TY - JOUR
T1 - Intracule functional models
T2 - Part III. The dot intracule and its Fourier transform
AU - Bernard, Yves A.
AU - Crittenden, Deborah L.
AU - Gill, Peter M.W.
PY - 2008
Y1 - 2008
N2 - The dot intracule D(x) of a system gives the Wigner quasi-probability of finding two of its electrons with u·v = x, where u and v are the interelectronic distance vectors in position and momentum space, respectively. In this paper, we discuss D(x) and show that its Fourier transform d(k) can be obtained in closed form for any system whose wavefunction is expanded in a Gaussian basis set. We then invoke Parseval's theorem to transform our intracule-based correlation energy method into a d(k)-based model that requires, at most, a one-dimensional quadrature.
AB - The dot intracule D(x) of a system gives the Wigner quasi-probability of finding two of its electrons with u·v = x, where u and v are the interelectronic distance vectors in position and momentum space, respectively. In this paper, we discuss D(x) and show that its Fourier transform d(k) can be obtained in closed form for any system whose wavefunction is expanded in a Gaussian basis set. We then invoke Parseval's theorem to transform our intracule-based correlation energy method into a d(k)-based model that requires, at most, a one-dimensional quadrature.
UR - http://www.scopus.com/inward/record.url?scp=44949127104&partnerID=8YFLogxK
U2 - 10.1039/b803919d
DO - 10.1039/b803919d
M3 - Article
SN - 1463-9076
VL - 10
SP - 3447
EP - 3453
JO - Physical Chemistry Chemical Physics
JF - Physical Chemistry Chemical Physics
IS - 23
ER -