Geometry Optimization Step Research Articles

Calculation of the formation enthalpy and the ionic equilibrium constant of organic substances by quantum chemistry methods

Using composite methods of quantum chemical calculations and the atomization method, the values of the enthalpy of formation for a test set of 79 compounds in gas phase were calculated with an accuracy of 3.8, 4.5, 4.7 kJ/mol for the G4, G4MP2, CBS-QB3 methods, respectively. According to the results of statistical analysis of deviations of theoretical values from experimental ones, the presence of an error occurring at the geometry optimization step due to unaccounted correlation effects was revealed. For aliphatic amines and alcohols from the considered set of compounds, the values of the p K a for aqueous solutions were calculated by the G4 method including solvent effects by CPCM model. The existence of a correlation between the error in the p K a calculation and the differences in energy values between the highest occupied and lowest unoccupied molecular orbitals for conjugated acidic and basic forms in the solution phase is revealed. A method is put forward to refine the calculation results, using which the p K a values for 20 amines and 20 alcohols were determined with an accuracy of 0.67 and 0.87 p K a units, respectively.

Geometry Optimization: A Comparison of Different Open-Source Geometry Optimizers.

Based on a series of energy minimizations with starting structures obtained from the Baker test set of 30 organic molecules, a comparison is made between various open-source geometry optimization codes that are interfaced with the open-source QUantum Interaction Computational Kernel (QUICK) program for gradient and energy calculations. The findings demonstrate how the choice of the coordinate system influences the optimization process to reach an equilibrium structure. With fewer steps, internal coordinates outperform Cartesian coordinates, while the choice of the initial Hessian and Hessian update method in quasi-Newton approaches made by different optimization algorithms also contributes to the rate of convergence. Furthermore, an available open-source machine learning method based on Gaussian process regression (GPR) was evaluated for energy minimizations over surrogate potential energy surfaces with both Cartesian and internal coordinates with internal coordinates outperforming Cartesian. Overall, geomeTRIC and DL-FIND with their default optimization method as well as with the GPR-based model using Hartree-Fock theory with the 6-31G** basis set needed a comparable number of geometry optimization steps to the approach of Baker using a unit matrix as the initial Hessian to reach the optimized geometry. On the other hand, the Berny and Sella offerings in ASE outperformed the other algorithms. Based on this, we recommend using the file-based approaches, ASE/Berny and ASE/Sella, for large-scale optimization efforts, while if using a single executable is preferable, we now distribute QUICK integrated with DL-FIND.

The Importance of Solvent Effects in Calculations of NMR Coupling Constants at the Doubles Corrected Higher Random-Phase Approximation

In this work, 242 NMR spin–spin coupling constants (SSCC) in 20 molecules are calculated, either with correlated wave function methods, SOPPA and HRPA(D), or with density functional theory based on the B3LYP, BHandH, or PBE0 functionals. The calculations were carried out with and without treatment of solvation via a polarizable continuum model in both the geometry optimization step and/or the SSCC calculation, and thereby, four series of calculations were considered (the full-vacuum calculation, the full-solvent calculation, and the two cross combinations). The results were compared with experimental results measured in a solvent. With the goal of reproducing experimental values, we find that the performance of the PBE0 and BHandH SSCCs improves upon including solvation effects. On the other hand, the quality of the B3LYP SSCCs worsens with the inclusion of solvation. Solvation had almost no effect on the performance of the SOPPA and HRPA(D) calculations. We find that the PBE0-based calculations of the spin–spin coupling constants have the best agreement with the experimental data.

Sella, an Open-Source Automation-Friendly Molecular Saddle Point Optimizer.

