Theory and range of modern semiempirical molecular orbital methods

Semiempirical molecular orbital methods have a long history. They serve to tackle large systems and complicated processes beyond the reach of ab initio or density functional methods. Although their setup is derived from Hartree–Fock theory, the design of approximate energy expressions and the empirical parameters are used to achieve higher accuracy than the underlying ab initio theory. In this way the effect of larger basis sets or correlation can be partially simulated. All widely used semiempirical methods establish their accuracy by error statistics for molecular properties with experimental and high-level ab initio or density functional theory calculations as a reference. Their computational efficiency makes them suitable for the study of biochemical systems and solid materials. The present review presents a variety of applications which demonstrate the need for and success of semiempirical methods.     

Assessing conformer energies using electronic structure and machine learning methods

We have performed a large‐scale evaluation of current computational methods, including conventional small‐molecule force fields; semiempirical, density functional, ab initio electronic structure methods; and current machine learning (ML) techniques to evaluate relative single‐point energies. Using up to 10 local minima geometries across ~700 molecules, each optimized by B3LYP‐D3BJ with single‐point DLPNO‐CCSD(T) triple‐zeta energies, we consider over 6500 single points to compare the correlation between different methods for both relative energies and ordered rankings of minima. We find that the current ML methods have potential and recommend methods at each tier of the accuracy‐time tradeoff, particularly the recent GFN2 semiempirical method, the B97‐3c density functional approximation, and RI‐MP2 for accurate conformer energies. The ANI family of ML methods shows promise, particularly the ANI‐1ccx variant trained in part on coupled‐cluster energies. Multiple methods suggest continued improvements should be expected in both performance and accuracy.     

Structural and optical properties of highly hydroxylated fullerenes: stability of molecular domains on the C60 surface

The excitation spectra and the structural properties of highly hydroxylated C(60)(OH)(x) fullerenes (so-called fullerenols) are analyzed by comparing optical absorption experiments on dilute fullerenol-water solutions with semiempirical and density functional theory electronic structure calculations. The optical spectrum of fullerenol molecules with 24-28 OH attached to the carbon surface is characterized by the existence of broad bands with reduced intensities near the ultraviolet region (below approximately 500 nm) together with a complete absence of optical transitions in the visible part of the spectra, contrasting with the intense absorption observed in C(60) solutions. Our theoretical calculations of the absorption spectra, performed within the framework of the semiempirical Zerner intermediate neglect of diatomic differential overlap method [Reviews in Computational Chemistry II, edited by K. B. Lipkowitz and D. B. Boyd (VCH, Weinheim, 1991), Chap. 8, pp. 313-316] for various gas-phase-like C(60)(OH)(26) isomers, reveal that the excitation spectra of fullerenol molecules strongly depend on the degree of surface functionalization, the precise distribution of the OH groups on the carbon structure, and the presence of impurities in the samples. Interestingly, we have surprisingly found that low energy atomic configurations are obtained when the OH groups segregate on the C(60) surface forming molecular domains of different sizes. This patchy behavior for the hydroxyl molecules on the carbon surface leads in general to the formation of fullerene compounds with closed electronic shells, large highest occupied molecular orbital-lowest unoccupied molecular orbital energy gaps, and existence of an excitation spectrum that accounts for the main qualitative features observed in the experimental data.     

Adsorption of functionalized benzoic acids on MgSO4.H2O (100).

Using a combination of ab initio and semiempirical methods, adsorption problems on surfaces with large unit cells and low symmetry can still be studied. Here, a hybrid approach of density functional theory (DFT) and Hartree-Fock (HF) was used. As an example, we determined the geometry and the electronic properties of benzoic acid (BA), salicylic acid (SA) and para-salicylic acid (p-SA) adsorbed on MgSO(4).H(2)O (100), which are used as conditioner molecules for the electrostatic separation of minerals. Contrary to general expectations, these molecules are chemisorbed, with binding energies around 1.9 eV, forming bonds through the carboxylic O atom of the COOH groups in a nonplanar geometry, although the surface is a stoichiometric wide-band-gap insulator and the molecules stay intact. In contrast, a planar adsorption geometry turned out to be nonbonding. Bonding takes place by means of surface-molecule resonances due to the overlap of the valence band with molecular orbitals, assisted by a small charge-transfer molecule to the surface of around 0.15e. These combined interactions cause an intramolecular twist between the COOH group and the benzene ring.     

