,..) |
Sine |
sin() |
sin(a), a in radians |
Hyperbolic sine |
sinh() |
sinh(a) |
Square root |
sqrt() |
sqrt(a) |
Tangent |
tan() |
tan(a), a in radians |
Hyperbolic tangent |
tanh() |
tanh(a) |