We present a new algorithm for the optimization of molecular structures to saddle points on the potential energy surface using a redundant internal coordinate system. This algorithm automates the procedure of defining the internal coordinate system, including the handling of linear bending angles, for example, through the addition of dummy atoms. Additionally, the algorithm supports constrained optimization using the null-space sequential quadratic programming formalism. Our algorithm determines the direction of the reaction coordinate through iterative diagonalization of the Hessian matrix and does not require evaluation of the full Hessian matrix. Geometry optimization steps are chosen using the restricted step partitioned rational function optimization method, and displacements are realized using a high-performance geodesic stepping algorithm. This results in a robust and efficient optimization algorithm suitable for use in automated frameworks. We have implemented our algorithm in Sella, an open-source software package designed to optimize atomic systems to saddle point structures. We also introduce a new benchmark test comprising 500 molecular structures that approximate saddle point geometries and show that our saddle point optimization algorithm outperforms the algorithms implemented in several leading electronic structure theory packages.

1H/13C chemical shift calculations for biaryls: DFT approaches to geometry optimization.

Twelve common density functional methods and seven basis sets for geometry optimization were evaluated on the accuracy of 1H/13C NMR chemical shift calculations for biaryls. For these functionals, 1H shifts calculations for gas phase optimized geometries were significantly less accurate than those for in-solution optimized structures, while 13C results were not strongly influenced by geometry optimization methods and solvent effects. B3LYP, B3PW91, mPW1PW91 and ωB97XD were the best-performing functionals with lowest errors; among seven basis sets, DGDZVP2 and 6-31G(d,p) outperformed the others. The combination of these functionals and basis sets resulted in high accuracy with CMAEmin = 0.0327 ppm (0.76%) and 0.888 ppm (0.58%) for 1H and 13C, respectively. The selected functionals and basis set were validated when consistently producing optimized structures with high accuracy results for 1H and 13C chemical shift calculations of two other biaryls. This study highly recommends the IEFPCM/B3LYP, B3PW91, mPW1PW91 or ωB97XD/DGDZVP2 or 6-31G(d,p) level of theory for the geometry optimization step, especially the solvent incorporation, which would lead to high accuracy 1H/13C calculation. This work would assist in the fully structural assignments of biaryls and provide insights into in-solution biaryl conformations.

Specific Optical Rotation and Absolute Configuration of Flexible Molecules Containing a 2‐Methylbutyl Residue

Establishing the absolute configuration of flexible molecules is difficult, and specific optical rotation (SOR) might be an optional strategy. However, complex conformation distributions inevitably generate ambiguous results. Herein, the relationship between SORs and the absolute configuration of flexible molecules containing a 2‐methylbutyl residue was studied using quantum chemical calculations. The existence of a nitrogen atom might increase the uncertainty of the predicted SOR. Compared with the optical rotation calculation step, the geometry optimization step is more influential. Computational parameters including hybrid functionals, basis sets, and solvation models could exert a great effect on the Boltzmann distribution, leading to substantial variation in the SORs. To achieve unambiguous SOR prediction results for flexible molecules, the calculation needs to be performed using at least two combinations of different levels.

An Application of the Polarizable Continnum Model for Obtaining Chalcones Magnetic Properties

Chalcones exhibit a wide variety of beneficial biological activities. In addition, these compounds include the prevention of diseases related to oxidative stress. The structural characterization of these molecules by means of analytical techniques can become a difficult task due to the complexity of some structures. However, cases of erroneously established natural product structure review are still found in the literature despite recent advances in spectroscopic techniques. Therefore, it is necessary to develop quantum calculation protocols that can aid in the correct structural ascertainment of these compounds. Thus, in this work, we tried to develop a parameterized protocol for calculations of chemical shift of carbon-13 nuclear magnetic resonance, in order to ensure a correct structural determination of polyphenols, with a focus on chalcones. For this, a series of molecules belonging to this class, with complex and varied structural skeletons, reliably elucidated in the literature, was selected and subjected to stochastic conformational searches using the Monte Carlo method and the Merk molecular force filed. The lower energy conformations of each molecule were selected for the geometry optimization step, performed at the mPW1PW91/6-31G(d) level. The chemical shifts of carbon-13 were calculated at the same level of theory, taking into account the population distribution of Boltzmann. The calculations were affected in both liquid phases, using the Polarizable Continuous Model as an implicit solvation model. The results show that the level of theory applied in the liquid phase allows a good reproduction of the experimental data. The application of the scaling factor allows the cancellation of systematic errors, which means that the values of scaled chemical shift are closer to the experimental ones. Thus, the parameterized protocol proved to be an important tool for the structural elucidation of polyphenols by calculations of carbon-13 nuclear magnetic resonance chemical shifts.

