Neglect Of Diatomic Differential Overlap Research Articles

ULYSSES: An Efficient and Easy to Use Semiempirical Library for C+.

We introduce ULYSSES, a user-friendly and robust C++ library for semiempirical quantum chemical calculations. In its current version, ULYSSES is equipped with a large set of different semiempirical models, most of which are based on the Neglect of Diatomic Differential Overlap (NDDO) approximation. Empirical corrections for dispersion and hydrogen bonding are available for most methods, so that higher quality is achieved in the calculation of energies of nonbonded complexes. The library is furthermore equipped with geometry optimization, as well as modules for calculating molecular properties of general interest. Ideal gas thermodynamics is available and allows single structure as well as conformer (multistructure) averaged properties to be calculated. We offer the possibility to use several vibrational partition functions according to the nature of interactions being studied: for covalent systems, the traditional harmonic oscillator approximation is available; for nonbonded complexes, we systematically extended the partition function proposed by Grimme for all thermodynamic functions. The library is also capable of running Born-Oppenheimer molecular dynamics.

Big data analysis of ab Initio molecular integrals in the neglect of diatomic differential overlap approximation.

Most modern semiempirical quantum-chemical (SQC) methods are based on the neglect of diatomic differential overlap (NDDO) approximation to ab initio molecular integrals. Here, we check the validity of this approximation by computing all relevant integrals for 32 typical organic molecules using Gaussian-type orbitals and various basis sets (from valence-only minimal to all-electron triple-ζ basis sets) covering in total more than 15.6 million one-electron (1-e) and 10.3 billion two-electron (2-e) integrals. The integrals are calculated in the nonorthogonal atomic basis and then transformed by symmetric orthogonalization to the Löwdin basis. In the case of the 1-e integrals, we find strong orthogonalization effects that need to be included in SQC models, for example, by strategies such as those adopted in the available OMx methods. For the valence-only minimal basis, we confirm that the 2-e Coulomb integrals in the Löwdin basis are quantitatively close to their counterparts in the atomic basis and that the 2-e exchange integrals can be safely neglected in line with the NDDO approximation. For larger all-electron basis sets, there are strong multishell orthogonalization effects that lead to more irregular patterns in the transformed 2-e integrals and thus cast doubt on the validity of the NDDO approximation for extended basis sets. Focusing on the valence-only minimal basis, we find that some of the NDDO-neglected integrals are reduced but remain sizable after the transformation to the Löwdin basis; this is true for the two-center 2-e hybrid integrals, the three-center 1-e nuclear attraction integrals, and the corresponding three-center 2-e hybrid integrals. We consider a scheme with a valence-only minimal basis that includes such terms as a possible strategy to go beyond the NDDO integral approximation in attempts to improve SQC methods. © 2018 Wiley Periodicals, Inc.

Semi-Empirical Born-Oppenheimer Molecular Dynamics (SEBOMD) within the Amber Biomolecular Package.

Semi-empirical quantum methods from the neglect of differential diatomic overlap (NDDO) family such as MNDO, AM1, or PM3 are fast albeit approximate quantum methods. By combining them with linear scaling methods like the divide & conquer (D&C) method, it is possible to quickly evaluate the energy of systems containing hundreds to thousands of atoms. We here present our implementation in the Amber biomolecular package of a SEBOMD module that provides a way to run semi-empirical Born-Oppenheimer molecular dynamics. At each step of a SEBOMD, a fully converged self-consistent field (SCF) calculation is performed to obtain the semiempirical quantum potential energy of a molecular system encaged or not in periodic boundary conditions. We describe the implementation and the features of our SEBOMD implementation. We show the requirements to conserve the total energy in NVE simulations, and how to accelerate SCF convergence through density matrix extrapolation. Specific ways of handling periodic boundary conditions using mechanical embedding or electrostatic embedding through a tailored quantum Ewald summation is developed. The parallel performance of SEBOMD simulations using the D&C scheme are presented for liquid water systems of various sizes, and a comparison between the traditional full diagonalization scheme and the D&C approach for the reproduction of the structure of liquid water illustrates the potentiality of SEBOMD to simulate molecular systems containing several hundreds of atoms for hundreds of picoseconds with a quantum mechanical potential in a reasonable amount of CPU time.

