Combining genetic algorithm and simulated annealing: a molecular geometry optimization study

We introduce a new hybrid approach to determine the ground state geometry of molecular systems. Firstly, we compared the ability of genetic algorithm (GA) and simulated annealing (SA) to find the lowest energy geometry of silicon clusters with six and 10 atoms. This comparison showed that GA exhibits fast initial convergence, but its performance deteriorates as it approaches the desired global extreme. Interestingly, SA showed a complementary convergence pattern, in addition to high accuracy. Our new procedure combines selected features from GA and SA to achieve weak dependence on initial parameters, parallel search strategy, fast convergence and high accuracy. This hybrid algorithm outperforms GA and SA by one order of magnitude for small silicon clusters (Si₆ and Si₁₀). Next, we applied the hybrid method to study the geometry of a 20-atom silicon cluster. It was able to find an original geometry, apparently lower in energy than those previously described in literature. In principle, our procedure can be applied successfully to any molecular system.     

Isomerization of stilbene using enforced geometry optimization

Using our recently proposed quantum chemical model to simulate the effect of external forces acting on a molecule (Wolinski and Baker, Mol Phys 2009, 107, 2403), which we subsequently termed enforced geometry optimization (EGO), we investigate structural isomerism in C₁₄H₁₂, starting from cis‐stilbene. By applying an external force to pairs of carbon atoms, one from each “half” of the molecule, we have generated 10 different structural isomers. Each was characterized as a minimum by vibrational analysis. Not only can EGO generate potentially new, metastable isomers it can also provide good initial guesses for transition states connecting the starting and final structures, thus giving an estimate of the stability of the new isomers to rearrangement back to the starting material. In addition to the new isomers, we provide a full set of vibrational fundamentals for cis‐ and trans‐stilbene and 4a,4b‐dihydrophenanthrene. The agreement with experimental assignments is excellent, with mean average deviations for the stilbenes of 5.0 cm^?1 or less. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

Invariance criteria and symmetry conservation rules for geometry optimizations

The objective of this paper is to analyze the behaviour of some minimization methods such as steepest descent method, generalized Newton and quasi-Newton methods under transformations of the variables of the function to be minimized. Energy and molecular coordinates are the function and the variables, respectively, in the case of geometry optimizations. Invariant levels are shown to be decisive for the area where the minimization methods can be successfully employed without rescaling of the coordinates. Specific conditions for symmetry conservation are worked out in context of invariant levels. Symmetry making, breaking and conservation are shown with working examples of geometry optimizations and calculation of energy minimum paths on the basis of certain kinds of molecular coordinates.     

The Cotton-Mouton effect of neon and argon: a benchmark study using highly correlated coupled cluster wave functions

The Cotton-Mouton effect (magnetic field induced linear birefringence) has been studied for neon and argon using state-of-the-art coupled cluster techniques. The coupled cluster singles, doubles and triples (CCSDT) approach has been used to obtain static benchmark results and the CC3 model with an approximate treatment of triple excitations to obtain frequency-dependent results. In the case of neon the effect of excitations beyond triples has also been estimated via coupled cluster calculations including quadruple excitations (CCSDTQ), pentuple excitations (CCSDTQP), etc. up to the full configuration-interaction level. The results obtained for the anisotropy of the hypermagnetizability Deltaeta(omega), the molecular property that determines the magnetic field induced birefringence of spherically symmetric systems, are Deltaeta=2.89 a.u. for neon and Deltaeta=24.7 a.u. for argon, with a negligible effect of frequency dispersion. For neon we could estimate an absolute error on Deltaeta of 0.1 a.u. The accuracy of these results surpasses that of recently reported experimental data.     

Electron localizability indicators ELI and ELIA: the case of highly correlated wavefunctions for the argon atom

Electron localizability indicators based on the same-spin electron pair density and the opposite-spin electron pair density are studied for correlated wavefunctions of the argon atom. Different basis sets and reference spaces are used for the multireference configuration interaction method following the complete active space calculations aiming at the understanding of the effect of local electron correlation when approaching the exact wavefunction. The populations of the three atomic shells of Ar atom in real space are calculated for each case.     

