In computational chemistry, natural resonance theory (NRT) is an iterative, variational functional embedded into the natural bond orbital (NBO) program, commonly run in Gaussian, GAMESS, ORCA, Ampac and other software packages.[1][2] NRT was developed in 1997 by Frank A. Weinhold and Eric D. Glendening, chemistry professors at University of Wisconsin-Madison and Indiana State University, respectively. Given a list of NBOs for an idealized natural Lewis structure, the NRT functional creates a list of Lewis resonance structures and calculates the resonance weights of each contributing resonance structure.[1] Structural and chemical properties, such as bond order, valency, and bond polarity, may be calculated from resonance weights.[2] Specifically, bond orders may be divided into their covalent and ionic contributions, while valency is the sum of bond orders of a given atom.[2][3] This aims to provide quantitative results that agree with qualitative notions of chemical resonance.[1] In contrast to the "wavefunction resonance theory" (i.e., the superposition of wavefunctions), NRT uses the density matrix resonance theory, performing a superposition of density matrices to realize resonance.[4][5][6] NRT has applications in ab initio calculations,[2][7][6] including calculating the bond orders of intra- and intermolecular interactions[8][9] and the resonance weights of radical isomers.[10]
^ abcGlendening, E. D.; Weinhold, F. (1998-04-30). <593::aid-jcc3>3.0.co;2-m "Natural resonance theory: I. General formalism". Journal of Computational Chemistry. 19 (6): 593–609. doi:10.1002/(sici)1096-987x(19980430)19:6<593::aid-jcc3>3.0.co;2-m. ISSN 0192-8651.
^ abcdGlendening, E. D.; Weinhold, F. (1998-04-30). <610::aid-jcc4>3.0.co;2-u "Natural resonance theory: II. Natural bond order and valency". Journal of Computational Chemistry. 19 (6): 610–627. doi:10.1002/(sici)1096-987x(19980430)19:6<610::aid-jcc4>3.0.co;2-u. ISSN 0192-8651.
^Glendening, Eric D.; Landis, Clark R.; Weinhold, Frank (January 2012). "Natural bond orbital methods". WIREs Computational Molecular Science. 2 (1): 1–42. doi:10.1002/wcms.51. ISSN 1759-0876. S2CID 95586513.
^Wang, Yang (2021-03-05). "Superposition of waves or densities: Which is the nature of chemical resonance?". Journal of Computational Chemistry. 42 (6): 412–417. doi:10.1002/jcc.26463. ISSN 0192-8651. PMID 33314179. S2CID 229173656.
^Wang, Yang (2021). "A reliable and efficient resonance theory based on analysis of DFT wave functions". Physical Chemistry Chemical Physics. 23 (3): 2331–2348. Bibcode:2021PCCP...23.2331W. doi:10.1039/D0CP06207C. ISSN 1463-9076. PMID 33449982. S2CID 231623526.
^ abGlendening, Eric D.; Landis, Clark R.; Weinhold, Frank (2019-03-13). "Resonance Theory Reboot". Journal of the American Chemical Society. 141 (10): 4156–4166. doi:10.1021/jacs.8b12336. ISSN 0002-7863. PMID 30742414. S2CID 73450515.
^Glendening, E. D.; Badenhoop, J. K.; Weinhold, F. (1998-04-30). <628::aid-jcc5>3.0.co;2-t "Natural resonance theory: III. Chemical applications". Journal of Computational Chemistry. 19 (6): 628–646. doi:10.1002/(sici)1096-987x(19980430)19:6<628::aid-jcc5>3.0.co;2-t. ISSN 0192-8651.
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