<!-- BaNnErBlUrFlE-BoDy-start -->
<!-- Preheader Text : BEGIN -->
<div style="display:none !important;display:none;visibility:hidden;mso-hide:all;font-size:1px;color:#ffffff;line-height:1px;height:0px;max-height:0px;opacity:0;overflow:hidden;">
I agree with the previous emails, but I wanted to point out that there is an extended Koopmans Theorem that does apply to general MCSCF wave functions. It involves the eigenvalue equation FC=DCE where F is one of the fock matrices we compute</div>
<!-- Preheader Text : END -->
<!-- Email Banner : BEGIN -->
<div style="display:none !important;display:none;visibility:hidden;mso-hide:all;font-size:1px;color:#ffffff;line-height:1px;max-height:0px;opacity:0;overflow:hidden;">ZjQcmQRYFpfptBannerStart</div>
<!--[if ((ie)|(mso))]>
<table border="0" cellspacing="0" cellpadding="0" width="100%" style="padding: 16px 0px 16px 0px; direction: ltr" lang="en"><tr><td>
<table border="0" cellspacing="0" cellpadding="0" style="padding: 0px 10px 5px 6px; width: 100%; border-radius:4px; border-top:4px solid #8c8e91;background-color:#CFD3D7;"><tr><td valign="top">
<table align="left" border="0" cellspacing="0" cellpadding="0" style="padding: 4px 8px 4px 8px">
<tr><td style="color:#000000; font-family: 'Arial', sans-serif; font-weight:bold; font-size:14px; direction: ltr">
This Message Is From an External Sender
</td></tr>
<tr><td style="color:#000000; font-weight:normal; font-family: 'Arial', sans-serif; font-size:12px; direction: ltr">
This message came from outside your organization.
</td></tr>
</table>
<![if ie]><br clear="all"><![endif]>
<table align="right" border="0" cellspacing="0" cellpadding="0" style="padding: 4px 0px 4px 0px"><tr>
<td style="direction: ltr"> <a target="_blank" href="https://us-phishalarm-ewt.proofpoint.com/EWT/v1/KGKeukY!vwQdMiaND6YBRRdxv46k9jxZlkgh9lJOKc2Y0xflhb9sZLTARW7AM1NQ3-r2G_ZYJHK1t7bc_yF1STTVu__UB3_RqPyCTKr8aj3CPmFs32L--booRksN1KIxhFFe1B62ncw9mvs1sHAcuG69$" style="mso-padding-alt: 7.5px; padding: 7.5px; border-radius: 2px; border: 1.5px solid #666666; "><strong style="font-weight: normal; color: #000000; text-decoration: none; font-family: 'Arial', sans-serif; font-size:14px; line-height: 40px; "> Report Suspicious </strong></a> </td>
</tr></table>
</td></tr></table>
</td></tr></table>
<![endif]-->
<![if !((ie)|(mso))]>
<div dir="ltr" lang="en" id="pfptBannerpc4d2p2" style="all: revert !important; display:block !important; text-align: left !important; margin:16px 0px 16px 0px !important; padding:8px 16px 8px 16px !important; border-radius: 4px !important; min-width: 200px !important; background-color: #CFD3D7 !important; background-color: #CFD3D7; border-top: 4px solid #8c8e91 !important; border-top: 4px solid #8c8e91;">
<div id="pfptBannerpc4d2p2" style="all: unset !important; float:left !important; display:block !important; margin: 0px 0px 1px 0px !important; max-width: 600px !important;">
<div id="pfptBannerpc4d2p2" style="all: unset !important; display:block !important; visibility: visible !important; background-color: #CFD3D7 !important; color:#000000 !important; color:#000000; font-family: 'Arial', sans-serif !important; font-family: 'Arial', sans-serif; font-weight:bold !important; font-weight:bold; font-size:14px !important; line-height:18px !important; line-height:18px">
This Message Is From an External Sender
</div>
<div id="pfptBannerpc4d2p2" style="all: unset !important; display:block !important; visibility: visible !important; background-color: #CFD3D7 !important; color:#000000 !important; color:#000000; font-weight:normal; font-family: 'Arial', sans-serif !important; font-family: 'Arial', sans-serif; font-size:12px !important; line-height:18px !important; line-height:18px; margin-top:2px !important;">
This message came from outside your organization.
