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Filename: drivers/Session_files_driver.php
Line Number: 177
Backtrace:
File: /var/www/html/index.php
Line: 316
Function: require_once
Severity: Warning
Message: session_start(): Failed to read session data: user (path: /var/lib/php/sessions)
Filename: Session/Session.php
Line Number: 137
Backtrace:
File: /var/www/html/index.php
Line: 316
Function: require_once
Severity: Warning
Message: file_get_contents(https://...@pubfacts.com&api_key=b8daa3ad693db53b1410957c26c9a51b4908&a=1): Failed to open stream: HTTP request failed! HTTP/1.1 429 Too Many Requests
Filename: helpers/my_audit_helper.php
Line Number: 197
Backtrace:
File: /var/www/html/application/helpers/my_audit_helper.php
Line: 197
Function: file_get_contents
File: /var/www/html/application/helpers/my_audit_helper.php
Line: 271
Function: simplexml_load_file_from_url
File: /var/www/html/application/helpers/my_audit_helper.php
Line: 1057
Function: getPubMedXML
File: /var/www/html/application/helpers/my_audit_helper.php
Line: 3175
Function: GetPubMedArticleOutput_2016
File: /var/www/html/application/controllers/Detail.php
Line: 575
Function: pubMedSearch_Global
File: /var/www/html/application/controllers/Detail.php
Line: 489
Function: pubMedGetRelatedKeyword
File: /var/www/html/index.php
Line: 316
Function: require_once
The concept of natural densitals (NDs) and their amplitudes is introduced. These quantities provide the spectral decomposition of the cumulant of the two-electron density that, by definition, quantifies the extent of electron correlation. Consequently, they are ideally suited for a rigorous description of electron correlation effects in Coulombic systems. Spin-summed and spin-resolved versions of the NDs and their amplitudes are defined, and their properties are discussed in detail. Unlike the nonnegative-valued occupation numbers of the natural orbitals (NOs), these amplitudes exhibit diverse sign patterns that emerge within different regimes of electron correlation. The descriptive power of this property is vividly illustrated with the ground state of the H molecule, in which the subtle interplay of various types of electron correlation is captured in detail by a straightforward examination of the amplitudes of the NDs alone. Offering the most compact bilinear representations of (a property analogous to that of the NOs with respect to the 1-matrix), the NDs open up entirely new vistas in the analysis of electronic structures of atoms and molecules.
Download full-text PDF |
Source |
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http://www.ncbi.nlm.nih.gov/pmc/articles/PMC11770769 | PMC |
http://dx.doi.org/10.1021/acs.jpclett.4c03166 | DOI Listing |
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