Semiempirical molecular orbital models based on the neglect of diatomic differential overlap approximation

AbstractSemiempirical molecular orbital (SEMO) models based on the neglect of diatomic differential overlap (NDDO) approximation efficiently solve the self‐consistent field equations by rather drastic approximations. The computational efficiency comes at the cost of an error in the electron‐electron repulsion integrals. The error may be compensated by the introduction of parametric expressions to evaluate the electron‐electron repulsion integrals, the one‐electron integrals, and the core‐core repulsion. We review the resulting formalisms of popular NDDO‐SEMO models (such as the MNDO(/d), AM1, PMx, and OMx models) in a concise and self‐contained manner. We discuss the approaches to implicitly and explicitly describe electron correlation effects within NDDO‐SEMO models and we dissect strengths and weaknesses of the different approaches in a detailed analysis. For this purpose, we consider the results of recent benchmark studies. Furthermore, we apply bootstrapping to perform a sensitivity analysis for a selection of parameters in the MNDO model. We also identify systematic limitations of NDDO‐SEMO models by drawing on an analogy to Kohn‐Sham density functional theory.

Improving solvation energy predictions using the SMD solvation method and semiempirical electronic structure methods.

The PM6 implementation in the GAMESS program is extended to elements requiring d-integrals and interfaced with the conducter-like polarized continuum model of solvation, including gradients. The accuracy of aqueous solvation energies computed using AM1, PM3, PM6, and DFT tight binding (DFTB) and the Solvation Model Density (SMD) continuum solvation model is tested using the Minnesota Solvation Database data set. The errors in SMD solvation energies predicted using Neglect of Diatomic Differential Overlap (NDDO)-based methods are considerably larger than when using density functional theory (DFT) and HF, with root mean square error (RMSE) values of 3.4-5.9 (neutrals) and 6-15 kcal/mol (ions) compared to 2.4 and ∼5 kcal/mol for HF/6-31G(d). For the NDDO-based methods, the errors are especially large for cations and considerably higher than the corresponding conductor-like screening model results, which suggests that the NDDO/SMD results can be improved by re-parameterizing the SMD parameters focusing on ions. We found that the best results are obtained by changing only the radii for hydrogen, carbon, oxygen, nitrogen, and sulfur, and this leads to RMSE values for PM3 (neutrals: 2.8/ions: ∼5 kcal/mol), PM6 (4.7/∼5 kcal/mol), and DFTB (3.9/∼5 kcal/mol) that are more comparable to HF/6-31G(d) (2.4/∼5 kcal/mol). Although the radii are optimized to reproduce aqueous solvation energies, they also lead more accurate predictions for other polar solvents such as dimethyl sulfoxide, acetonitrile, and methanol, while the improvements for non-polar solvents are negligible.

Comprehensive Analysis of the Neglect of Diatomic Differential Overlap Approximation.

Many modern semiempirical molecular orbital models are built on the neglect of diatomic differential overlap (NDDO) approximation. An in-depth understanding of this approximation is therefore indispensable to rationalize the success of these semiempirical molecular orbital models and to develop further improvements on them. The NDDO approximation provides a recipe to approximate electron-electron repulsion integrals (ERIs) in a symmetrically orthogonalized basis based on a far smaller number of ERIs in a locally orthogonalized basis. We first analyze the NDDO approximation by comparing ERIs in both bases for a selection of molecules and for a selection of basis sets. We find that the errors in Hartree-Fock and second-order Møller-Plesset perturbation theory energies grow roughly linearly with the number of basis functions. We then examine different approaches to correct for the errors caused by the NDDO approximation and propose a strategy to directly correct for them in the two-electron matrices that enter the Fock operator.

Random versus Systematic Errors in Reaction Enthalpies Computed Using Semiempirical and Minimal Basis Set Methods.