</div>
</div>
<div id="pfptBannerpc4d2p2" style="all: unset !important; float: right !important; display: block !important; display: block; margin: 0px 0px 0px 16px !important; text-align: right !important; width: fit-content !important;">
<a id="pfptBannerpc4d2p2" href="https://us-phishalarm-ewt.proofpoint.com/EWT/v1/KGKeukY!vwQdMiaND6YBRRdxv46k9jxZlkgh9lJOKc2Y0xflhb9sZLTARW7AM1NQ3-r2G_ZYJHK1t7bc_yF1STTVu__UB3_RqPyCTKr8aj3CPmFs32L--booRksN1KIxhFFe1B62ncw9mvs1sHAcuG69$"
style="all: unset !important; display: inline-block !important; text-decoration: none">
<div class="pfptPrimaryButtonpc4d2p2" style="display: inline-block !important; display: inline-block; visibility: visible !important; opacity: 1 !important; color: #000000 !important; color: #000000; font-family: 'Arial', sans-serif !important; font-family: 'Arial', sans-serif; font-size: 14px !important; font-weight: normal !important; text-decoration: none !important; border-radius: 2px !important; padding: 7.5px 16px !important; margin: 3px 0 3px 16px !important; white-space: nowrap !important; width: fit-content !important;
border: 1px solid #666666">
Report Suspicious
</div>
</a>
</div>
<div style="clear: both !important; display: block !important; visibility: hidden !important; line-height: 0 !important; font-size: 0.01px !important; height: 0px"> </div>
</div>
<![endif]>
<div style="display:none !important;display:none;visibility:hidden;mso-hide:all;font-size:1px;color:#ffffff;line-height:1px;max-height:0px;opacity:0;overflow:hidden;">ZjQcmQRYFpfptBannerEnd</div>
<!-- Email Banner : END -->
<!-- BaNnErBlUrFlE-BoDy-end -->
<html xmlns:o="urn:schemas-microsoft-com:office:office" xmlns:w="urn:schemas-microsoft-com:office:word" xmlns:m="http://schemas.microsoft.com/office/2004/12/omml" xmlns="http://www.w3.org/TR/REC-html40">
<head><!-- BaNnErBlUrFlE-HeAdEr-start -->
<style>
#pfptBannerpc4d2p2 { all: revert !important; display: block !important;
visibility: visible !important; opacity: 1 !important;
background-color: #CFD3D7 !important;
max-width: none !important; max-height: none !important }
.pfptPrimaryButtonpc4d2p2:hover, .pfptPrimaryButtonpc4d2p2:focus {
background-color: #adb0b4 !important; }
.pfptPrimaryButtonpc4d2p2:active {
background-color: #8c8e91 !important; }
</style>
<!-- BaNnErBlUrFlE-HeAdEr-end -->
<meta http-equiv="Content-Type" content="text/html; charset=utf-8">
<meta name="Generator" content="Microsoft Word 15 (filtered medium)">
<style><!--
/* Font Definitions */
@font-face
{font-family:"Cambria Math";
panose-1:2 4 5 3 5 4 6 3 2 4;}
@font-face
{font-family:Aptos;
panose-1:2 11 0 4 2 2 2 2 2 4;}
@font-face
{font-family:"Times New Roman \(Body CS\)";
panose-1:2 2 6 3 5 4 5 2 3 4;}
/* Style Definitions */
p.MsoNormal, li.MsoNormal, div.MsoNormal
{margin:0in;
font-size:12.0pt;
font-family:"Aptos",sans-serif;}
a:link, span.MsoHyperlink
{mso-style-priority:99;
color:blue;
text-decoration:underline;}
span.EmailStyle18
{mso-style-type:personal-reply;
font-family:"Aptos",sans-serif;
color:windowtext;}
.MsoChpDefault
{mso-style-type:export-only;
font-size:10.0pt;
mso-ligatures:none;}
@page WordSection1
{size:8.5in 11.0in;
margin:1.0in 1.0in 1.0in 1.0in;}
div.WordSection1
{page:WordSection1;}
--></style>
</head>
<body lang="EN-US" link="blue" vlink="purple" style="word-wrap:break-word">
<div class="WordSection1">
<p class="MsoNormal">I agree with the previous emails, but I wanted to point out that there is an extended Koopmans Theorem that does apply to general MCSCF wave functions. It involves the eigenvalue equation FC=DCE where F is one of the fock matrices we compute
