07132
10.1351/goldbook.ZT07132
ZT07132
current
IUPAC Gold Book  zero differential overlap (ZDO) approximation
zero differential overlap (ZDO) approximation
 ZDO
2.3.3
20140224

1
An approach to the systematic neglect of the smallinvalue electron repulsion integrals which is used in a number of approximate selfconsistent field molecular orbital schemes. It means that all the products of atomic orbitals χ µ χ ν are set to zero and the overlap integralS µ ν = δ µ ν (where δ µ ν is the Kronecker delta). The ZDO approximation greatly simplifies the computation of wavefunctions by eliminating many of twoelectron integrals. At the ZDO approximation all three and fourcentered integrals vanish.

molecular orbital
goldify
https://dev.goldbook.iupac.org/terms/view/M03996

overlap integral
goldify
https://dev.goldbook.iupac.org/terms/view/O04357
$\chi \; \mu \; \chi \; \nu \backslash unicode[Times]\{x3C7\}\; \_\{\backslash unicode[Times]\{x3BC\}\; \}\backslash \; \backslash unicode[Times]\{x3C7\}\; \_\{\backslash unicode[Times]\{x3BD\}\; \}S\; \mu \; \; \nu \; =\; \delta \; \mu \; \; \nu \backslash text\{S\}\_\{\backslash unicode[Times]\{x3BC\}\; \backslash unicode[Times]\{x3BD\}\; \}\; =\; \backslash unicode[Times]\{x3B4\}\; \_\{\backslash unicode[Times]\{x3BC\}\; \backslash unicode[Times]\{x3BD\}\; \}\delta \; \mu \; \; \nu \backslash unicode[Times]\{x3B4\}\_\{\backslash unicode[Times]\{x3BC\}\backslash unicode[Times]\{x3BD\}\; \}$
 PAC, 1999, 71, 1919. 'Glossary of terms used in theoretical organic chemistry' on page 1970 (https://doi.org/10.1351/pac199971101919)
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Citation: 'zero differential overlap (ZDO) approximation' in IUPAC Compendium of Chemical Terminology, 3rd ed. International Union of Pure and Applied Chemistry; 2006. Online version 3.0.1, 2019. 10.1351/goldbook.ZT07132
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