The connectivity-based hierarchy (CBH) protocol for computing accurate reaction enthalpies developed by Sengupta and Raghavachari is tested for fast ab initio methods (PBEh-3c, HF-3c, and HF/STO-3G), tight-binding density functional theory (DFT) methods (GFN-xTB, DFTB, and DFTB-D3), and neglect-of-diatomic-differential-overlap (NDDO)-based semiempirical methods (AM1, PM3, PM6, PM6-DH+, PM6-D2, PM6-D3H+, PM6-D3H4X, PM7, and OM2) using the same set of 25 reactions as in the original study. For the CBH-2 scheme, which reflects the change in the immediate chemical environment of all of the heavy atoms, the respective mean unsigned error relative to G4 for PBEh-3c, HF-3c, HF/STO-3G, GFN-xTB, DFTB-D3, DFTB, PM3, AM1, PM6, PM6-DH+, PM6-D3, PM6-D3H+, PM6-D3H4X, PM7, and OM2 are 1.9, 2.4, 3.0, 3.9, 3.7, 4.5, 4.8, 5.5, 5.4, 5.3, 5,4, 6.5, 5.3, 5.2, and 5.9 kcal/mol, with a single outlier removed for HF-3c, PM6, PM6-DH+, PM6-D3, PM6-D3H4X, and PM7. The increase in accuracy for the NDDO-based methods is relatively modest due to the random errors in predicted heats for formation.

A Multidimensional B-Spline Correction for Accurate Modeling Sugar Puckering in QM/MM Simulations.

The computational efficiency of approximate quantum mechanical methods allows their use for the construction of multidimensional reaction free energy profiles. It has recently been demonstrated that quantum models based on the neglect of diatomic differential overlap (NNDO) approximation have difficulty modeling deoxyribose and ribose sugar ring puckers and thus limit their predictive value in the study of RNA and DNA systems. A method has been introduced in our previous work to improve the description of the sugar puckering conformational landscape that uses a multidimensional B-spline correction map (BMAP correction) for systems involving intrinsically coupled torsion angles. This method greatly improved the adiabatic potential energy surface profiles of DNA and RNA sugar rings relative to high-level ab initio methods even for highly problematic NDDO-based models. In the present work, a BMAP correction is developed, implemented, and tested in molecular dynamics simulations using the AM1/d-PhoT semiempirical Hamiltonian for biological phosphoryl transfer reactions. Results are presented for gas-phase adiabatic potential energy surfaces of RNA transesterification model reactions and condensed-phase QM/MM free energy surfaces for nonenzymatic and RNase A-catalyzed transesterification reactions. The results show that the BMAP correction is stable, efficient, and leads to improvement in both the potential energy and free energy profiles for the reactions studied, as compared with ab initio and experimental reference data. Exploration of the effect of the size of the quantum mechanical region indicates the best agreement with experimental reaction barriers occurs when the full CpA dinucleotide substrate is treated quantum mechanically with the sugar pucker correction.

The hpCADD NDDO Hamiltonian: Parametrization.

A neglect of diatomic differential overlap (NDDO) Hamiltonian has been parametrized as an electronic component of a polarizable force field. Coulomb and exchange potentials derived directly from the NDDO Hamiltonian in principle can be used with classical potentials, thus forming the basis for a new generation of efficiently applicable multipolar polarizable force fields. The new hpCADD Hamiltonian uses force-field-like atom types and reproduces the electrostatic properties (dipole moment, molecular electrostatic potential) and Koopmans' theorem ionization potentials closely, as demonstrated for a large training set and an independent test set of small molecules. The Hamiltonian is not intended to reproduce geometries or total energies well, as these will be controlled by the classical force-field potentials. In order to establish the hpCADD Hamiltonian as an electronic component in force-field-based calculations, we tested its performance in combination with the 3D reference interaction site model (3D RISM) for aqueous solutions. Comparison of the resulting solvation free energies for the training and test sets to atomic charges derived from standard procedures, exact solute-solvent electrostatics based on high-level quantum-chemical reference data, and established semiempirical Hamiltonians demonstrates the advantages of the hpCADD parametrization.