Electronic coupling matrix elements from charge constrained density functional theory calculations using a plane wave basis set

We present a plane wave basis set implementation for the calculation of electronic coupling matrix elements of electron transfer reactions within the framework of constrained density functional theory (CDFT). Following the work of Wu and Van Voorhis [J. Chem. Phys. 125, 164105 (2006)], the diabatic wavefunctions are approximated by the Kohn-Sham determinants obtained from CDFT calculations, and the coupling matrix element calculated by an efficient integration scheme. Our results for intermolecular electron transfer in small systems agree very well with high-level ab initio calculations based on generalized Mulliken-Hush theory, and with previous local basis set CDFT calculations. The effect of thermal fluctuations on the coupling matrix element is demonstrated for intramolecular electron transfer in the tetrathiafulvalene-diquinone (Q-TTF-Q(-)) anion. Sampling the electronic coupling along density functional based molecular dynamics trajectories, we find that thermal fluctuations, in particular the slow bending motion of the molecule, can lead to changes in the instantaneous electron transfer rate by more than an order of magnitude. The thermal average, (<|H(ab)|(2)>)(1/2)=6.7 mH, is significantly higher than the value obtained for the minimum energy structure, |H(ab)|=3.8 mH. While CDFT in combination with generalized gradient approximation (GGA) functionals describes the intermolecular electron transfer in the studied systems well, exact exchange is required for Q-TTF-Q(-) in order to obtain coupling matrix elements in agreement with experiment (3.9 mH). The implementation presented opens up the possibility to compute electronic coupling matrix elements for extended systems where donor, acceptor, and the environment are treated at the quantum mechanical (QM) level.     

Electronic structures and molecular properties of chalcogen nitrides Se2N2 and SeSN2

The electronic structures and molecular properties of S2N2 as well as the currently unknown chalcogen nitrides Se2N2 and SeSN2 have been studied using various ab initio and density functional methods. All molecules share a qualitatively similar electronic structure and can be primarily described as 2pi-electron aromatics having minor singlet diradical character of 6-8% that can be attributed solely to the nitrogen atoms. This diradical character is manifested in the prediction of their molecular properties, in which coupled cluster and multiconfigurational approaches, as well as density functional methods, show the best performance. The conventional ab initio methods RHF and MP2 completely fail to describe these systems. Predictions for the vibrational frequencies, IR intensities, Raman activities, and 14N, 15N, and 77Se chemical shifts, as well as singlet excitation energies of Se2N2 and SeSN2, have been made. The computed high-level spectroscopic data will be of considerable value in future efforts aimed at the preparation of the conducting polymers (SeN)x and (SeNSN)x.     

Scalable fine-grained parallelization of plane-wave-based ab initio molecular dynamics for large supercomputers

Many systems of great importance in material science, chemistry, solid-state physics, and biophysics require forces generated from an electronic structure calculation, as opposed to an empirically derived force law to describe their properties adequately. The use of such forces as input to Newton's equations of motion forms the basis of the ab initio molecular dynamics method, which is able to treat the dynamics of chemical bond-breaking and -forming events. However, a very large number of electronic structure calculations must be performed to compute an ab initio molecular dynamics trajectory, making the efficiency as well as the accuracy of the electronic structure representation critical issues. One efficient and accurate electronic structure method is the generalized gradient approximation to the Kohn-Sham density functional theory implemented using a plane-wave basis set and atomic pseudopotentials. The marriage of the gradient-corrected density functional approach with molecular dynamics, as pioneered by Car and Parrinello (R. Car and M. Parrinello, Phys Rev Lett 1985, 55, 2471), has been demonstrated to be capable of elucidating the atomic scale structure and dynamics underlying many complex systems at finite temperature. However, despite the relative efficiency of this approach, it has not been possible to obtain parallel scaling of the technique beyond several hundred processors on moderately sized systems using standard approaches. Consequently, the time scales that can be accessed and the degree of phase space sampling are severely limited. To take advantage of next generation computer platforms with thousands of processors such as IBM's BlueGene, a novel scalable parallelization strategy for Car-Parrinello molecular dynamics is developed using the concept of processor virtualization as embodied by the Charm++ parallel programming system. Charm++ allows the diverse elements of a Car-Parrinello molecular dynamics calculation to be interleaved with low latency such that unprecedented scaling is achieved. As a benchmark, a system of 32 water molecules, a common system size employed in the study of the aqueous solvation and chemistry of small molecules, is shown to scale on more than 1500 processors, which is impossible to achieve using standard approaches. This degree of parallel scaling is expected to open new opportunities for scientific inquiry.     

