Determination of extremely localized molecular orbitals in the framework of density functional theory

Extremely localized molecular orbitals are rigorously localized on only a preselected set of atoms and do not have any tails outside the localization region. The importance of these orbitals lies in their ability to be transferred from one molecule to another one. A new algorithm to determine extremely localized molecular orbitals in the framework of the density functional theory method is presented. This could also be a valuable tool in the quantum mechanics/molecular mechanics methodology where localized molecular orbitals are used to describe covalent bonds across the frontier region. The present approach is used to build up the electron density of thymopentin, a polypeptide constituted by five residues, starting from extremely localized molecular orbitals determined on a set of model molecules. The results obtained confirm good transferability properties for these orbitals.Proceedings of the 11th International Congress of Quantum Chemistry satellite meeting in honor of Jean-Louis Rivail     

Maximal orbital analysis of molecular wavefunctions

We describe a new way to decompose one-electron orbitals of a molecule into atom-centered or fragment-centered orbitals by an approach that we call “maximal orbital analysis” (MOA). The MOA analysis is based on the corresponding orbital transformation (COT) that has the unique mathematical property of maximizing any sub-trace of the overlap matrix, in Hilbert metric sense, between two sets of nonorthogonal orbitals. Here, one set comprises the molecule orbitals (Hartree–Fock, Kohn–Sham, complete-active-space, or any set of orthonormal molecular orbitals), the other set comprises the basis functions associated with an atom or a group of atoms. We show in prototypical molecular systems such as a water dimer, metal carbonyl complexes, and a mixed-valent transition metal complex, that the MOA orbitals capture very well key aspects of wavefunctions and the ensuing chemical concepts that govern electronic interactions in molecules. © 2019 Wiley Periodicals, Inc.     

Localization of molecular orbitals on fragments

A non‐iterative algorithm for the localization of molecular orbitals (MOs) from complete active space self consistent field (CASSCF) and for single‐determinantal wave functions on predefined moieties is given. The localized fragment orbitals can be used to analyze chemical reactions between fragments and also the binding of fragments in the product molecule with a fragments‐in‐molecules approach by using a valence bond expansion of the CASSCF wave function. The algorithm is an example of the orthogonal Procrustes problem, which is a matrix optimization problem using the singular value decomposition. It is based on the similarity of the set of MOs for the moieties to the localized MOs of the molecule; the similarity is expressed by overlap matrices between the original fragment MOs and the localized MOs. For CASSCF wave functions, localization is done independently in the space of occupied orbitals and active orbitals, whereas, the space of virtual orbitals is mostly uninteresting. Localization of Hartree–Fock or Kohn–Sham density functional theory orbitals is not straightforward; rather, it needs careful consideration, because in this case some virtual orbitals are needed but the space of virtual orbitals depends on the basis sets used and causes considerable problems due to the diffuse character of most virtual orbitals. © 2012 Wiley Periodicals, Inc.     

Optimization of molecular electronic structure calculations. 1. Local symmetry and local symmetricized orbitals

A formalism is suggested of the so-called local symmetricized orbitals to be used for the construction of a symmetricized basis in molecular electronic structure calculations. The local symmetricized orbitals are defined as additive contributions to the symmetry orbitals of a molecule that arise from symmetry operations of a corresponding atom. The local symmetricized orbitals are transformed according to the irreducible representations of the molecular symmetry group. This approach appears to be most suitable for the optimization of quantum mechanical calculations accounting for the spatial symmetry of compounds under consideration. This fact is due to the formalism of the local symmetricized orbitals that explicitly accounts for the local symmetry of basis function centers, which is essential for such optimization.     

Core electron transitions as a probe for molecular chirality: natural circular dichroism at the carbon K-edge of methyloxirane

We have measured for the first time the X-ray natural circular dichroism (XNCD) of a chiral molecule in an isotropic medium. In this condition the only surviving term contributing to CD is the cross product between the electric dipole and the magnetic dipole transition moments. The non-zero value of the magnetic dipole transition moment in a 1s-to-valence electron transition is attributed to contribution of valence states to core molecular orbitals. These results open the way to a "local" chiral molecular analysis and to the study of stereochemically selected photochemical processes.     