Assessment of semi-empirical molecular orbital calculations for describing magnetic interactions

We report a thorough comparison between the spin-unrestricted semi-empirical molecular orbital (SE-UMO) and density functional theory (UDFT) calculations for a variety of π-conjugated diradical molecules which exhibit through-bond magnetic exchange interactions. The spin-unrestricted neglect of diatomic differential overlap (NDDO)-based methods (UPM6 and UrPM6) and self-consistent charge density functional tight-biding (UDFTB) are examined. The UCAM-B3LYP method is used as a representative of UDFT. We have found that NDDO-based and UDFTB methods give different performances with respect to the results of UCAM-B3LYP. The degree of diradical character in the target systems decreases in the order of UPM6>UrPM6≈UCAM-B3LYP>UDFTB. The conventional UPM6 and UDFTB calculations tend to overestimate and underestimate the diradical character, respectively, whereas UrPM6 is able to provide much the same results as UCAM-B3LYP. This is convincing evidence that UrPM6 will be useful for in silico screening of materials science at much lower computational cost.

Semiempirical Quantum-Chemical Orthogonalization-Corrected Methods: Benchmarks for Ground-State Properties.

The semiempirical orthogonalization-corrected OMx methods (OM1, OM2, and OM3) go beyond the standard MNDO model by including additional interactions in the electronic structure calculation. When augmented with empirical dispersion corrections, the resulting OMx-Dn approaches offer a fast and robust treatment of noncovalent interactions. Here we evaluate the performance of the OMx and OMx-Dn methods for a variety of ground-state properties using a large and diverse collection of benchmark sets from the literature, with a total of 13035 original and derived reference data. Extensive comparisons are made with the results from established semiempirical methods (MNDO, AM1, PM3, PM6, and PM7) that also use the NDDO (neglect of diatomic differential overlap) integral approximation. Statistical evaluations show that the OMx and OMx-Dn methods outperform the other methods for most of the benchmark sets.

Computer simulation and study of the IR spectra of irradiated polymer materials

Within the framework of MDDP the calculations of IR spectra have been performed for the initial polyethylene terephthalate (PET) and its state with the cation which satisfactorily describing experimental data. The calculations were made using the MDDP (modified neglect of diatomic differential overlap), implemented in the program MOPAC 2012. A feature of the method is that the overlap integrals are replaced by the δ-function, single-site Coulomb and exchange integrals are calculated by atomic parameters Slater-Condon. In recent years the studies of the structure and physico-chemical properties of polyethylene terephthalate and composites made on it basis have got the intensive development. Comparison of calculations with experimental data gives their satisfactory agreement.

Nucleic acid reactivity: challenges for next-generation semiempirical quantum models.

Semiempirical quantum models are routinely used to study mechanisms of RNA catalysis and phosphoryl transfer reactions using combined quantum mechanical (QM)/molecular mechanical methods. Herein, we provide a broad assessment of the performance of existing semiempirical quantum models to describe nucleic acid structure and reactivity to quantify their limitations and guide the development of next-generation quantum models with improved accuracy. Neglect of diatomic differential overlap and self-consistent density-functional tight-binding semiempirical models are evaluated against high-level QM benchmark calculations for seven biologically important datasets. The datasets include: proton affinities, polarizabilities, nucleobase dimer interactions, dimethyl phosphate anion, nucleoside sugar and glycosidic torsion conformations, and RNA phosphoryl transfer model reactions. As an additional baseline, comparisons are made with several commonly used density-functional models, including M062X and B3LYP (in some cases with dispersion corrections). The results show that, among the semiempirical models examined, the AM1/d-PhoT model is the most robust at predicting proton affinities. AM1/d-PhoT and DFTB3-3ob/OPhyd reproduce the MP2 potential energy surfaces of 6 associative RNA phosphoryl transfer model reactions reasonably well. Further, a recently developed linear-scaling "modified divide-and-conquer" model exhibits the most accurate results for binding energies of both hydrogen bonded and stacked nucleobase dimers. The semiempirical models considered here are shown to underestimate the isotropic polarizabilities of neutral molecules by approximately 30%. The semiempirical models also fail to adequately describe torsion profiles for the dimethyl phosphate anion, the nucleoside sugar ring puckers, and the rotations about the nucleoside glycosidic bond. The modeling of pentavalent phosphorus, particularly with thio substitutions often used experimentally as mechanistic probes, was problematic for all of the models considered. Analysis of the strengths and weakness of the models suggests that the creation of robust next-generation models should emphasize the improvement of relative conformational energies and barriers, and nonbonded interactions.