Optimal Design of a Compliant Constant-Force Mechanism to Deliver a Nearly Constant Output Force Over a Range of Input Displacements

This study presents an optimal design procedure, including topology and geometry optimization methods to design a compliant constant-force mechanism, which can generate a nearly constant output force over a range of input displacements. The proposed constant-force mechanism is a passive force regulation device that can be used in various applications such as precision manipulation and overload protection. The numerical optimization problem is treated as an error minimization problem between output and objective forces. Both material and geometric nonlinearities are considered in topology and geometry optimization steps. Although the element stiffness for void and gray elements after topology optimization are quite small comparing with solid elements, their existence also contributes to the output force characteristic of the synthesized mechanisms. As these low-stiffness elements are not easy to manufacture in physical prototype, a helical compression spring is introduced in the topology optimized constant-force mechanism to account for the effect of low-stiffness elements, and an additional geometry optimization step is utilized to identify the spring constant as well as to fine-tune the geometric parameters. The optimized constant-force mechanism is prototyped by three-dimensional printing using flexible thermoplastic elastomer. The experimental results show that the proposed design can generate a nearly constant output force in the input displacement range of 3-6 mm. The developed constant-force mechanism is installed on an electric gripper drive mounted on a robot arm for robotic picking and placing application. Test results show the constant-force gripper can be used in handling of size-varied fragile objects.

Layout optimization of simplified trusses using mixed integer linear programming with runtime generation of constraints

Traditional truss layout optimization employing the ground structure method will often generate layouts that are too complex to fabricate in practice. To address this, mixed integer linear programming can be used to enforce buildability constraints, leading to simplified truss forms. Limits on the number of joints in the structure and/or the minimum angle between connected members can be imposed, with the joints arising from crossover of pairs of members accounted for. However, in layout optimization, the number of constraints arising from ‘crossover joints’ increases rapidly with problem size, along with computational expense. To address this, crossover constraints are here dynamically generated and added at runtime only as required (so-called lazy constraints); speedups of more than 20 times are observed whilst ensuring that there is no loss of solution quality. Also, results from the layout optimization step are shown to provide a suitable starting point for a non-linear geometry optimization step, enabling results to be obtained that are in agreement with literature solutions. It is also shown that symmetric problems may not have symmetric optimal solutions, and that multiple distinct and equally optimal solutions may be found.

Conceptual design of AM components using layout and geometry optimization

In this paper truss layout optimization is used in conjunction with geometry optimization to provide the basis for a powerful conceptual design tool for additively manufactured (AM) components, particularly useful when the degree of design freedom is high. With layout optimization the design domain is discretized using a grid of nodes which are interconnected with discrete line elements, forming a ‘ground structure’. Linear optimization can then be used to identify the subset of elements forming the minimum volume structure required to carry the applied loading. A nonlinear geometry optimization step, which involves adjusting the positions of the nodes, can subsequently be undertaken to simplify and improve the solution. Simple geometrical rules can then be used to automatically transform a line element layout into a 3D continuum, ready for validation and/or manufacture. Various extensions to the basic method are described in the paper, including AM build direction constraints and techniques to permit user-interaction with candidate designs, which has been found to be invaluable at the conceptual design stage. Finally the approach described is applied to a range of design problems, including the redesign of an airbrake hinge for the Bloodhound Supersonic Car.