DFT study of bis(picolinato-N,O)-copper(II) complex

The geometry of bis(pyridine-2-carboxylato-N,O)-copper(II) complex is optimized at B3LYP/6-311G^∗ level of theory and compared with experimental data. Comparing the electronic structure of this complex with that of its anionic ligand does not indicate any mechanical strain in the five-membered Cu–O–C–C–N metallocycle. The copper d-electron population of 9.2 corresponds to Cu(II) oxidation state. Using 6-31G^∗ basis sets produces an incorrect non-planar structure of the complex.     

Performance of the semiempirical PM3 (tm) method in the geometry optimization of transition metal complexes

The geometries of three different sets of transition metal compounds are optimized with the semiempirical PM3 (tm) method. The systems under test are: (i) products of cyclometallation, like [Pd{C₆H₄[CH(Me)NH₂]}Br(PPh₃)], (ii) molecular dihydrogen complexes, like [W(CO)₃(H₂)(PR₃)₂], and (iii) H‐BR₂ σ complexes of titanium, like TiCp₂(HBcat)₂ (cat = O₂C₆H₄). The results are compared with available X‐ray and neutron diffraction data, as well as with ab initio molecular orbital and density functional theory results published in the literature. The performance of the PM3 (tm) method ranges from excellent in the case of dihydrogen complexes to very poor in the case of H‐BR₂ complexes. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 562–571, 2000     

Biosynthesis optimization of silver nanoparticles (AgNPs) using Trichoderma longibranchiatum and biosafety assessment with silkworm (Bombyx mori)

Silver nanoparticles (AgNPs) have raised public concern due to their widespread application in the field of agriculture, medicine, and environment and their potential toxic effects on humans and the environments. In this study, biosynthesis of nanosilver particles mediated by Trichoderma longibranchiatum using orthogonal experimental design (OED) was optimized. Silkworm larvae were exposed via the mulberry leaves to AgNPs to evaluate their toxic effects. The results showed that 2 mmol/L silver nitrate and 55 °C of reaction temperature at pH 7.0 for 24 h were the optimum values for AgNPs biosynthesis with the synthesis amount and antifungal activity of AgNPs as the indices. The characterization of the biosynthesized AgNPs was conducted using electron microscopy, energy dispersive X-ray analysis (EDS), UV/visible spectrophotometry, Fourier transform infrared spectroscopy (FTIR), and X-ray diffraction (XRD). The crystalline structured nanoparticles were spherical or polyhedral with a mean size ranging about 5–50 nm. FTIR showed that many functional group moieties (–OH, –CH₃, –C–O, etc.) involved as a capping and reducing agent in AgNPs biosynthesis. After the larvae were fed with 50 mg/mL AgNPs, there were no obvious adverse effects on the growth of larvae and cocoon quality. Further supplement of AgNPs-B could promote the weight of larvae and the cocoon shell ratio. The data presented herein provided valuable information on a reliable eco-friendly, simple, low-cost biosynthesis of AgNPs and its biosafety evaluation which may contribute to its increased application in the future.     

Proton and lithium cation affinities calculated with floating orbital geometry optimization (FOGO)

The FOGO method is used to calculate proton affinities and lithium cation affinities. The molecules of primary interest in this study are the methyl-substituted amines. In addition, the lithium cation affinity of HF, H₂O, CH₃OH, H₂CO, and HCN are calculated for comparison. Geometries of all species are fully optimized with a double-zeta (DZ) basis set, including polarization on hydrogen and the first-row elements by floating orbitals. Comparison with experimental values demonstrates that structural data and proton affinities resulting from this type of ab initio calculation are of chemical accuracy. The lithium cation affinities are also reasonably well reproduced, but the small experimental differences are not within the accuracy, which can be expected from this type of calculation.     

Geometry optimization and conformational analysis of (C60)N clusters using a dynamic lattice-searching method.