Quantifying the symmetry content of the electronic structure of molecules: molecular orbitals and the wave function

A scheme to quantify the symmetry content of the electronic wave function and molecular orbitals for arbitrary molecules is developed within the formalism of Continuous Symmetry Measures (CSMs). After defining the symmetry operation expectation values (SOEVs) as the key quantity to gauge the symmetry content of molecular wavefunctions, we present the working equations to be implemented in order to carry out real calculations using standard quantum chemistry software. The potentialities of a symmetry analysis using this new method are shown by means of some illustrative examples such as the changes induced in the molecular orbitals of a diatomic molecule by an electronegativity perturbation, the breaking of orbital symmetry along the dissociation path of the H(2) molecule, the changes in the molecular orbitals upon a geometrical distortion of the benzene molecule, and the inversion symmetry content in the different spin states of the [Fe(CH(3))(4)](2-) complex.     

An ab initio method for approximation of the frozen molecular fragment

An ab initio method for calculation on many-electron molecular systems with the approximation of the inactive part of a molecule by frozen molecular fragment is presented. In the following method the SCF calculations are performed in two series. First the molecular orbitals resulting from the first SCF calculation (modest basis set) are localized. In the second SCF run, the basis set is extended for the active part of the molecule, while molecular orbitals of the inactive part, selected from the localized set, are kept frozen. The results are in good agreement with the extended basis set calculation.     

STM studies of single molecules: molecular orbital aspects

As a fundamental and frequently referred concept in modern chemistry, the molecular orbital plays a vital role in the science of single molecules, which has become an active field in recent years. For the study of single molecules, scanning tunneling microscopy (STM) has been proven to be a powerful scientific technique. Utilizing specific distribution of the molecular orbitals at spatial, energy, and spin scales, STM can explore many properties of single molecule systems, such as geometrical configuration, electronic structure, magnetic polarization, and so on. Various interactions between the substrate and adsorbed molecules are also understood in terms of the molecular orbitals. Molecular engineering methods, such as mode-selective chemistry based on the molecular orbitals, and resonance tunneling between the molecular orbitals of the molecular sample and STM tip, have stimulated new advances of single molecule science.     

Correlation regions within a localized molecular orbital approach

A hybrid scheme for the computation of reaction energies in large molecular systems is proposed. The approach is based on localized orbitals and allows for the treatment of different parts of a molecule at different computational levels. The localized orbitals are assigned to regions, and then different local correlation methods, such as local MP2 or local CCSD(T), can be applied to different regions. In contrast to previous hybrid schemes, the molecule does not have to be split into parts and, therefore, it is not necessary to saturate dangling bonds using link atoms. For fixed region sizes, the cost of the high-level calculation becomes independent of the molecular size, and it is demonstrated that O(1) scaling can be achieved. Illustrative applications are presented and the convergence of the results with respect to the size of the regions is investigated for reaction energies, barrier heights, and weakly bound complexes.     

A combined freeze-and-cut strategy for the description of large molecular systems using a localized orbitals approach

A technique to reduce the computational effort in calculating ab initio energies using a localized orbitals approach is presented. By exploiting freeze strategy at the self-consistent field (SCF) level and a cut of the unneeded atomic orbitals, it is possible to perform a localized complete active space (CAS-SCF) calculation on a reduced system. This will open the possibility to perform ab initio treatments on very large molecular systems, provided that the chemically important phenomena happen in a localized zone of the molecule. Two test cases are discussed, to illustrate the performance of the method: the cis-trans interconversion curves for the (7Z)-13 ammoniotridec-7-enoate, which demonstrates the ability of the method to reproduce the interactions between charged groups; and the cisoid-transoid energy barrier for the aldehydic group in the C13 polyenal molecule.     

On the defects of molecular symmetry-lobe orbitals

It is proved that two molecular symmetry-lobe orbitals, belonging to different irreducible representations, can have a non-negligible overlap. Using a previously reported multipolar analysis of Gaussian-lobe orbitals (GLOs), it is demonstrated that such defects occur when individual symmetry orbitals (SOs) are both contaminated in a given Y_1m subspace, even if such contaminations are very small. A numerical application illustrates this result in the case of the NH₃ molecule, and it is shown that axial-GLOs allow for the exact cancellation of the symmetry defects.     

