Open-shell NBOs

Theoretical and Practical Difficulties of Open-Shell NBO Description... 

Open-shell NBOs and Maximum Spin-paired NBOs... 

Figures 2.1-2.3 and Table 2.1 emphasize the important differences between spin-orbitals that are considered equivalent in elementary treatments. This is particularly true for open-shell species, where the notion of pairing electrons of opposite spin in the same spatial orbital is generally unrealistic. Instead, one should visualize open-shell electronic distributions in terms of different orbitals for different spins (DODS), recognizing that distinct Coulomb and exchange forces will generally split paired electrons into spatially distinct spin-orbitals (see Sidebar 2.2). The DODS concept is automatically incorporated into open-shell NBO analysis, where analysis of a and p spin sets proceeds independently in separate output sections, with no presumed relationship between natural orbitals of the two spin sets. Only in rather exceptional cases (e.g., uncorrelated closed-shell singlet species in near-equilibrium geometry) will electrons be found to pair up in the restrictive manner envisioned in elementary textbooks. The DODS concept is generally a more satisfactory conceptual foundation on which to build an accurate and robust picture of closed- and open-shell electronic phenomena.

Open-shell NBO hybridization and bonding patterns present some of the starkest conflicts with freshman textbook concepts. Indeed, elementary textbooks often give no hint of the open-shell (partial diradical) character of open-shell singlet systems... 

In the vertical (trans conformer) geometry of the ground singlet species, the open-shell NBO Lewis structures of the excited triplet species are found to be represented by... 

Table 4.6. Geometries and NBO descriptors 0/MH2 and MH3 metal hydrides of the third transition series of various spin multiplicities (IS + I), illustrating the correlations of metal charge (Qu) with metal hybrid d character (%d, taken as the average of a and 3 hybrids for open-shell species), bond length (Ruw) and angle (9hmh)> and average absolute deviation (Dev. = average %mh — 90" ), from idealized covalent geometry...

However, we can recognize that the essential feature of a Lewis structiu-e is the localized 1-c, 2-c bonding pattern rather than electron pairing per se. Moreover, the a and 3 electrons of open-shell species necessarily experience different Coulomb and exchange forces and may hence lead to different spatial distributions, spin orbitals, and localization patterns. The familiar open-shell concept of different orbitsds for different spins can therefore be extended to a different Lewis structures for different spins (DLSDS) picture, where as usual we associate a Lewis structure with a specified pattern of one-center and two-center (spin-)NBOs. Because the NBO... 

For open-shell systems, where 1-electron density matrices for a and spin sets are no longer equivalent, it is straightforward to analyze each spin density separately for the distinct hybrids and Lewis structures of opposite spin. This emphasizes that the NBO Lewis structure concept refers to a particular localized bonding pattern of one- and two-center interactions rather than to electron pairing per se. Since Coulomb and exchange interactions for a and fi electrons differ appreciably in open-shell systems, the associated spin polarization effects are most naturally described in terms of different Lewis structures for different spins, the default NBO procedure. 

As a somewhat more complex example, let us now consider the case of ozone (O3), which has an open-shell singlet ground state (Sidebar 3.2). The Gaussian input file to obtain the open-shell wavefunction and default NBO analysis for experimental equilibrium geometry Roo= 1-272, 0= 116.8 ) is shown below. 

In this book, we focus primarily on how to obtain the NAO/NBO/NRT descriptors of a chosen wavefunction, rather than on how a wavefunction is chosen. The NAO/NBO/NRT descriptors of UHF-type description (as used throughout this book for open-shell systems) can be compared with the corresponding descriptors of more accurate wavefunctions for insights into the chemically significant differences, if any, that justify a more complex theoretical level. 

Table 4.4 Optimal spin-NBOs for spin-Lewis structures of molecular O2 [Text (4.46a,P)], showing occupancy (and parenthesized degeneracy) for each distinct Ic (no) or 2c ((Too, T oo) feature of the open-shell Lewis structure.

Further examples of open-shell NRTSTR keylists and other special NRT job control keywords for difficult cases (see NBO Manual, p. B-75ff) will be illustrated in the following chapters. 

How can we understand the chemical origins of these spin density patterns The starting point is the different Lewis structures for different spins NBO description of open-shell systems (cf. Section 4.5), which leads to the two distinct spin NBO representations of the Tempone nitroxide bonding pattern, as shown in (7.6a,p) ... 

The nbo aonbo=cs keyword requests storing the CIS-level NBOs in the shared checkpoint file where guess=read will read them as initial guess for the CAS/NBO job. Note that CAS identifies the 1st excited state as nroot=2 whereas CIS uses root=l for this state. Note also that the Gaussian open-shell CAS implementation faik to provide relevant spin density information to NBO, forcing spin-averaged NBO description of reduced accuracy. This restriction strongly detracts from the potential usefulness of CAS calculations for excited-state analysis. However, illustrative use of this method allows one to see how one can still obtain useful NBO-based descriptors of the excited state despite loss of spin information. 

The previous chapter has given considerable evidence for the accuracy of the -based picture in a variety of open- and closed-shell species, based on the high percentage of electron density that is accounted for in Lewis-type NBOs alone. The complete NBO basis set Q, naturally separates into Lewis and non-Lewis components,... 

The high %-Pl (or low %-Pnl) exhibited by numerous open- and closed-shell species gives strong (but indirect) evidence that the resonance-free world described by 4 must closely resemble the full solution 4 of Schrodinger s equation, at least in some average or overall sense. Nevertheless, we expect that the small correction 4 will play the dominant role in certain chemical phenomena of interest, such as aromaticity. In this chapter, we wish to characterize L-type versus NL-type contributions to chemical properties in more direct fashion, seeking to understand the subtle influences of resonance-type delocalization corrections to the localized 4 -based picture. The NBO program includes a powerfiil array of perturbative and... 

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