A newly developed unbiased global optimization method, named dynamic lattice searching (DLS), is used to locate putative global minima for all (C6O)N clusters with Girifalco potential up to N=150. A simple greedy strategy is adopted for the basic frame, so DLS has a very high convergence speed and may converge at various configurations. As most structures are packed by basic tetrahedra, some sequences are defined by both configurations and the size of the basic tetrahedra. A sequence-based conformational analysis is carried out with the defined sequences by counting the hit number over 10,000 independent DLS runs for all the cases up to N = 5. It was found that the hit rate of a sequence is related to the size of the basic tetrahedra. U.e of this method proved that the Leary tetrahedral sequence is dominant in a certain range of cluster sizes, although the sequence has no potential energy advantage. The calculation results are also consistent with those of annealing experiments at high temperature, both in magic numbers and height of the peaks in the mass spectrum.     

WebMTA: a web-interface for ab initio geometry optimization of large molecules using molecular tailoring approach

A web-interface for geometry optimization of large molecules using a linear scaling method, i.e., cardinality guided molecular tailoring approach (CG-MTA), is presented. CG-MTA is a cut-and-stitch, fragmentation-based method developed in our laboratory, for linear scaling of conventional ab initio techniques. This interface provides limited access to CG-MTA-enabled GAMESS. It can be used to obtain fragmentation schemes for a given spatially extended molecule depending on the maximum allowed fragment size and minimum cut radius values provided by the user. Currently, we support submission of single point or geometry optimization jobs at Hartree-Fock and density functional theory levels of theory for systems containing between 80 to 200 first row atoms and comprising up to 1000 basis functions. The graphical user interface is built using HTML and Python at the back end. The back end farms out the jobs on an in-house Linux-based cluster running on Pentium-4 Class or higher machines using an @Home-based parallelization scheme (http://chem.unipune.ernet.in/ approximately tcg/mtaweb/).     

FT-IR, FT-Raman spectra, density functional computations of the vibrational spectra and molecular geometry of biomolecule 5-aminouracil

FT-IR and FT-Raman spectra of the biomolecule 5-aminouracil were recorded in the regions 400–4000 cm⁻¹ and 10–3500 cm⁻¹, respectively. The observed vibrational wavenumbers were analyzed and assigned to different normal modes of vibration of the molecule. Density functional calculations were performed to support wavenumber assignments of the observed bands. A comparison with the molecule of uracil was made, and specific scale factors were employed in the predicted wavenumbers of 5-aminouracil. With the purpose of study the important molecule 5-aminouracil, its equilibrium geometry and harmonic wavenumbers were calculated for the first time by the B3LYP DFT method. The vibrational wavenumbers were compared with IR and Raman experimental data. Also good reproduction of the experimental wavenumbers is obtained and the % error is very small. All the tautomeric forms of 5-aminouracil were determined and optimized. The dimer forms were also simulated. The energy, atomic charges and dipole moments were discussed and several general conclusions were underlined.     

Multistructural microiteration technique for geometry optimization and reaction path calculation in large systems

We propose a multistructural microiteration (MSM) method for geometry optimization and reaction path calculation in large systems. MSM is a simple extension of the geometrical microiteration technique. In conventional microiteration, the structure of the non‐reaction‐center (surrounding) part is optimized by fixing atoms in the reaction‐center part before displacements of the reaction‐center atoms. In this method, the surrounding part is described as the weighted sum of multiple surrounding structures that are independently optimized. Then, geometric displacements of the reaction‐center atoms are performed in the mean field generated by the weighted sum of the surrounding parts. MSM was combined with the QM/MM‐ONIOM method and applied to chemical reactions in aqueous solution or enzyme. In all three cases, MSM gave lower reaction energy profiles than the QM/MM‐ONIOM‐microiteration method over the entire reaction paths with comparable computational costs. © 2017 Wiley Periodicals, Inc.     

