Orthogonal Molecular Orbitals Research Articles

Heavy-atom-free orthogonal configurative dye 1,7-di-anthra-aza-BODIPY for singlet oxygen generation

Spin-orbit, charge-transfer intersystem crossing (SOCT-ISC) can directly overcome the disadvantages of the traditional heavy-atom effect and improve the generation efficiency of reactive oxygen species (ROS). Since orthogonal molecular orbitals of donor-acceptor (D-A) pairs favor the SOCT-ISC transition, herein aza-borondipyrromethenes (aza-BODIPYs) with 1,7-di-anthracyl groups (An-azaBDP) was successfully prepared, owing to steric hindrance to produce a big dihedral angle between the two molecular orbital (MO) planes. Moreover, according to density functional theory (DFT) and time-dependent density functional theory (TDDFT), the energy difference between the S1-T1 orbitals of An-azaBDP is small and more inclined towards ISC. An-azaBDP can effectively generate singlet oxygen under light irradiation. An-azaBDP with light irradiation can induce apoptosis in SW620 cells, and can serve as a potential candidate for the treatment of cancer cells and tumors.

The spectrum of the atomic orbital overlap matrix and the locality of the virtual electronic density matrix

It is well known that near-linear dependencies in the atomic orbital (AO) basis will impede electronic-structure calculations since the inverse AO overlap matrix will be ill-defined. However, small eigenvalues will also impact the locality of the virtual density matrix. The virtual density matrix is relevant for developing efficient local approaches in electronic-structure theory, and recent literature shows that orthogonal molecular orbitals (MOs) are not optimal for exploiting locality. As size of molecules treated is increasing and high-quality basis sets are used, the problem is becoming more pronounced and challenges similar to those for extended systems appear. Here it is shown that the spectrum of the AO overlap matrix puts severe restrictions on the locality of the virtual density matrix, and that locality cannot be recovered by excluding components corresponding to near-singular eigenvalues. The effect is seen even when eigenvalues are orders of magnitude from being near-singular, and occurs also for small basis sets such as cc-pVDZ depending on the molecular system. Non-orthogonal orbitals do not constitute a solution to the problem, but they may be more convenient since lack of locality in the density matrix can be shifted from MO coefficients to the inverse MO overlap matrix.

Diabatization by Localization in the Framework of Configuration Interaction Based on Floating Occupation Molecular Orbitals (FOMO−CI)

AbstractWe present a diabatization method of general applicability, based on the localization of molecular orbitals on user specified groups of atoms. The method yields orthogonal molecular orbitals similar to the canonical ones for the isolated atom groups, that are the basis to build reference spin‐adapted configurations representing localized or charge transfer excitations. An orthogonal transformation from the adiabatic to the quasi‐diabatic basis is defined by requiring maximum overlap with the diabatic references. We present the diabatization algorithm as implemented in the framework of semiempirical configuration interaction based on floating occupation molecular orbitals (FOMO−CI), but the same transformation can also be applied to ab initio wavefunctions, obtained for instance with state‐average CASSCF. The diabatic representation so obtained and the associated hamiltonian matrix are particularly suited to assess quantitatively the interactions that account for charge and energy transfer transitions, and to analyze the results of nonadiabatic dynamics simulations involving such phenomena.

Dynamic correlation for non-orthogonal reference states: Improved perturbational and variational methods.

The use of non-orthogonal orbitals allows the construction and use of more compact wave functions than offered by standard methods using orthogonal molecular orbitals; in particular, for molecules containing partly occupied atomic orbitals as present, for example, in transition metal complexes. With the purpose of developing efficient dynamic correlation methods, we discuss several new internal correlation methods employing a reference state containing non-orthogonal active orbitals. The non-orthogonal internally contracted perturbation theory approach is improved in several directions. The major improvements are the use of the Dyall Hamiltonian including two-electron interactions within the active space as the zero-order operator, the calculation of third-order energy-corrections, and the inclusion of excitations in the space of active orbitals. The latter improvement corrects for the use of an incomplete reference state. The improvements are tested for the nitrogen molecule and the challenging chromium dimer. The combined use of the improved zero-order Hamiltonian and the inclusion of active space excitations allow us to obtain potential curves for the chromium dimer that are close to those obtained using the larger complete active space reference wave function.