in COLUMBUS and D is the 1-RDM. The eigenvalues E correspond to ionization potentials.<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">As for orbital energies in general, we compute two different fock matrices in the MCSCF code in COLUMBUS, one we call F and the other we call Q. They both map to the closed-shell RHF fock matrix in that limit, but they generally differ
otherwise. We use the Q matrix to bring the doubly occupied and virtual (unoccupied) orbitals to a canonical form. It is possible for CASSCF wave functions to also diagonalize the active orbitals and to represent the wave function in those orbitals. However,
these orbitals generally do not correspond to any kind of optimal mean field conditions, so they are otherwise less useful than the closed-shell RHF case. As Felix said, we rather more typically diagonalize the 1-RDM rather than a fock matrix to define the
active orbitals.<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">-Ron<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:0in;margin-right:0in;margin-bottom:12.0pt;margin-left:.5in">
On 3/24/25, 5:20<span style="font-family:"Arial",sans-serif"> </span>AM, "Columbus" <columbus-bounces+shepard=tcg.anl.gov@lists.osc.edu> wrote:<o:p></o:p></p>
<div>
<p class="MsoNormal" style="margin-left:.5in">Dear Yincheng, Just an additional comment on this. The thing that's slightly tricky about MCSCF is that the interpretation of the orbital energies is more involved than for standard SCF jobs. In most cases, when
discussing MCSCF, we talk about<o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="margin-left:.5in">ZjQcmQRYFpfptBannerStart<o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="margin-left:.5in">This Message Is From an External Sender
<o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="margin-left:.5in">This message came from outside your organization.
<o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="margin-left:.5in"><o:p> </o:p></p>
</div>
<div>
<p class="MsoNormal" style="margin-left:.5in"><o:p> </o:p></p>
</div>
<div>
<p class="MsoNormal" style="margin-left:.5in"><o:p> </o:p></p>
</div>
<div>
<p class="MsoNormal" style="margin-left:.5in">ZjQcmQRYFpfptBannerEnd<o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="margin-left:.5in">Dear Yincheng, Just an additional comment on this. The thing that's slightly tricky about MCSCF is that the interpretation of the orbital energies is more involved than for standard SCF jobs. In most cases, when
discussing MCSCF, we talk about<o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="margin-left:.5in"><o:p> </o:p></p>
</div>
<div>
<p class="MsoNormal" style="margin-left:.5in">Dear Yincheng,<o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="margin-left:.5in">Just an additional comment on this. The thing that's slightly tricky about MCSCF is that the interpretation of the orbital energies is more involved than for standard SCF jobs.<o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="margin-left:.5in">In most cases, when discussing MCSCF, we talk about natural orbitals (NOs). NOs have occupations, because we diagonalised the density matrix. But NOs don't have energies.<o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="margin-left:.5in">If you want MO energies, then you have to diagonalise the Fock matrix. This will give you some indication about where the orbitals are. But you should realise that there is no such thing as Koopmans theorem for