Constrained numerical gradients and composite gradients: Practical tools for geometry optimization and potential energy surface navigation

A method is proposed to easily reduce the number of energy evaluations required to compute numerical gradients when constraints are imposed on the system, especially in connection with rigid fragment optimization. The method is based on the separation of the coordinate space into a constrained and an unconstrained space, and the numerical differentiation is done exclusively in the unconstrained space. The decrease in the number of energy calculations can be very important if the system is significantly constrained. The performance of the method is tested on systems that can be considered as composed of several rigid groups or molecules, and the results show that the error with respect to conventional optimizations is of the order of the convergence criteria. Comparison with another method designed for rigid fragment optimization proves the present method to be competitive. The proposed method can also be applied to combine numerical and analytical gradients computed at different theory levels, allowing an unconstrained optimization with numerical differentiation restricted to the most significant degrees of freedom. This approach can be a practical alternative when analytical gradients are not available at the desired computational level and full numerical differentiation is not affordable. © 2015 Wiley Periodicals, Inc.     

A new module for constrained multi‐fragment geometry optimization in internal coordinates implemented in the MOLCAS package

A parallel procedure for an effective optimization of relative position and orientation between two or more fragments has been implemented in the MOLCAS program package. By design, the procedure does not perturb the electronic structure of a system under the study. The original composite system is divided into frozen fragments and internal coordinates linking those fragments are the only optimized parameters. The procedure is capable to handle fully independent (no border atoms) fragments as well as fragments connected by covalent bonds. In the framework of the procedure, the optimization of relative position and orientation of the fragments are carried out in the internal “Z‐matrix” coordinates using numerical derivatives. The total number of required single points energy evaluations scales with the number of fragments rather than with the total number of atoms in the system. The accuracy and the performance of the procedure have been studied by test calculations for a representative set of two‐ and three‐fragment molecules with artificially distorted structures. The developed approach exhibits robust and smooth convergence to the reference optimal structures. As only a few internal coordinates are varied during the procedure, the proposed constrained fragment geometry optimization can be afforded even for high level ab initio methods like CCSD(T) and CASPT2. This capability has been demonstrated by applying the method to two larger cases, CCSD(T) and CASPT2 calculations on a positively charged benzene lithium complex and on the oxygen molecule interacting to iron porphyrin molecule, respectively. © 2013 Wiley Periodicals, Inc.     

A flexible correlation group table (CGT) method for the relativistic configuration interaction wavefunctions

A generalized correlation group table (CGT) method is described for the relativistic configuration interaction (RCI) wavefunctions of molecules containing heavy atoms. In this method first four keywords are defined and two properties are discussed in terms of spectroscopic states and double group theory. These definitions and properties are then used to summarize six principles to stipulate the relationship among relativistic states, nonrelativistic states, as well as RCI configurations. The definitions, properties, and principles comprise the generalized CGT method, which facilitates the classification and assignment of the RCI wavefunctions, and thus, provide a general technique for complex systems containing several open shells. Finally, the techniques are exemplified with a few computational models.     

A highly diastereo- and enantioselective copper(I)-catalyzed Henry reaction using a bis(sulfonamide)-diamine ligand

A series of bis(sulfonamide)-diamine (BSDA) ligands were synthesized from commercially available chiral α-amino alcohols and diamines. The chiral BSDA ligand 3a, coordinated with Cu(I), catalyzes the enantioselective Henry reaction with excellent enantioselectivity (up to 99%). Moreover, with the assistance of pyridine, a CuBr-3a system promotes the diastereoselective Henry reaction with various aldehyde substrates and gives the corresponding syn-selective adduct with up to a 99% yield and 32.3:1 syn/anti selectivity. The enantiomeric excess of the syn adduct was 97%.     

Computer Automated Structure Evaluation (CASE) of the teratogenicity of retinoids with the aid of a novel geometry index

Summary The CASE (Computer Automated Structure Evaluation) program, with the aid of a geometry index for discriminating cis and trans isomers, has been used to study a set of retinoids tested for teratogenicity in hamsters. CASE identified 8 fragments, the most important representing the non-polar terminus of a retinoid with an additional ring system which introduces some rigidity in the isoprenoid side chain. The geometry index helped to identify relevant fragments with an all-trans configuration and to distinguish them from irrelevant fragments with other configurations.