An efficient method for constructing nonorthogonal localized molecular orbitals.

A new method for constructing nonorthogonal localized molecular orbitals (NOLMOs) is presented. The set of highly localized NOLMOs is obtained by minimization of the spread functional starting from an initial set of canonical orthogonal molecular orbitals. To enhance the stability and efficiency, the centroids of the NOLMOs are constrained to be those of the corresponding orthogonal localized molecular orbitals (OLMOs), which are obtained with the Boys criterion in advance. In particular, these centroid constraints make the optimization for each NOLMO independent of the others, which is an attractive feature for application to large systems. The minimization with the constraints incorporated through the multiplier-penalty function method is stable and efficient in convergence. While exhibiting the classical bonding pattern in chemistry and sharing a spatial distribution similar to that of the corresponding OLMOs, the obtained NOLMOs are more compact than the corresponding OLMOs with about 10%-28% reduction in the value of the spread functional and devoid of the troublesome "orthogonalization tails."

Augmented Lagrangian method for order-N electronic structure

Molecular electronic ground-state theories, whether ab initio, or semiempirical are most often formulated as a variational principle, where the electronic ground-state energy, considered a linear or nonlinear functional of a reduced density matrix, obtains a constrained minimum. In this communication, we present a Lagrangian analysis of the self-consistent-field electronic structure problem, which does not resort to the concept of orthogonal molecular orbitals. We also develop a method of constrained minimization efficiently applicable to nonlinear energy functional minimization, as well as to linear models such as tight-binding. The method is able to treat large molecules with an effort that scales linearly with the system size. It has built-in robustness and leads directly to the desired minimal solution. Performance is demonstrated on linear alkane and polyene chains.

Analysis of large-scale multi-configuration self-consistent field wave functions by expectation values of local operators

We have developed a method to analyze multi-configuration self-consistent field wave functions for open-shell systems, which may consist of a very large number of Slater determinants, by calculating their expectation values for (local) one- and two-particle operators in a numerically efficient way. Although the proposed formalism is fully general and applies to any operators referring to a subset of arbitrary orthogonal molecular orbitals, the local operators we use here are defined in terms of localized molecular orbitals. This choice permits to perform a chemically intuitive analysis of the local spin, population and charge fluctuation, also allowing to study electron correlation effects in chemical bonding. We present some applications for ionic and covalent systems considering four small molecules, H2, N2, H2O and CH4, as well as a binary transition metal complex, [Fe2S6]6−.

A molecular orbital valence bond study of 3-methyl sydnone and 3-methyl pseudosydnone

A pair-excitation-multiconfigurational-self-consistent-field (PEMCSCF) study with 10 configurations has been carried out on 3-methyl-1,2,4-oxadiazolin-5-one (3-methyl pseudosydnone) which has normal covalent bonds but is isoelectronic with 3-methyl sydnone for which no single covalent valence bond structure can be drawn. The PEMCSCF results were found to be very similar for the two isoelectronic compounds and an attempt was made to represent the bonding of the sydnone in only two simple molecular-orbital-valence-bond (MOVB) configurations using a Luken-type correlating orbital. A compact minimum basis of Slater–Transform–Preuss functions fitted by six cartesian gaussian orbitals (STP–6G) is used to express the compact representation for chemical comparison to experiment. The molecular geometry was gradient-optimized at the single determinantal level using a 6–31G extended basis set. “Orthonormal Resonance Analysis” is given for the two dominant configurations by noting that the Boys–Reeves configuration interaction algorithm is identical to the Pauling valence bond algorithm except for use of orthogonal molecular orbitals instead of atomic hybrid orbitals. This equivalence permits use of PEMCSCF atomic charges, bond orders, and dipole moments in a slightly modified valence bond interpretation of the unusual bonding of this compound. Although forcing a larger PEMCSCF problem into a minimum basis and only two configurations raises the energy, chemical interpretation is simplified. This comparison between a mesoionic compound and an isoelectric compound with normal bonding offers new understanding of the mesoionic effect.