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.     

Localized orbitals based on the fermi hole

The Fermi hole provides a direct (non-iterative) method for tansforming canonical SCF molecular orbitals into localized orbitals. Except for simple overlap integrals required to maintain orthogonality, this method requires no integrals over orbitals or basis functions. This method is demonstrated by application to a furanone (C₄H₄O₂), methylacetylene, and boron trifluoride. The results of these calculations are compared to those determined by the orbital centroid criterion of localization.     

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     

Extremely localized molecular orbitals: theory and applications

Orbitals that are extremely localized on molecular fragments represent a powerful tool for a number of purposes: to cite a few examples, they allow to reduce strongly the complexity of calculations on large systems and are easily transferable from one molecule to another, providing a suitable and efficient way to build up the electronic structure of large molecules. Recently, we have developed efficient algorithms to determine extremely localized molecular orbitals (ELMOs), which will be reviewed in this paper. As a rigorous localization is strictly connected to a reduction in the number of variational parameters, which reflects into an increased value of the associated energy with respect to the Hartree Fock value, we have developed a number of strategies to relax the wavefunction built up using transferred localized orbitals. The extreme localization has also been exploited in connection with the “Divide and Conquer” technique to determine the electron densities of large polypeptides assembled from orbitals computed on small model molecules. Moreover, we will discuss the recent application of the ELMOs in the framework of the hybrid QM/MM methods to describe the frontier region. We will also show that the ELMOs can be used to extract chemical interpretations from numerical results. A variety of applications will be presented.     

Extremely localized molecular orbitals (ELMO): a non-orthogonal Hartree-Fock method

A new optimization method for extremely localized molecular orbitals (ELMO) is derived in a non-orthogonal formalism. The method is based on a quasi Newton-Raphson algorithm in which an approximate diagonal-blocked Hessian matrix is calculated through the Fock matrix. The Hessian matrix inverse is updated at each iteration by a variable metric updating procedure to account for the intrinsically small coupling between the orbitals. The updated orbitals are obtained with approximately n ² operations. No n ³ processes such as matrix diagonalization, matrix multiplication or orbital orthogonalization are employed. The use of localized orbitals allows for the creation of high-quality initial “guess” orbitals from optimized molecular orbitals of small systems and thus reduces the number of iterations to converge. The delocalization effects are included by a Jacobi correction (JC) which allows the accurate calculation of the total energy with a limited number of operations. This extension, referred to as ELMO(JC), is a variational method that reproduces the Hartree-Fock (HF) energy with an error of less than 2 kcal/mol for a reduced total cost compared to standard HF methods. The small number of variables, even for a very large system, and the limited number of operations potentially makes ELMO a method of choice to study large systems. Received: 30 December 1996 / Accepted: 5 June 1997     

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.     

Localized orbitals for optimal decomposition of molecular properties

We present the procedure for transforming delocalized molecular orbitals into the localized property-optimized orbitals (LPOs) designed for building the most accurate, in the Frobenius norm sense, approximation to the first-order reduced density matrix in form of the sum of localized monoatomic and diatomic terms. In this way, a decomposition of molecular properties into contributions associated with individual atoms and the pairs of atoms is obtained with the a priori known upper bound for the decomposition accuracy. Additional algorithm is proposed for obtaining the set of “the Chemist's LPOs” (CLPOs) containing a single localized orbital, with nearly double occupancy, per a pair of electrons. CLPOs form an idealized Lewis structure optimized for the closest possible reproduction of one-electron properties derived from the original many-electron wavefunction. The computational algorithms for constructing LPOs and CLPOs from a general wavefunction are presented and their implementation within the open-source freeware program JANPA ( http://janpa.sourceforge.net /) is discussed. The performance of the proposed procedures is assessed using the test set of density matrices of 33 432 small molecules obtained at both Hartree-Fock and second-order Moller-Plesset theory levels and excellent agreement with the chemist's Lewis-structure picture is found.     