An Average Solvent Electrostatic Configuration Protocol for QM/MM Free Energy Optimization: Implementation and Application to Rhodopsin Systems

A novel atomistic methodology to perform free energy geometry optimization of a retinal chromophore covalently bound to any rhodopsin-like protein cavity is presented and benchmarked by computing the absorption maxima wavelengths (λmax) of distant rhodopsin systems. The optimization is achieved by computing the Nagaoka's Free Energy Gradient (FEG) within an Average Solvent Electrostatic Configuration (ASEC) atomistic representation of the thermodynamic equilibrium and minimizing such quantity via an iterative procedure based on sequential classical MD and constrained QM/MM geometry optimization steps. The performance of such an ASEC-FEG protocol is assessed at the CASPT2//CASSCF/Amber level by reproducing the λmax values observed for 12 mutants of redesigned human cellular retinol binding protein II (hCRBPII) systems; a set of 10 distant wild-type rhodopsins from vertebrates, invertebrates, eubacteria, and archaea organisms; and finally a set of 10 rhodopsin mutants from an eubacterial rhodopsin. The results clearly show that the proposed protocol, which can be easily extended to any protein incorporating a covalently bound ligand, yields correct λmax trends with limited absolute errors.

Efficient Geometry Minimization and Transition Structure Optimization Using Interpolated Potential Energy Surfaces and Iteratively Updated Hessians.

An efficient geometry optimization algorithm based on interpolated potential energy surfaces with iteratively updated Hessians is presented in this work. At each step of geometry optimization (including both minimization and transition structure search), an interpolated potential energy surface is properly constructed by using the previously calculated information (energies, gradients, and Hessians/updated Hessians), and Hessians of the two latest geometries are updated in an iterative manner. The optimized minimum or transition structure on the interpolated surface is used for the starting geometry of the next geometry optimization step. The cost of searching the minimum or transition structure on the interpolated surface and iteratively updating Hessians is usually negligible compared with most electronic structure single gradient calculations. These interpolated potential energy surfaces are often better representations of the true potential energy surface in a broader range than a local quadratic approximation that is usually used in most geometry optimization algorithms. Tests on a series of large and floppy molecules and transition structures both in gas phase and in solutions show that the new algorithm can significantly improve the optimization efficiency by using the iteratively updated Hessians and optimizations on interpolated surfaces.

QSAR Analysis of Benzothiazole Derivatives of Antimalarial Compounds Based On AM1 Semi-Empirical Method

Quantitative Structure and Activity Relationship (QSAR) analysis of 13 benzothiazoles derivatives compound as antimalarial compounds have been performed using electronic descriptor of the atomic net charges (q), dipole moment (μ), ELUMO, EHOMO and polarizability (α). The electronic structures as descriptors were calculated through HyperChem for Windows 7.0 using AM1 semi-empirical method. The descriptors were obtained through molecules modeling to get the most stable structure after geometry optimization step. The antimalarial activity (IC50) were taken from literature. The best model of QSAR model was determined by multiple linear regression approach and giving equation of QSAR: Log IC50 = 23.527 + 4.024 (qC4) + 273.416 (qC5) + 141.663 (qC6) – 0.567 (ELUMO) – 3.878 (EHOMO)– 2.096 (α). The equation was significant on the 95% level with statistical parameters: n = 13, r = 0.994, r2 = 0.987, SE = 0.094, Fcalc/Ftable = 11.212, and gave the PRESS = 0.348. Its means that there were only a relatively few deviations between the experimental and theoretical data of antimalarial activity.

Atomistic modeling of crystal structure of Ca1.67SiHx

The atomic structure of calcium-silicate-hydrate (C1.67-S-Hx) has been investigated by theoretical methods in order to establish a better insight into its structure. Three models for C-S-H all derived from tobermorite are proposed and a large number of structures were created within each model by making a random distribution of silica oligomers of different size within each structure. These structures were subjected to structural relaxation by geometry optimization and molecular dynamics steps. That resulted in a set of energies within each model. Despite an energy distribution between individual structures within each model, significant energy differences are observed between the three models. The C-S-H model related to the lowest energy is considered as the most probable. It turns out to be characterized by the distribution of dimeric and pentameric silicates and the absence of monomers. This model has mass density which is closest to the experimental one.