Why many semiempirical molecular orbital theories fail for liquid water and how to fix them.

Water is an extremely important liquid for chemistry and the search for more accurate force fields for liquid water continues unabated. Neglect of diatomic differential overlap (NDDO) molecular orbital methods provide and intriguing generalization of classical force fields in this regard because they can account both for bond breaking and electronic polarization of molecules. However, we show that most standard NDDO methods fail for water because they give an incorrect description of hydrogen bonding, water's key structural feature. Using force matching, we design a reparameterized NDDO model and find that it qualitatively reproduces the experimental radial distribution function of water, as well as various monomer, dimer, and bulk properties that PM6 does not. This suggests that the apparent limitations of NDDO models are primarily due to poor parameterization and not to the NDDO approximations themselves. Finally, we identify the physical parameters that most influence the condensed phase properties. These results help to elucidate the chemistry that a semiempirical molecular orbital picture of water must capture. We conclude that properly parameterized NDDO models could be useful for simulations that require electronically detailed explicit solvent, including the calculation of redox potentials and simulation of charge transfer and photochemistry.

Nitrogen and Sulfur Compounds in Atmospheric Aerosols: A New Parametrization of Polarized Molecular Orbital Model Chemistry and Its Validation against Converged CCSD(T) Calculations for Large Clusters.

The parametrization of the polarized molecular orbital (PMO) method, which is a neglect-of-diatomic-differential-overlap (NDDO) semiempirical method that includes polarization functions on hydrogens, is extended to include the constituents that dominate the nucleation of atmospheric aerosols, including ammonia, sulfuric acid, and water. The parametrization and validation are based mainly on CCSD(T)/CBS results for atmospheric clusters composed of sulfuric acid, dimethylamine, and ammonia and on M06-2X exchange-correlation functional calculations for other constituents of the atmospheric aerosols. The resulting model, called PMO2a, is parametrized for molecules containing any type of H, C, or O, amino or ammonium N, and S atoms bonded to O. The new method gives greatly improved electric polarization compared to any other member of the family of NDDO methods. In addition, PMO2a is shown to outperform previous NDDO methods for atomization energies and atmospheric aerosol reaction energies; therefore, its use can be recommended for realistic simulations.

Improvement of DNA and RNA Sugar Pucker Profiles from Semiempirical Quantum Methods.

Neglect of diatomic differential overlap (NDDO) and self-consistent density-functional tight-binding (SCC-DFTB) semiempirical models commonly employed in combined quantum mechanical/molecular mechanical simulations fail to adequately describe the deoxyribose and ribose sugar ring puckers. This failure limits the application of these methods to RNA and DNA systems. In this work, we provide benchmark ab initio gas-phase two-dimensional potential energy scans of the RNA and DNA sugar puckering. The benchmark calculations are compared with semiempirical models. Pucker corrections are introduced into the semiempirical models via B-spline interpolation of the potential energy difference surface relative to the benchmark data. The corrected semiempirical models are shown to well reproduce the ab initio puckering profiles. Furthermore, we demonstrate that the uncorrected semiempirical models do not usually produce a transition state between the A-form and B-form sugar puckers, but the ab initio transition state is reproduced when the B-spline correction is used.

Can Semi-empirical Calculations Help Solve Mass Spectrometry Problems? Protonation Sites and Proton Affinities of Amino Acids.

