LSF
Local scaling (scale) factor
LSMF
Least-squares merit function
NIC
Natural internal coordinate
PEC
Potential energy curve
PES
Potential energy (hyper)surface
PIC
Primitive internal coordinate
QC
Quantum chemistry (methods, calculations…)
RMS
Root-mean-square (deviation)
SF
Scaling factors
SQM(FF) Scaled quantum mechanical (force field) method; simply SQM
US
Uniform scaling
WDC
Wilson–Decius–Cross method
WLS
Wavenumber linear scaling
X
A general second-row atom
Y
A general third-row atom
ZPVE
Zero-point vibrational energy correction
Symbols Used in Mathematical Formulas
A, B, …
General indices used in summations over atoms
B
Transformation matrix between internal and Cartesian
coordinates
f ¼ f 1 ; f 2 ; . . .; f N scl
ð
Þ
A vector with scaling factors
f
eff
¼ f
eff
1 ; f
eff
2 ; . . .; f
eff
K
À
Á Effective scaling factors
f
opt
¼ f
opt
1 ; f
opt
2 ; . . .; f
opt
N scl
À
Á A vector with optimal scaling factors
f
x
Cartesian force constant matrix with elements f
x
ij
F
Force constant matrix in internal coordinate representation with elements F lm
i, j, …
General indices used in summations over Cartesian
coordinates
I, J, …
General indices used to indicate types of internal
coordinates in multi-parameter scaling procedures
K
Number of vibrational degrees of freedom, K = 3N − 6
(or K = 3N − 5 in the case of linear molecules)
L
Number of redundant primitive internal coordinates
(typically L > 3N)
L
Transformation matrix between Cartesian displacements and normal coordinates
N
Number of atoms in a molecule
N mol
Number of molecules in a training set
N scl
Number of scaling factors
N typ
Number of types (groups) of internal coordinates (=N scl )
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O. Bąk and P. Borowski