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<META NAME="AUTHOR" CONTENT="Edward Valeev">
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<H3>General</H3>
<P>Program <FONT COLOR="#ff3333">CINTS</FONT> can evaluate integrals
over Gaussian functions of the following one- and two-electron
operators which appear in quantum chemical theories:</P>
<UL>
<LI><P>overlap</P>
<LI><P>electron kinetic energy</P>
<LI><P>nuclear attraction</P>
<LI><P>electron repulsion (ERI)</P>
<LI><P>anticoulombic (r<SUB>12</SUB>-operator)</P>
<LI><P>[r<SUB>12</SUB>,T<I><SUB>i</SUB></I>] operator (<I>i</I><SPAN STYLE="font-style: normal">=1,2)</SPAN></P>
<LI><P STYLE="font-style: normal">various one-electron property
operators (currently, only dipole moment and electronic nabla operators)
</P>
</UL>
<P>First-order derivatives with respect to nuclear positions may be
evaluated for the first four types of integrals. (Derivative)
integrals are evaluated over symmetry-adapted Cartesian and Spherical
Harmonics contracted Gaussian functions. Symmetry use is restricted
to <I>D</I><SUB>2h</SUB> and it's subgroups. The program does not
have theoretical limits on the number of basis functions or the
maximum angular momentum of Gaussian functions in the basis.</P>
<H3>Tasks</H3>
<P>As integrals are evaluated, the program can either write them out
to disk (available for only up-to first-order derivative integrals) or contract them
with appropriate quantities to form various entities of interest.
</P>
<H4>Disk storage</H4>
<P>Integrals are written to disk in the new Integrals With Labels
(<FONT COLOR="#ff3333">IWL</FONT>) format (see PSI 3 Programmer's
Manual, section on <FONT COLOR="#ff3333">LIBIWL)</FONT><FONT COLOR="#000000">.
<FONT COLOR="#ff0000">LIBIWL</FONT> functions provide the interface
which may be used to access integrals files. Non-zero, unique with
respect to index permutations<A CLASS="sdfootnoteanc" NAME="sdfootnote1anc" HREF="#sdfootnote1sym"><SUP>1</SUP></A>
two-electron integrals are written in shell-quartet order, i.e. all
integrals which belong to the same quartet of (symmetry unique)
shells are written together. There are no markers between
shell-quartets. However, there's a particular order in which
shell-quartets of ERIs get stored to disk. Shell-quartets of ERIs
which contribute to the same shell-quartet of supermatrix integrals P
and K are written together. The last integral in each PK-block is
written with its first index set to the negative of itself so that
<FONT COLOR="#ff0000">CSCF</FONT> knows where it can stop and dump a
complete block of P and K elements to disk.</FONT></P>
<H4>Contraction</H4>
<P><FONT COLOR="#000000">Depending on the keywords or command-line
options specified, the following types of contractions can be
performed:</FONT></P>
<UL>
<LI><P>formation of the two-electron part of Fock matrix
(spin-restricted for closed- and high-spin open-shell systems and
spin-unrestricted cases) from ERIs (works in conjunction with <FONT COLOR="#ff0000">CSCF</FONT>)</P>
<LI><P>restricted integral-direct transformation to compute RHF MP2
energy</P>
<LI><P>restricted integral-direct transformation to compute and dump
MO integrals that appear in the RHF MP2-R12 energy expression (MO
integrals are used by program <FONT COLOR="#ff0000">MP2R12</FONT>)</P>
<LI><P>evaluate energy gradients at Hartree-Fock and correlated
levels</P>
</UL>
<P><BR><BR>
</P>
<DIV ID="sdfootnote1">
<P CLASS="sdfootnote" STYLE="margin-bottom: 0.2in"><A CLASS="sdfootnotesym" NAME="sdfootnote1sym" HREF="#sdfootnote1anc">1</A>Two-electron
integrals of Hermitian operators have the usual 8-fold permutation
symmetry. Operator [r<SUB>12</SUB>,T<I><SUB>i</SUB></I>] is
non-Hermitian, hence a permutation of its integrals's bra and ket
does not leave the integral invariant. See Wim Klopper's article in
Theor. Chim. Acta..</P>
</DIV>
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