From owner-chemistry@ccl.net Fri Dec 5 06:07:01 2008 From: "Nand Ng andyng111*hotmail.com" To: CCL Subject: CCL: Molecular integrals using gaussian functions (using boys algorithm) Message-Id: <-38253-081205060433-1724-aBBmRyDympMQMQK6dntJ4A__server.ccl.net> X-Original-From: "Nand Ng" Date: Fri, 5 Dec 2008 06:04:28 -0500 Sent to CCL by: "Nand Ng" [andyng111{=}hotmail.com] Dear all, > From Boys algorithm, we can get higher angular momentum by differentiating by the positions of the atoms, if we differentiate a s-orbital by Xa, we will have a p_x-orbitals d/dXa exp^(-a* ((x-Xa)^2 + (y-Ya)^2 +(z-Za)^2)) / 2a = (x-Xa) * exp^(-a* ((x-Xa)^2 + (y-Ya)^2 +(z-Za)^2)) however, I found that if I differentiate a p_x-orbitals by Xa, I will get a d_x^2-orbitals plus an extra s-orbital term. d/dXa (x-Xa) * exp^(-a* ((x-Xa)^2 + (y-Ya)^2 +(z-Za)^2)) / 2a =(x-Xa)^2 * exp^(-a* ((x-Xa)^2 + (y-Ya)^2 +(z-Za)^2)) - exp^(-a* ((x-Xa)^2 + (y-Ya)^2 +(z-Za)^2)) / 2a If I need to calcuate an overlap integral between a d_x^2-orbital and a s-orbital, how do I elimate this extra term? Thank you for your help. Regards, Nand From owner-chemistry@ccl.net Fri Dec 5 10:22:00 2008 From: "Gustavo Mercier gamercier-#-yahoo.com" To: CCL Subject: CCL:G: Molecular integrals using gaussian functions (using boys algorithm) Message-Id: <-38254-081205083659-5789-66xJgG2CraHJ45FhYyoAqg\a/server.ccl.net> X-Original-From: Gustavo Mercier Content-Type: text/plain; charset=us-ascii Date: Fri, 5 Dec 2008 04:36:48 -0800 (PST) MIME-Version: 1.0 Sent to CCL by: Gustavo Mercier [gamercier[A]yahoo.com] Hi! Take your last equation, multiply by your s function and integrate to get an overlap integral. = -(1/2a) D = d/dXa and D^2=d2/dXa2 (second derivative w.r.t. nuclear coordinates). Because the derivatives are w.r.t. nuclear coordinates and the integrals are over electronic coordinates, you can pull the derivative out of the integra.... = D^2() You have an analytic form for , so you can compute D^2() term and rewriting the first equation above: = D^2() + (1/2a) In the end you have a series of recursions to solve your integrals. Hope this helps! -- Gustavo A. Mercier, Jr. MD,PhD Boston Medical Center Radiology - Nuclear Medicine and Molecular Imaging, Chief gamercier{}yahoo.com (preferred e-mail address) Gustavo.Mercier{}bmc.org gumercie{}bu.edu cell: 469-396-6750 work: 617-638-6610; 617-414-6457 ----- Original Message ---- > From: Nand Ng andyng111*hotmail.com To: "Mercier, Gustavo, " Sent: Friday, December 5, 2008 6:04:28 AM Subject: CCL: Molecular integrals using gaussian functions (using boys algorithm) Sent to CCL by: "Nand Ng" [andyng111{=}hotmail.com] Dear all, > From Boys algorithm, we can get higher angular momentum by differentiating by the positions of the atoms, if we differentiate a s-orbital by Xa, we will have a p_x-orbitals d/dXa exp^(-a* ((x-Xa)^2 + (y-Ya)^2 +(z-Za)^2)) / 2a = (x-Xa) * exp^(-a* ((x-Xa)^2 + (y-Ya)^2 +(z-Za)^2)) however, I found that if I differentiate a p_x-orbitals by Xa, I will get a d_x^2-orbitals plus an extra s-orbital term. d/dXa (x-Xa) * exp^(-a* ((x-Xa)^2 + (y-Ya)^2 +(z-Za)^2)) / 2a =(x-Xa)^2 * exp^(-a* ((x-Xa)^2 + (y-Ya)^2 +(z-Za)^2)) - exp^(-a* ((x-Xa)^2 + (y-Ya)^2 +(z-Za)^2)) / 2a If I need to calcuate an overlap integral between a d_x^2-orbital and a s-orbital, how do I elimate this extra term? Thank you for your help. Regards, Nandhttp://www.ccl.net/cgi-bin/ccl/send_ccl_messagehttp://www.ccl.net/chemistry/sub_unsub.shtmlhttp://www.ccl.net/spammers.txt From owner-chemistry@ccl.net Fri Dec 5 12:28:01 2008 From: "Nand Ng andyng111],[hotmail.com" To: CCL Subject: CCL: Molecular integrals using gaussian functions (using boys algorithm Message-Id: <-38255-081205122612-12279-RtUHdgPHJRAIkBfWgbV7TA(~)server.ccl.net> X-Original-From: "Nand Ng" Date: Fri, 5 Dec 2008 12:26:09 -0500 Sent to CCL by: "Nand Ng" [andyng111!^!hotmail.com] Thank you very much for your help. It seems for higher angular momentum, Boys algorithm is not enough. We have to calculate it through some lower angular momentum integrals, am I right? We cannot simply get d-orbitals integrals by D^2 . We can only do it for p-orbitals? Sent to CCL by: Gustavo Mercier [gamercier[A]yahoo.com] Hi! Take your last equation, multiply by your s function and integrate to get an overlap integral. = -(1/2a) D = d/dXa and D^2=d2/dXa2 (second derivative w.r.t. nuclear coordinates). Because the derivatives are w.r.t. nuclear coordinates and the integrals are over electronic coordinates, you can pull the derivative out of the integra.... = D^2() You have an analytic form for , so you can compute D^2() term and rewriting the first equation above: = D^2() + (1/2a) In the end you have a series of recursions to solve your integrals. Hope this helps! -- Gustavo A. Mercier, Jr. MD,PhD Boston Medical Center Radiology - Nuclear Medicine and Molecular Imaging, Chief gamercier{}yahoo.com (preferred e-mail address) Gustavo.Mercier{}bmc.org gumercie{}bu.edu cell: 469-396-6750 work: 617-638-6610; 617-414-6457