Reference manuals - CBS -‹#›Petr
Kulhanek
kulhanek@chemi.muni.cz
National Center for Biomolecular Research, Faculty of Science
Masaryk University, Kotlářská 2, CZ-61137 Brno
CBS
Reference manuals
Reference manuals - CBS -‹#›Extrapolation
to CBS
Reference manuals - CBS -‹#›-
Extrapolation
Bx
CBS AeExE −
+=)(
Because we have four input energies (for x=2, 3, 4, and 5) and only three unknowns (ECBS, A
and B) we must use the least squares method. The aim of the method is to find the value of
the parameters ECBS, A and B so that the purpose (error) function is minimal.
  min!)(),,,(),,(
5
2
2
=−= =x
HFCBSCBS xEBAExEBAEf
We can use the fit method from the program gnuplot to find the optimal parameters.
See original documentation gnuplot or:
http://www.root.cz/clanky/gnuplot-prikaz-fit/
Reference manuals - CBS -‹#›-
Procedure
▪ Prepare a text file data.txt, which will contain two columns: the cardinal number of the
base (2, 3, 4, ...) and the energy calculated by the HF method.
▪ Run the program gnuplot and display the energy profile from the file data.txt:
▪ Define a function for extrapolation:
▪ Set the default values ​​of the parameter for optimization:
▪ Perform pre-optimization of the parameters ECBS and A and then final optimization of
all parameters:
gnuplot> plot './data.txt' using 1:2 with points
gnuplot> E(x) = Ecbs + A * exp(-B*x)
gnuplot> A = 1
gnuplot> B = 1
gnuplot> Ecbs= -80 # lower than the smallest calculated energy
gnuplot> fit E(x) "./data.txt" via Ecbs, A
gnuplot> fit E(x) "./data.txt" via Ecbs, A, B
Reference manuals - CBS -‹#›Procedure,
cont.
▪ Display the input data, E(x) function and the value of ECBS. Perform a visual inspection
of the obtained results. The E(x) function must pass through all points and approach
the found value of E as a CBS limit.
▪ Print the exact value of ECBS
gnuplot> set xrange[2:7]
gnuplot> plot './data.txt' using 1:2 with points, E(x), Ecbs
gnuplot> print Ecbs