(Hyper)polarizability density analysis for open-shell molecular systems based on natural orbitals and occupation numbers

123

121

The fractional occupation number weighted density (FOD) analysis is explored as a general theoretical diagnostic for complicated electronic structures. Its main feature is to provide robustly and quickly the information on the localization of "hot" (strongly correlated and chemically active) electrons in a molecule. We demonstrate its usage in four different prototypical applications: 1) As a new and fast measure of the biradical character of polycyclic aromatic hydrocarbons, 2) for the selection of active orbital spaces in multiconfigurational or complete active space self consistent field (MCSCF/CASSCF) treatments, 3) as a possibility to describe molecular-energy landscapes consistently in regions with varying biradical character, as exemplified by partial double-bond torsions, and 4) as a powerful visualization method for static electron correlation effects in large biomolecules in connection with an efficient semi-empirical tight-binding molecular orbital scheme. The last application opens a full quantum-mechanical, unbiased route to the automatic detection of errors in experimental protein X-ray structures, such as false protonation states or misplaced atoms. In the first example, the complete (unfragmented) quantum-chemical calculation of the FOD for an entire metalloprotein with more than 7500 atoms is described.

Section: Resultsmentioning

confidence: 99%

The Fractional Occupation Number Weighted Density as a Versatile Analysis Tool for Molecules with a Complicated Electronic Structure

Bauer

Hansen

Grimme

2017

123

121

“…The term min(2− n k , n k ) can be regarded as the probability for the electron of being unpaired in the k th NO φ k ( r ). In the case of n HONO + n LUNO =2, which is satisfied exactly in single‐determinant schemes and approximately in general, the diradical character leads y =Tr[

D \binom{odd}{y}

( r )]/2, highlighting that the spatial distribution of y is described by the odd electron densities …”

Section: Model Systems and Calculation Methodsmentioning

confidence: 75%

“…The diradical character y 0 is defined by the occupation numbers ( n L ) of the lowest unoccupied natural orbital (LUNO) . The open‐shell character of a molecule can be described by the spatial distribution of the odd‐electron densities

D \binom{odd}{LUNO}

( r ) and

D \binom{odd}{HONO}

( r ), where HONO means the highest occupied natural orbital.…”

Section: Model Systems and Calculation Methodsmentioning

confidence: 99%

“…The open‐shell character of a molecule can be described by the spatial distribution of the odd‐electron densities

D \binom{odd}{LUNO}

( r ) and

D \binom{odd}{HONO}

( r ), where HONO means the highest occupied natural orbital. We obtained

D \binom{odd}{y}

( r )=

D \binom{odd}{HONO}

( r )+

D \binom{odd}{LUMO}

( r ), where each of the contributions is defined as

D \binom{odd}{k}

( r )=min(2− n k , n k )

ϕ \binom{*}{k}

( r ) φ k ( r ) . The term min(2− n k , n k ) can be regarded as the probability for the electron of being unpaired in the k th NO φ k ( r ).…”

Section: Model Systems and Calculation Methodsmentioning

confidence: 99%

See 1 more Smart Citation

Diradical Character Tuning for the Third‐Order Nonlinear Optical Properties of Quinoidal Oligothiophenes by Introducing Thiophene‐S,S‐dioxide Rings

Kishi

Ochi

Izumi

et al. 2015

Self Cite

To create a design guideline for efficient third-order nonlinear optical (NLO) molecules, the chain-length (n) dependences of the diradical character y and the longitudinal second hyperpolarizability γ of quinoidal oligothiophenes (QTs), from monomers to octamers, involving thiophene-S,S-dioxide rings are investigated by using the density functional theory method. It turns out that the diradical character of the modified QTs is reduced as compared to those of the pristine QTs. By introducing an appropriate number of oxidized rings into the QT framework, intermediate y values can be achieved even in the systems with large values of n, in which the pristine QTs are predicted to have pure diradical character. Such intermediate diradical oligomers are shown to exhibit enhanced γ values as compared to the pristine QTs with the same value for n. From the calculation results, the introduction of the optimal number of thiophene-S,S-dioxide rings is predicted to be an efficient chemical modification for optimizing the third-order NLO properties of open-shell QTs through tuning the diradical characters.

“…Spatial contributions of electrons to y and γ can be visualized by applying analyses of the odd‐electron and γ densities . The odd‐electron density

D_{y}^{odd} (boldr)

related to y is defined by Equation :

true y = \frac{1}{2} \int D_{y}^{odd} (boldr) d r = \frac{1}{2} \int [n_{normalH} {(||, ϕ_{H} (r))}^{2} + n_{normalL} {(||, ϕ_{L} (r))}^{2}] d r

…”

Section: Computational Detailsmentioning

confidence: 99%

Tunability of Open‐Shell Character, Charge Asymmetry, and Third‐Order Nonlinear Optical Properties of Covalently Linked (Hetero)Phenalenyl Dimers

Minamida

Kishi

Fukuda

et al. 2018

Self Cite

Tunability of the open-shell character, charge asymmetry, and third-order nonlinear optical (NLO) properties of covalently linked (hetero)phenalenyl dimers are investigated by using the density functional theory method. By changing the molecular species X and substitution position (i, j) for the linker part, a variety of intermonomer distances R and relative alignments between the phenalenyl dimers can be realized from the geometry optimizations, resulting in a wide-range tuning of diradical character y and charge asymmetry. It is found that the static second hyperpolarizabilities along the stacking direction, γ , are one-order enhanced for phenalenyl dimer systems exhibiting intermediate y, a feature that is in good agreement with the "y-γ correlation". By replacing the central carbon atoms of the phenalenyl rings with a boron or a nitrogen, we have also designed covalently linked heterophenalenyl dimers. The introduction of such a charge asymmetry to the open-shell systems, which leads to closed-shell ionic ground states, is found to further enhance the γ values of the systems having longer intermonomer distance R with intermediate ionic character, that is, charge asymmetry. The present results demonstrate a promising potential of covalently linked NLO dimers with intermediate open-shell/ionic characters as a new building block of highly efficient NLO systems.