Calculations of molecules,clusters, and solids with a simplified LCAO-DFT-LDA scheme

A simplified LCAO-DFT-LDA scheme for calculations of structure and electronic structure of large molecules, clusters, and solids is presented. Forces on the atoms are calculated in a semiempirical way considering the electronic states. The small computational effort of this treatment allows one to perform molecular dynamics (MD ) simulations of molecules and clusters up to a few hundred atoms as well as corresponding simulations of condensed systems within the Born-Oppenheimer approximation. The accuracy of the method is illustrated by the results of calculations for a series of small molecules and clusters. © 1996 John Wiley & Sons, Inc.     

Quantum chemical study of electronic and structural properties of retinal and some aromatic analogs

The electronic and structural properties of retinal and four analogs were studied using semiempirical, ab initio Hartree-Fock, and density functional theory methods with the aim to evaluate the effects caused by some structural modifications in the ring bound to the polyenic chain and compared with the all-E-trans-retinal molecule. Therefore, some properties such as bond lengths, bond angles, atomic charges derived from electrostatic potential charges from electrostatic potential using grid based method as well as frontier orbitals of the polyenic chain were analyzed. Furthermore, the transition energies of the molecules were also calculated using the Zerner's intermediate neglect of differential overlap-spectroscopic, time-dependent Hartree-Fock, and time-dependent density functional theory methods. The results indicate that in spite of the structural modifications of retinal derivatives in comparison with all-E-trans-retinal, their properties seem similar. Thus, these molecules may behave similarly to all-E-trans-retinal and possibly be attempted in the search of novel molecular devices.     

A sobering assessment of small‐molecule force field methods for low energy conformer predictions

We have carried out a large scale computational investigation to assess the utility of common small‐molecule force fields for computational screening of low energy conformers of typical organic molecules. Using statistical analyses on the energies and relative rankings of up to 250 diverse conformers of 700 different molecular structures, we find that energies from widely used classical force fields (MMFF94, UFF, and GAFF) show unconditionally poor energy and rank correlation with semiempirical (PM7) and Kohn–Sham density functional theory (DFT) energies calculated at PM7 and DFT optimized geometries. In contrast, semiempirical PM7 calculations show significantly better correlation with DFT calculations and generally better geometries. With these results, we make recommendations to more reliably carry out conformer screening.     

Ab initio quality one-electron properties of large molecules: development and testing of molecular tailoring approach

The development of a linear-scaling method, viz. "molecular tailoring approach" with an emphasis on accurate computation of one-electron properties of large molecules is reported. This method is based on fragmenting the reference macromolecule into a number of small, overlapping molecules of similar size. The density matrix (DM) of the parent molecule is synthesized from the individual fragment DMs, computed separately at the Hartree-Fock (HF) level, and is used for property evaluation. In effect, this method reduces the O(N(3)) scaling order within HF theory to an n.O(N'(3)) one, where n is the number of fragments and N', the average number of basis functions in the fragment molecules. An algorithm and a program in FORTRAN 90 have been developed for an automated fragmentation of large molecular systems. One-electron properties such as the molecular electrostatic potential, molecular electron density along with their topography, as well as the dipole moment are computed using this approach for medium and large test chemical systems of varying nature (tocopherol, a model polypeptide and a silicious zeolite). The results are compared qualitatively and quantitatively with the corresponding actual ones for some cases. This method is also extended to obtain MP2 level DMs and electronic properties of large systems and found to be equally successful.     

Implementation of the SCC-DFTB method for hybrid QM/MM simulations within the amber molecular dynamics package

Self-consistent charge density functional tight-binding (SCC-DFTB) is a semiempirical method based on density functional theory and has in many cases been shown to provide relative energies and geometries comparable in accuracy to full DFT or ab initio MP2 calculations using large basis sets. This article shows an implementation of the SCC-DFTB method as part of the new QM/MM support in the AMBER 9 molecular dynamics program suite. Details of the implementation and examples of applications are shown.     

