Natural transition orbitals

In this appendix, we describe the detailed definition of y. The Nocc X ( act + JVvir) rectangular block transition density matrix T is translated to diagonalized rectangular matrix by using the corresponding orbital [77] or natural transition orbital [78, 79] method as follows. 

Fig. 6 Illustrations of the natural transition orbitals (NTO) describing the PCPDTBT So Sj transition as determined with TDDFT at the B3LYP/6-31G level of theory, k is the fraction of the hole-particle contribution to the excitation...

Martin RL (2003) Natural transition orbitals. J Chem Phys 118 4775... 

In the present article, the absorption properties of the two native proteins, as well as the ESR and circular dichroism (CD) parameters, will be analyzed, at density functional theory (DFT) and time-dependent DFT (TD-DFT) level. The use of hybrid QM/MM approach will allow us to take into account the role of the macromolecular environment [32-37]. The evolution of the spectroscopic parameters with mutations will be also considered. The use of natural transition orbitals (NTOs) [26, 38] techniques will allow us to perform a systematic analysis of the nature and electronic properties of the excited states. 

R. L. Martin,/. Chem. Phys., 118, A775-A777 (2003). Natural Transition Orbitals. 

Fig. 27 Natural transition orbitals (NTOs) of the relaxed Si->So transitions (a-d) and So- -Si transitions (e-h) for pp and po arrangements of PV and PV3 segments (from [125])...

Electron transfer processes induce variations in the occupancy and/or the nature of orbitals which are essentially localized at the redox centers. However, these centers are embedded in a complex dielectric medium whose geometry and polarization depend on the redox state of the system. In addition, a finite delocalization of the centers orbitals through the medium is essential to-promote long-range electron transfers. The electron transfer process must therefore be viewed as a transition between two states of the whole system. The expression of the probability per unit time of this transition may be calculated by the general formahsm of Quantum Mechanics. 

A natural bond orbital-based CI/MP through-space/bond interaction analysis of the Sn2 reaction between allyl bromide and ammonia17 showed that allyl bromide reacted faster than propyl bromide because the a - n and n — a interactions stabilize the allyl bromide transition state equally. 

Other theoretical studies discussed above include investigations of the potential energy profiles of 18 gas-phase identity S 2 reactions of methyl substrates using G2 quantum-chemical calculations," the transition structures, and secondary a-deuterium and solvent KIEs for the S 2 reaction between microsolvated fluoride ion and methyl halides,66 the S 2 reaction between ethylene oxide and guanine,37 the complexes formed between BF3 and MeOH, HOAc, dimethyl ether, diethyl ether, and ethylene oxide,38 the testing of a new nucleophilicity scale,98 the potential energy surfaces for the Sn2 reactions at carbon, silicon, and phosphorus,74 and a natural bond orbital-based CI/MP through-space/bond interaction analysis of the S 2 reaction between allyl bromide and ammonia.17... 

Natural Atomic Orbital and Natural Bond Orbital Analysis 230 9.7 Computational Considerations 232 9.8 Examples 232 References 234 10 Molecular Properties 235 104 Examples 236 References 294 12 Transition State Theory and Statistical Mechanics 296 12.1 Transition State Theory 296 12.2 Statistical Mechanics 298 12.2.1 ans 299 12.2.2 300... 

It is interesting that these results were recently rediscovered [46,47]. At present, such CIS or CIS-like natural orbitals are frequently termed transition orbitals (see [46,48] and similar works on TDDFT calculations). 

Remarkable differences in the retention transition structures between the 1,3-silyl migrations in formyhnethylsilane and the 1,3-silyl migrations in allylsilane are revealed by detailed analysis of geometries, natural bond orbitals, and the Laplacian of the electron density. The presence of BCPs and RCPs was monitored and some typical properties were evaluated at the BCPs. 

Schleyer et al. combine Weinhold s natural bond orbital analysis with calculations using nonrelativistic and quasi-relativistic ECPs to analyze relativistic effects on the Pb—C and Pb—Pb rotational barriers. This work shows that, although relativity has a large effect on interactions between vicinal T—H and T —H bonds that control the barrier height, the effect is of similar magnitude for the minimum (eclipsed conformer) and transition state (staggered conformer), so that rotational barriers are not affected. 

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