Optimal group symmetric localized molecular orbitals

Summary The concept and generating method of optimum group symmetric localized molecular orbitals (OSLMOs) are proposed. The OSLMOs have strong points of orthogonality, equivalence and symmetry, and they are simultaneously as close to the classical VB structure as possible. By using the OSLMOs as one-electron orbitals the multiconfigurational correlation calculations are reduced. The scheme is also a valuable popularization and development to hybridization theory.     

Mixing of generalized parity in molecular orbitals

The concept of generalized parity is introduced. It allows mixing of different symmetries in molecular orbitals in the framework of the Parity Mixing in Orbitals method. An extension of this SCF calculational scheme is also discussed and the relevant secular equations are reported.Alexander von Humboldt Fellow. On leave from the Institute Rudjer Bokovi, Zagreb, Croatia, Yugoslavia.     

On the suitability of strictly localized orbitals for hybrid QM/MM calculations

In the QM/MM method we have developed (LSCF/MM), the QM and the MM parts are held together by means of strictly localized bonding orbitals (SLBOs). Generally these SLBOs are derived from localized bond orbitals (LBOs) that undergo tails deletion, resulting in a nonpredictable change of their properties. An alternative set of SLBOs is provided by the extremely localized molecular orbitals (ELMOs) approach, where the orbitals are rigorously localized on some prefixed atoms without tails on the other atoms of the molecule. A comparative study of SLBOs arising from various localization schemes and ELMOs is presented to test the reliability and the transferability of these functions within the Local Self-Consistent Field (LSCF) framework. Two types of chemical bonds were considered: C--C and C--O single bonds. The localized functions are obtained on the ethane and the methanol molecules, and are tested on beta-alanine and diethyl ether molecules. Moreover, the various protonation forms of beta-alanine have been investigated to illustrate how well the polarity variation of the chemical bond can be handled throughout a chemical process. At last, rotation energy profiles around C--C and C--O bonds are reproduced for butane and fluoromethanol. Energetic, geometric, as well as electronic factors all indicate that ELMO functions are much more transferable from one molecule to another, leading to results closer to the usual SCF reference than any other calculations involving any other localized orbitals. When the shape of the orbital is the most important factor then ELMO functions will perform as well as any other localized orbital.     

The linear combination of localized orbitals methods (LCLO) for polymers

The application of the Linear Combination of Localized Orbitals (LCLO) method to the band structure of polyethylene in the T, TG, TGTG' and G conformations is reported. The method uses full ab initio results on molecules to construct Fock matrix elements and deduce the energy bands. The main advantages of the technique are the low cost and the simplicity. Results are compared with those obtained from published ab initio and empirical calculations.Chargé de Recherches of the Fonds National Belge de la Recherche Scientifique.Titulaire d'une bourse de spécialisation I.R.S.I.A.     

Pseudosymmetry analysis of molecular orbitals

We introduce a pseudosymmetry analysis of molecular orbitals by means of the newly proposed irreducible representation measures. To do that we define first what we consider as molecular pseudosymmetry and the relationships of this concept with those of approximate symmetry and quasisymmetry. We develop a general algorithm to quantify the pseudosymmetry content of a given object within the framework of the finite group algebra. The obtained mathematical expressions are able to decompose molecular orbitals by means of the irreducible representations of any reference symmetry point group. The implementation and usefulness of the pseudosymmetry analysis of molecular orbitals is demonstrated in the study of σ and π orbitals in planar and nonplanar polycyclic aromatic hydrocarbons and the t_2g and e_g character of the d‐orbitals in the [FeH₆]^3? anion in its high spin state along the Bailar twist pathway. © 2013 Wiley Periodicals, Inc.     

An analysis of the complex molecular orbitals method

Numerical results for the ground state of the HN ₂ ⁺ and HCO⁺ molecular ions at their near equilibrium geometry, obtained by the complex molecular orbitals (CMO) method in the extended basis set, are reported. The CMO wavefunction of the HN ₂ ⁺ ion is compared with the CI wavefunction obtained in the same basis set. This reveals the nature of approximations inherent in the CMO method. A peculiar feature of the occupation numbers of the CMO natural orbitals is also explained.Alexander von Humboldt Fellow. On leave from the Institute Rudjer Bokovi, Zagreb, Croatia, Yugoslavia.     