25Mg Solid-State NMR of Magnesium Phosphates: High Magnetic Field Experiments and Density Functional Theory Calculations

Natural-abundance 25Mg solid-state NMR data obtained using very high magnetic fields of 17.6, 20.0, and 30.0 T are reported for a series of magnesium phosphate compounds, some of which are of potential biomedical interest. The 25Mg NMR parameters have been calculated by using the DFT PAW and GIPAW methods, for both the experimental and DFT atomic position optimized structures. For most of the studied compounds, the geometry optimization step improves significantly the accuracy of the calculations and good correlations between experimental and calculated 25Mg chemical shifts and quadrupolar coupling constants were achieved showing that this approach can be used to obtain unambiguous assignments of the 25Mg resonances in more complex phosphate compounds. The possibility of recording natural abundance 25Mg NMR spectra in materials with very low Mg content is illustrated for a ∼10% Mg-substituted hydroxyapatite sample. In this case, the distribution of 25Mg quadrupolar coupling measured experimentally has bee...

Quantitative Structure Property Relationship Modeling for Prediction of Retention Index for a Set of Some Organic Compounds

One of the most ubiquitous challenges of the scientists is the theoretical evaluation of experimental parameters to validate and improve their ability. Plant essential oils and their extracts have been greatly employed in folk medicine, food flavoring, fragrance and pharmaceutical industries. This work is a part of our comprehensive investigation to correlate the experimental and calculated retention indices (RI) of the some organic compounds from K. Javidnia et al. The structures of all organic compounds were drawn into the HYPERCHEM program and optimized using semi-empirical AM1 method, applying a gradient limit of 0.01 kcal/A as a stopping criterion for optimized structures prior to geometry optimization step. Then molecular descriptors were calculated for each compound by the DRAGON software on the minimal energy conformations. The Stepwise SPSS was used for the selection of the variables that resulted in the best fitted models. By molecular modeling and calculation of descriptors, four significant descriptors (XMOD, PCD, MATS2e, GATS2e) related to the retention indices values of the essential oils, were identified. After the variables selection, the MLR method used for building the regression models. The statistical figures obtained by the proposed model are R 2 =0.989, RMSEP=53.08, REP =3.83 and SEP =54.94. In the final step, models generated were used to predict the retention index for a set of test compounds.

Quantitative Structure Property Relationship Modeling for Prediction of Retention Index for a Set of Some Organic Compounds

One of the most ubiquitous challenges of the scientists is the theoretical evaluation of experimental parameters to validate and improve their ability. Plant essential oils and their extracts have been greatly employed in folk medicine, food flavoring, fragrance and pharmaceutical industries. This work is a part of our comprehensive investigation to correlate the experimental and calculated retention indices (RI) of the some organic compounds from K. Javidnia et al. The structures of all organic compounds were drawn into the HYPERCHEM program and optimized using semi-empirical AM1 method, applying a gradient limit of 0.01 kcal/A as a stopping criterion for optimized structures prior to geometry optimization step. Then molecular descriptors were calculated for each compound by the DRAGON software on the minimal energy conformations. The Stepwise SPSS was used for the selection of the variables that resulted in the best fitted models. By molecular modeling and calculation of descriptors, four significant descriptors (XMOD, PCD, MATS2e, GATS2e) related to the retention indices values of the essential oils, were identified. After the variables selection, the MLR method used for building the regression models. The statistical figures obtained by the proposed model are R 2 =0.989, RMSEP=53.08, REP =3.83 and SEP =54.94. In the final step, models generated were used to predict the retention index for a set of test compounds.