MCSCF. Therefore, it is not so common to report orbital energies, because they don't actually have a physical meaning.<o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="margin-left:.5in">Best<o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="margin-left:.5in">Felix<o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="margin-left:.5in"><o:p> </o:p></p>
</div>
<div>
<p class="MsoNormal" style="margin-left:.5in">On 23/03/2025 16:39, Hans Lischka via Columbus wrote:<o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="margin-left:.5in"><o:p> </o:p></p>
</div>
<div>
<p class="MsoNormal" style="margin-left:.5in">** <o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="margin-left:.5in"><o:p> </o:p></p>
</div>
<div>
<p class="MsoNormal" style="margin-left:.5in">Dear Yincheng, Look into the file mcscfls, there you will find the orbital energies of the mcscf calculation. Best regards, Hans On 3/22/2025 6: 11 AM, Yicheng Zhu via Columbus wrote: Dear Columbus Admins: Is there
a way for me to obtain molecular<o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="margin-left:.5in"><o:p> </o:p></p>
</div>
<div>
<p class="MsoNormal" style="margin-left:.5in">Dear Yincheng,<o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="margin-left:.5in">Look into the file mcscfls, there you will find the orbital energies of the mcscf calculation.<o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="margin-left:.5in">Best regards, Hans<o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="margin-left:.5in"><o:p> </o:p></p>
</div>
<div>
<p class="MsoNormal" style="margin-left:.5in">On 3/22/2025 6:11 AM, Yicheng Zhu via Columbus wrote: Dear Columbus Admins: Is there a way for me to obtain molecular orbital energies from running MCSCF calculations? If so, which file should I look into? Best,
Yicheng _______________________________________________ Columbus mailing list <a href="mailto:Columbus@lists.osc.edu">
Columbus@lists.osc.edu</a> <mailto:<a href="mailto:Columbus@lists.osc.edu">Columbus@lists.osc.edu</a>>
<a href="https://lists.osu.edu/mailman/listinfo/columbus">https://lists.osu.edu/mailman/listinfo/columbus</a> <<a href="https://urldefense.com/v3/__https://urldefense.us/v3/__https:/lists.osu.edu/mailman/listinfo/columbus__;!!G_uCfscf7eWS!dDLutbqxQ_L3QD6f1cbHZItLyXYskwtZmKmSUI_rT70jlkMLft8-N-AHAREHqg85JDF--WZhg_IAUb7-DbxSLDN7$__;!!KGKeukY!ylrqTUVhHjJQGacBWlmK5ku8DlLL3Ioguvaon_Il7HHBcOhkmeR12mpoNP8B5qyef4WHFbkP801IgDyPRzkGEcUu$">https://urldefense.us/v3/__https://lists.osu.edu/mailman/listinfo/columbus__;!!G_uCfscf7eWS!dDLutbqxQ_L3QD6f1cbHZItLyXYskwtZmKmSUI_rT70jlkMLft8-N-AHAREHqg85JDF--WZhg_IAUb7-DbxSLDN7$</a>>
<o:p></o:p></p>
</div>
<div>
<p class="MsoNormal" style="margin-left:.5in"><o:p> </o:p></p>
</div>
<div>
<p class="MsoNormal" style="margin-left:.5in"><o:p> </o:p></p>
</div>
<div>
<p class="MsoNormal" style="margin-left:.5in">_______________________________________________ Columbus mailing list
<a href="mailto:Columbus@lists.osc.edu">Columbus@lists.osc.edu</a> <mailto:<a href="mailto:Columbus@lists.osc.edu">Columbus@lists.osc.edu</a>>
<a href="https://lists.osu.edu/mailman/listinfo/columbus">https://lists.osu.edu/mailman/listinfo/columbus</a> <<a href="https://urldefense.com/v3/__https://urldefense.us/v3/__https:/lists.osu.edu/mailman/listinfo/columbus__;!!G_uCfscf7eWS!dDLutbqxQ_L3QD6f1cbHZItLyXYskwtZmKmSUI_rT70jlkMLft8-N-AHAREHqg85JDF--WZhg_IAUb7-DbxSLDN7$__;!!KGKeukY!ylrqTUVhHjJQGacBWlmK5ku8DlLL3Ioguvaon_Il7HHBcOhkmeR12mpoNP8B5qyef4WHFbkP801IgDyPRzkGEcUu$">https://urldefense.us/v3/__https://lists.osu.edu/mailman/listinfo/columbus__;!!G_uCfscf7eWS!dDLutbqxQ_L3QD6f1cbHZItLyXYskwtZmKmSUI_rT70jlkMLft8-N-AHAREHqg85JDF--WZhg_IAUb7-DbxSLDN7$</a>>
<o:p></o:p></p>
</div>
</div>
</body>
</html>