Owing to the recent development of the PM6 and PM6-DH+ semi-empirical methodologies, which belong to the neglect of diatomic differential overlap (NDDO) family, it was decided to carry out a study to assess whether these inexpensive and fast methodologies could be used with confidence to help solve mass spectrometry problems. As such, a report on the feasibility of using semi-empirical calculations to identify probable protonation sites in amino acids is presented. The optimised geometries obtained by the semi-empirical calculations were compared to several structures reported in the literature (obtained through high-level theoretical calculations) and reasonable agreement was found. The proton affinities derived from semi-empirical calculations were also compared with experimental data and benchmarked as well with predicted values from the literature (also obtained through high-level theoretical calculations). Semi-empirical calculations accurately predicted the most probable protonation site for all amino acids considered; thus leading to results comparable to those obtained by high-level calculations at an extremely low computational cost. Regarding the proton affinity estimates, deviations from the available experimental values are greater for the semi-empirical proton affinities than for those observed for high-level calculations. A statistical analysis of the data, at a confidence level of 99 %, also showed that the semi-empirical proton affinities were different from experimental values and high-level proton affinities were equivalent to experimental values. Nevertheless, the overall correlation of the semi-empirical data with experimental values is, at least, satisfactory. We believe therefore that this paper shows that semi-empirical methodologies, which are fast and inexpensive, can indeed solve mass spectrometry problems, or at least, facilitate a quicker path to the solution.

Polarized Molecular Orbital Model Chemistry 3. The PMO Method Extended to Organic Chemistry.

The polarized molecular orbital (PMO) method, a neglect-of-diatomic-differential-overlap (NDDO) semiempirical molecular orbital method previously parameterized for systems composed of O and H, is here extended to carbon. We modified the formalism and optimized all the parameters in the PMO Hamiltonian by using a genetic algorithm and a database containing both electrostatic and energetic properties; the new parameter set is called PMO2. The quality of the resulting predictions is compared to results obtained by previous NDDO semiempirical molecular orbital methods, both including and excluding dispersion terms. We also compare the PMO2 properties to SCC-DFTB calculations. Within the class of semiempirical molecular orbital methods, the PMO2 method is found to be especially accurate for polarizabilities, atomization energies, proton transfer energies, noncovalent complexation energies, and chemical reaction barrier heights and to have good across-the-board accuracy for a range of other properties, including dipole moments, partial atomic charges, and molecular geometries.

The SOA formation model combined with semiempirical quantum chemistry for predicting UV-Vis absorption of secondary organic aerosols

A new model for predicting the UV-visible absorption spectra of secondary organic aerosols (SOA) has been developed. The model consists of two primary parts: a SOA formation model and a semiempirical quantum chemistry method. The mass of SOA is predicted using the PHRCSOA (Partitioning Heterogeneous Reaction Consortium Secondary Organic Aerosol) model developed by Cao and Jang [Environ. Sci. Technol., 2010, 44, 727]. The chemical composition is estimated using a combination of the kinetic model (MCM) and the PHRCSOA model. The absorption spectrum is obtained by taking the sum of the spectrum of each SOA product calculated using a semiempirical NDDO (Neglect of Diatomic Differential Overlap)-based method. SOA was generated from the photochemical reaction of toluene or α-pinene at different NO(x) levels (low NO(x): 24-26 ppm, middle NO(x): 49 ppb, high NO(x): 104-105 ppb) using a 2 m(3) indoor Teflon film chamber. The model simulation reasonably agrees with the measured absorption spectra of α-pinene SOA but underestimates toluene SOA under high and middle NO(x) conditions. The absorption spectrum of toluene SOA is moderately enhanced with increasing NO(x) concentrations, while that of α-pinene SOA is not affected. Both measured and calculated UV-visible spectra show that the light absorption of toluene SOA is much stronger than that of α-pinene SOA.

Semiempirical Self-Consistent Polarization Description of Bulk Water, the Liquid−Vapor Interface, and Cubic Ice

We have applied an efficient electronic structure approach, the semiempirical self-consistent polarization neglect of diatomic differential overlap (SCP-NDDO) method, previously parametrized to reproduce properties of water clusters by Chang, Schenter, and Garrett [ J. Chem. Phys. 2008 , 128 , 164111 ] and now implemented in the CP2K package, to model ambient liquid water at 300 K (both the bulk and the liquid-vapor interface) and cubic ice at 15 and 250 K. The SCP-NDDO potential retains its transferability and good performance across the full range of conditions encountered in the clusters and the bulk phases of water. In particular, we obtain good results for the density, radial distribution functions, enthalpy of vaporization, self-diffusion coefficient, molecular dipole moment distribution, and hydrogen bond populations, in comparison to experimental measurements.