Density matrix renormalization group calculations on relative energies of transition metal complexes and clusters

The accurate first-principles calculation of relative energies of transition metal complexes and clusters is still one of the great challenges for quantum chemistry. Dense lying electronic states and near degeneracies make accurate predictions difficult, and multireference methods with large active spaces are required. Often density functional theory calculations are employed for feasibility reasons, but their actual accuracy for a given system is usually difficult to assess (also because accurate ab initio reference data are lacking). In this work we study the performance of the density matrix renormalization group algorithm for the prediction of relative energies of transition metal complexes and clusters of different spin and molecular structure. In particular, the focus is on the relative energetical order of electronic states of different spin for mononuclear complexes and on the relative energy of different isomers of dinuclear oxo-bridged copper clusters.     

Electronic structure contributions to electron-transfer reactivity in iron-sulfur active sites: 1. Photoelectron spectroscopic determination of electronic relaxation

Electronic relaxation, the change in molecular electronic structure as a response to oxidation, is investigated in [FeX(4)](2)(-)(,1)(-) (X = Cl, SR) model complexes. Photoelectron spectroscopy, in conjunction with density functional methods, is used to define and evaluate the core and valence electronic relaxation upon ionization of [FeX(4)](2)(-). The presence of intense yet formally forbidden charge-transfer satellite peaks in the PES data is a direct reflection of electronic relaxation. The phenomenon is evaluated as a function of charge redistribution at the metal center (Deltaq(rlx)) resulting from changes in the electronic structure. This charge redistribution is calculated from experimental core and valence PES data using a valence bond configuration interaction (VBCI) model. It is found that electronic relaxation is very large for both core (Fe 2p) and valence (Fe 3d) ionization processes and that it is greater in [Fe(SR)(4)](2)(-) than in [FeCl(4)](2)(-). Similar results are obtained from DFT calculations. The results suggest that, although the lowest-energy valence ionization (from the redox-active molecular orbital) is metal-based, electronic relaxation causes a dramatic redistribution of electron density ( approximately 0.7ē) from the ligands to the metal center corresponding to a generalized increase in covalency over all M-L bonds. The more covalent tetrathiolate achieves a larger Deltaq(rlx) because the LMCT states responsible for relaxation are significantly lower in energy than those in the tetrachloride. The large observed electronic relaxation can make significant contributions to the thermodynamics and kinetics of electron transfer in inorganic systems.     

Effects of the 3- and 4-methoxy and acetamide substituents and solvent environment on the electronic properties of N-substituted 1,8-naphthalimide derivatives

The photophysical properties of polar molecules in solution with an intramolecular charge-transfer effect in the excited state depend strongly on the polarity and proticity of the solvents. UV-visible spectra of 1,8-naphthalimide and some N-substituted derivatives in acetic acid, acetonitrile, dichloromethane, and p-dioxane were carried out. Several molecular cluster geometries formed with N-substituted 1,8-naphthalimide derivatives and a large set of random positioning of some solvent molecules in their environment were optimized by a semiempirical method. It provided a complete screening of possible solute-solvent configurations and resulted in a multiple minima hypersurface of the supramolecular systems. With such local minima energies, the main thermodynamic association functions were found. They also provided selected cluster geometries for calculations of vertical electronic transitions with a time-dependent density functional theory (TD-DFT), if the lowest energy structures were considered. Calculated vertical electronic transition energies at the TD-DFT level were compared with experimental data. The experimental absorption UV-visible spectra for the six compounds in the four solvents were performed in our laboratory. Moreover, X-ray photoelectron spectroscospy of the 1,8-naphthalimide was carried out in the ICP-CSIC laboratory. Thermodynamic function values show different association energies between each solvent and the molecules, in correlation with the possibility of hydrogen bond formation and the polarity and dielectric constant of the solvents. The 3- and 4-acetamide 1,8-naphthalimide derivatives have the highest conformer number and the most negative Gibbs free association energy values for a determined solvent. This indicates the importance of the entropic factors.     

A global investigation of excited state surfaces within time-dependent density-functional response theory

This work investigates the capability of time-dependent density functional response theory to describe excited state potential energy surfaces of conjugated organic molecules. Applications to linear polyenes, aromatic systems, and the protonated Schiff base of retinal demonstrate the scope of currently used exchange-correlation functionals as local, adiabatic approximations to time-dependent Kohn-Sham theory. The results are compared to experimental and ab initio data of various kinds to attain a critical analysis of common problems concerning charge transfer and long range (nondynamic) correlation effects. This analysis goes beyond a local investigation of electronic properties and incorporates a global view of the excited state potential energy surfaces.