From owner-chemistry@ccl.net Mon Sep 28 16:42:01 2015
From: "Thomas Manz tmanz],[nmsu.edu" <owner-chemistry+/-server.ccl.net>
To: CCL
Subject: CCL:G: two-electron range-separated Coulomb and exchange integrals
Message-Id: <-51785-150928163958-8852-/8atZjQvhEPx5Ie8fjWWZg+/-server.ccl.net>
X-Original-From: Thomas Manz <tmanz(!)nmsu.edu>
Content-Type: multipart/alternative; boundary=001a11473bb2c5e9480520d4b2c0
Date: Mon, 28 Sep 2015 14:39:47 -0600
MIME-Version: 1.0


Sent to CCL by: Thomas Manz [tmanz]![nmsu.edu]
--001a11473bb2c5e9480520d4b2c0
Content-Type: text/plain; charset=UTF-8

Hi,

The range-separated Coulomb integral

1/r = erf(k*r)/r + (1-erf(k*r))/r

arises in range-separated hybrid functionals.
There are many papers about functionals that use this kind of
range-separation.
My question is regarding the 2-electron integral terms (i.e., exchange and
Coulomb integrals)
using this type of range separation. Does anyone know where the analytic
forms for this have been published?

They should be of the form
<g1(r1)*g2(r1)*(erf(k*r)/r)*g3(r2)*g4(r1)>
where <> means integrate over positions r1 and r2 and g1, g2, g3, g4 are
Gaussian basis sets.

We are actually trying to do the analogous Coulomb/exchange integrals for
electrons confined to a plane (i.e., two-dimensional Gaussians), but we
maybe could figure out how to do this by looking at the three-dimensional
case.

I would be grateful if anyone could provide references on the mathematical
derivations of the analytic integrals for the three-dimensional case.

Sincerely,


Tom Manz

--001a11473bb2c5e9480520d4b2c0
Content-Type: text/html; charset=UTF-8
Content-Transfer-Encoding: quoted-printable

<div dir=3D"ltr">Hi,<div><br></div><div>The range-separated Coulomb integra=
l</div><div><br></div><div>1/r =3D erf(k*r)/r + (1-erf(k*r))/r</div><div><b=
r></div><div>arises in range-separated hybrid functionals.</div><div>There =
are many papers about functionals that use this kind of range-separation.</=
div><div>My question is regarding the 2-electron integral terms (i.e., exch=
ange and Coulomb integrals)</div><div>using this type of range separation. =
Does anyone know where the analytic forms for this have been published?</di=
v><div><br></div><div>They should be of the form=C2=A0</div><div>&lt;g1(r1)=
*g2(r1)*(erf(k*r)/r)*g3(r2)*g4(r1)&gt;</div><div>where &lt;&gt; means integ=
rate over positions r1 and r2 and g1, g2, g3, g4 are Gaussian basis sets.</=
div><div><br></div><div>We are actually trying to do the analogous Coulomb/=
exchange integrals for electrons confined to a plane (i.e., two-dimensional=
 Gaussians), but we maybe could figure out how to do this by looking at the=
 three-dimensional case.</div><div><br></div><div>I would be grateful if an=
yone could provide references on the mathematical derivations of the analyt=
ic integrals for the three-dimensional case.</div><div><div><br></div><div>=
Sincerely,</div><div><br></div><div><br clear=3D"all"><div><div class=3D"gm=
ail_signature"><div dir=3D"ltr"><p style=3D"margin-top:0px;margin-bottom:0p=
x;color:rgb(0,0,0)"><font face=3D"tahoma, sans-serif">Tom Manz</font></p></=
div></div></div></div></div></div>

--001a11473bb2c5e9480520d4b2c0--