Construction of molecular orbitals localized on polyatomic fragments

A simple method of localizing molecular orbitals on polyatomic molecular fragments is proposed; the method allows one to separate orbitals in the structural units of extended molecules. The method is illustrated by semiempirical calculations of the binuclear bridged complexes [(NH₃)₅Rupy-(C₂H₂)_n-py-Ru(NH₃)₅]⁵⁺ (n = 0,1,2,3). One of possible application is construction of orbital bases for calculations by the configuration interaction method with limited sets of active MOs. Translated fromZhumal Strukturnoi Khimii, Vol. 39, No. 4, pp. 571–578, July–August, 1998.     

Calculation of wave‐functions with frozen orbitals in mixed quantum mechanics/molecular mechanics methods. II. Application of the local basis equation

The application of the local basis equation (Ferenczy and Adams, J. Chem. Phys. 2009 , 130, 134108) in mixed quantum mechanics/molecular mechanics (QM/MM) and quantum mechanics/quantum mechanics (QM/QM) methods is investigated. This equation is suitable to derive local basis nonorthogonal orbitals that minimize the energy of the system and it exhibits good convergence properties in a self‐consistent field solution. These features make the equation appropriate to be used in mixed QM/MM and QM/QM methods to optimize orbitals in the field of frozen localized orbitals connecting the subsystems. Calculations performed for several properties in divers systems show that the method is robust with various choices of the frozen orbitals and frontier atom properties. With appropriate basis set assignment, it gives results equivalent with those of a related approach [G. G. Ferenczy previous paper in this issue] using the Huzinaga equation. Thus, the local basis equation can be used in mixed QM/MM methods with small size quantum subsystems to calculate properties in good agreement with reference Hartree–Fock–Roothaan results. It is shown that bond charges are not necessary when the local basis equation is applied, although they are required for the self‐consistent field solution of the Huzinaga equation based method. Conversely, the deformation of the wave‐function near to the boundary is observed without bond charges and this has a significant effect on deprotonation energies but a less pronounced effect when the total charge of the system is conserved. The local basis equation can also be used to define a two layer quantum system with nonorthogonal localized orbitals surrounding the central delocalized quantum subsystem. © 2013 Wiley Periodicals, Inc.     

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 use of local basis sets for localized molecular orbitals

Two procedures are discussed for the direct variational optimization of localized molecular orbitals which are expanded in local subsets of the molecular basis set. It is shown that a Newton-Raphson approach is more efficient than an iterative diagonalization scheme. The effect of the basis-set truncation on the quality ofab-initio SCF results is investigated for Be, Li₂, HF, H₂O, NH₃, CH₄ and C₂H₆.     

Trap mechanism based on frontier molecular orbitals of additives in polyethylene insulators: A theoretical study and molecular design strategy

In this work, the energy gaps (E_g) of highest occupied orbitals and lowest unoccupied orbitals, trap energies (E_t(e) and E_t(h)) and excited energies of polyethylene model compound, typical defect compound, acetophonene, and 33 designed additives are obtained using density functional method at B3LYP/6–311+G(d, p) level. The correlation between trapping‐electrons (holes) abilities of additives and molecular frontier orbitals is established, and a new understanding for trap mechanism based on chemical molecular orbital levels is given for the first time which could be used to filter qualitative additives as voltage stabilizers of polyethylene. The role of trap energies and the energy gaps on discussing space charge accumulation and electric breakdown is analyzed in detail. A molecular design strategy for potential additives of cross‐linked polyethylene insulated high‐voltage cable is shown based on conjugation effect, substituents character, and polycyclic aromatic compounds. © 2015 Wiley Periodicals, Inc.