Structure Resolution of Ba5Al3F19 and Investigation of Fluorine Ion Dynamics by Synchrotron Powder Diffraction, Variable-Temperature Solid-State NMR, and Quantum Computations

The room temperature structure of Ba(5)Al(3)F(19) has been solved using electron microscopy and synchrotron powder diffraction data. One-dimensional (1D) (27)Al and ultrafast magic-angle-spinning (MAS) (19)F NMR spectra have been recorded and are in agreement with the proposed structural model for Ba(5)Al(3)F(19). The (19)F isotropic chemical shift and (27)Al quadrupolar parameters have been calculated using the CASTEP code from the experimental and density functional theory geometry-optimized structures. After optimization, the calculated NMR parameters of both the (19)F and (27)Al nuclei show improved consistency with the experimental values, demonstrating that the geometry optimization step is necessary to obtain more accurate and reliable structural data. This also enables a complete and unambiguous assignment of the (19)F MAS NMR spectrum of Ba(5)Al(3)F(19). Variable-temperature 1D MAS (19)F NMR experiments have been carried out, showing the occurrence of fluorine ion mobility. Complementary insights were obtained from both two-dimensional (2D) exchange and 2D double-quantum dipolar recoupling NMR experiments, and a detailed analysis of the anionic motion in Ba(5)Al(3)F(19) is proposed, including the distinction between reorientational processes and chemical exchange involving bond breaking and re-formation.

How the energy evaluation method used in the geometry optimization step affect the quality of the subsequent QSAR/QSPR models

The quantitative influence of the choice of energy evaluation method used in the geometry optimization step prior to the calculation of molecular descriptors in QSAR and QSPR models was investigated. A total of 11 energy evaluation methods on three molecular datasets (toxicological compounds, aromatic compounds and PPARgamma agonists) were studied. The methods employed were: MMFF94 s, MM3* with epsilon(r) (relative dielectric constant) = 1, MM3* with epsilon(r) = 80, AM1, PM3, HF/STO-3G, HF/6-31G, HF/6-31G(d,p), B3LYP/STO-3G, B3LYP/6-31G, and B3LYP/6-31G(d,p). The 3D-descriptors used in the QSAR/QSPR models were calculated with commercially available molecular descriptor programs primarily directed toward pharmaceutical research. In order to evaluate the uncertainties involved in the QSAR/QSPR predictions bootstrapping was used to validate all models using 1,000 drawings for each data set. The scale free error-term, q(2), was used to compare the relative quality of the models resulting from different optimization methods on the same set of molecules. Depending on the dataset, the average 0.632 bootstrap estimated q(2) varies from 0.55 to 0.57 for the toxicological compounds, from 0.58 to 0.62 for the aromatic compounds, and from 0.69 to 0.75 for the PPARgamma agonists. The B3LYP/6-31G(d,p) provided the best overall results, albeit the increase in q(2) was small in all cases. The results clearly indicate that the choice of the energy evaluation method has very limited impact. This study suggests that QSAR or QSPR studies might benefit from the choice of a rapid optimization method with little or no loss in model accuracy.

Implementation and benchmark tests of the DFTB method and its application in the ONIOM method

AbstractWe present the theoretical and implementation details of the DFTB method with analytical gradients into the Gaussian package. SCF optimization performance with DIIS method is compared with modified Broyden method and Anderson methods, from which DIIS method is to be preferred. The number of geometry optimization steps can be significantly decreased with the Berny algorithm compared to the conjugated gradient method. From the comparison of geometry parameters as well as trends in the change of HOMO and LUMO energies, the results show clearly that DFTB can reproduce values obtained at the B3LYP/6‐31G(d) level well. We also investigated the DFTB method as the low level quantum mechanical (QM) method in an ONIOM (QM:QM′) description for an amino acid model system and found DFTB promising as a method to describe polarization and charge‐transfer effects in large systems. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009