Optical properties of current carrying molecular wires

We consider several fundamental optical phenomena involving single molecules in biased metal-molecule-metal junctions. The molecule is represented by its highest occupied and lowest unoccupied molecular orbitals, and the analysis involves the simultaneous consideration of three coupled fluxes: the electronic current through the molecule, energy flow between the molecule and electron-hole excitations in the leads, and the incident and/or emitted photon flux. Using a unified theoretical approach based on the nonequilibrium Green's function method we derive expressions for the absorption line shape (not an observable but a useful reference for considering yields of other optical processes) and for the current induced molecular emission in such junctions. We also consider conditions under which resonance radiation can induce electronic current in an unbiased junction. We find that current driven molecular emission and resonant light induced electronic currents in single molecule junctions can be of observable magnitude under appropriate realizable conditions. In particular, light induced current should be observed in junctions involving molecular bridges that are characterized by strong charge-transfer optical transitions. For observing current induced molecular emission we find that in addition to the familiar need to control the damping of molecular excitations into the metal substrate the phenomenon is also sensitive to the way in which the potential bias is distributed on the junction.     

Quadratically convergent calculation of localized molecular orbitals

Two iterative procedures for the transformation of canonical self-consistent field molecular orbitals to intrinsic localized molecular orbitals are proposed. A first-order method based on a series of (n × n) unitary transformations may be applied to orbitals which are far from convergence. The second method, based on Newton's method, yields quadratic convergence. Numerical results based on Boys' criterion are presented for water, carbon monoxide, boron fluoride, nitric oxide, and methylacetylene. A composite method may be used to obtain rapid convergence for large molecules for which it is not practical to calculate the entire hessian matrix. The performance of the composite method is demonstrated by application to the dinitrogen tetroxide molecule. Highly converged localized molecular orbitals may be obtained for most molecules with five to eight first-order iterations followed by three or four iterations based on either the second-order or composite method.     

Nonequilibrium electronic transport of 4,4'-bipyridine molecular junction

The electronic transport properties of a 4,4'-bipyridine molecule sandwiched between two Au(111) surfaces are studied with a fully self-consistent nonequilibrium Green's-function method combined with the density-functional theory. The 4,4'-bipyridine molecule prefers to adsorb near the hollow site of the Au(111) surface and distorts slightly. The modifications on the electronic structure of the molecule due to the presence of the electrodes are described by the renormalized molecular orbitals, which correspond well to the calculated transmission peaks. The average Fermi level lies close to the lowest unoccupied renormalized molecular orbital, which determines the electronic transport property of the molecular junction under a small bias voltage. The total transmission is contributed by a single channel. The transmission peaks shift with the applied bias voltage, and this behavior depends on the spatial distribution of the renormalized molecular orbitals and the voltage drop along the molecular junction. The shape of the calculated conductance curve of the equilibrium geometric configuration reproduces the main feature of the experimental results, but the value is larger than the measured data by about 6 times. Good agreement with the experimental measurements can be obtained by elongating the molecular junction. The electronic transport behaviors depend strongly on the interface configuration.     

Optimal virtual orbitals to relax wave functions built up with transferred extremely localized molecular orbitals

Extremely localized molecular orbitals (ELMOs), namely orbitals strictly localized on molecular fragments, are easily transferable from one molecule to another one. Hence, they provide a natural way to set up the electronic structure of large molecules using a data base of orbitals obtained from model molecules. However, this procedure obviously increases the energy with respect to a traditional MO calculation. To gain accuracy, it is important to introduce a partial electron delocalization. This can be carried out by defining proper optimal virtual orbitals that supply an efficient set for nonorthogonal configurations to be employed in VB-like expansions.     

Graph theory of molecular orbitals beyond tight-binding approximation

The graph theory of molecular orbitals including second neighbor interactions (η) is considered here. Graphical methods of getting the characteristic polynomial for the π system of a conjugated molecule are given. It is shown that the characteristic polynomial can be factorized if there are symmetries in the molecule.