Partial Geometry Optimization Research Articles

Analytic geometric gradients for the polarizable density embedding model

AbstractThe polarizable density embedding (PDE) model is an advanced fragment‐based QM/QM embedding model closely related to the earlier polarizable embedding (PE) model. PDE features an improved description of permanent electrostatics and further includes non‐electrostatic repulsion. We present an implementation of analytic geometric gradients for the PDE model, which allows for partial geometry optimizations of QM regions embedded in large molecular environments. We benchmark the quality of structures from PE‐QM and PDE‐QM geometry optimizations on a diverse set of small organic molecules embedded in four solvents. The PDE model performs well when targeting Hartree–Fock calculations, but density functional theory (DFT) calculations prove more challenging. We suggest a hybrid PDE‐LJ model which produces solute–solvent structures of good quality for DFT. Finally, we apply the developed model to a theoretical estimation of the solvatochromic shift on the fluorescence emission energy of the environment‐sensitive 4‐aminophthalimide probe based on state‐specific multiconfigurational PDE‐QM calculations.

Data sampling scheme for reproducing energies along reaction coordinates in high-dimensional neural network potentials.

We propose a data sampling scheme for high-dimensional neural network potentials that can predict energies along the reaction pathway calculated using the hybrid density functional theory. We observed that a data sampling scheme that combined partial geometry optimization of intermediate structures with random displacement of atoms successfully predicted the energies along the reaction path with respect to five chemical reactions: Claisen rearrangement, Diels-Alder reaction, [1,5]-sigmatropic hydrogen shift, concerted hydrogen transfer in the water hexamer, and Cornforth rearrangement.

Strength of Si\u2013H \u22ef B charge-inverted hydrogen bonds in 1-silacyclopent-2-enes and 1-silacyclohex-2-enes

It is shown that the H ⋯ B contacts in 1-silacyclohex-2-enes are clearly stabilizing and strong, whereas those in 1-silacyclopent-2-enes are much weaker. This result is supported by analysis of QTAIM-based parameters and appropriate structural changes taking place upon the open form → closed form transformation and is in full agreement with previous NMR spectroscopic data [Wrackmeyer et al. (2006) Appl Organometal Chem 20:99–105]. Also, the influence of electronic and steric effects originating from the presence of specific substituents on the strength of the H ⋯ B contacts is discussed in detail. Some problems and ideas associated with the use of the so-called open-closed method utilized in assessing values of interaction energies are discussed in detail. Particular attention is paid to the correct choice of reference open systems. It is shown that their partial geometry optimization leads to reliable values of interaction energies.

Molecular simulations and density functional theory calculations of bromine in clathrate hydrate phases.

Bromine forms a tetragonal clathrate hydrate structure (TS-I) very rarely observed in clathrate hydrates of other guest substances. The detailed structure, energetics, and dynamics of Br2 and Cl2 in TS-I and cubic structure I (CS-I) clathrate hydrates are studied in this work using molecular dynamics and quantum chemical calculations. X-ray diffraction studies show that the halogen-water-oxygen distances in the cages of these structures are shorter than the sum of the van der Waals radii of halogen and oxygen atoms. This suggests that the stabilizing effects of halogen bonding or other non-covalent interactions (NCIs) may contribute to the formation of the unique tetragonal bromine hydrate structure. We performed molecular dynamics simulations of Br2 and Cl2 clathrate hydrates using our previously developed five-site charge models for the dihalogen molecules [Dureckova et al. Can. J. Chem. 93, 864 (2015)] which reproduce the computed electrostatic potentials of the dihalogens and account for the electropositive σ-hole of the halogen bond donor (the dihalogen). Analysis of the radial distribution functions, enthalpies of encapsulation, velocity and orientation autocorrelation functions, and polar angle distributions are carried out for Br2 and Cl2 guests in various cages to contrast the properties of these guests in the TS-I and CS-I phases. Quantum chemical partial geometry optimizations of Br2 and Cl2 guests in the hydrate cages using the M06-2X functional give short halogen-water distances compatible with values observed in X-ray diffraction experiments. NCI plots of guest-cage structures are generated to qualitatively show the relative strength of the non-bonding interactions between dihalogens and water molecules. The differences between behaviors of Br2 and Cl2 guests in the hydrate cages may explain why bromine forms the unique TS-I phase.

Adsorption behavior of Co and C2H2 on the graphite basal surface: A quantum chemistry study

The adsorption of CO and C2H2 molecules on the perfect basal surface of graphite is investigated by adopting cluster models in conjunction with quantum chemical calculations. The noncovalent interaction potential energy curves for three different orientations of CO and C2H2 molecules with respect to the inert basal plane of graphite are calculated via semi-empirical and Moller-Plesset ab initio methods. Then, we have considered the effects of interaction energies on the C≡O and C≡C bond lengths by performing the partial geometry optimization procedure on the CO-graphite and C2H2-graphite systems in various intermolecular distances. The computational analysis of all physical noncovalent potential energy curves reveals that the relative configurations in which CO and C2H2 molecules approach the graphite sheet from out of the plane have stronger interaction energy and so is more favorable from the energetic viewpoint. This means that the graphite layer prefers to increase its thickness via the chemical vapor deposition of CO and C2H2 on the graphite.

Theoretical study of N20, C20, and B20 clusters “squeezed” inside icosahedral C80 and He80 cages

The equilibrium geometries and spectroscopic and energetic characteristics of model endohedral M20@C 80 n− clusters, in which the guest clusters M20 = N20, C20, and B20 are squeezed inside the fullerene C 80 n− cages (n = 0, 2, 4, and 6), have been calculated at the density functional theory B3LYP/6-31G and B3LYP/6-31G* levels. Analogous calculations with partial geometry optimization have been performed for their congeners M20@He 80 n− with a fixed icosahedral helium cage He80. According to the calculations, all the structures of the N20@C80, C20@C80, and B20@C80 series correspond to local minima of the potential energy surface (all vibrational frequencies are real). In the first cluster, the N20 guest has a structure of a dodecahedron with a diameter of ∼4.0 A. The alternative 10N2@C80 structure containing ten separated endohedral N2 molecules is considerably less favorable and transforms without a barrier to the dodecahedral N20@C80 isomer upon geometry optimization. It has been suggested that, under extreme supercompresison conditions, molecular nitrogen can be associated without barriers into highly endothermal chemically bound clusters of the N20 type. In the helium analogues, the relative position of the N20@He80 and 10N20@He80 structures on the energy scale is determined by the degree of compression and can change its sign with a change in the diameter of the external cage D(He80). The mechanism of gradual assembly of the N20 dodecahedron from the 10N2 set has been traced with a decrease in the diameter D(He80) in the range 7.5–8.6 A. In the C20@C80 cluster, the C20 guest has a structure of a distorted dodecahedron bound to the C80 cage through four “inner” (endohedral) bonds. In the B20@C80 cluster, the B20 guest is severely squeezed along the C5 axis. Its equatorial atoms form ten endohedral B-C bonds to C80 cage atoms. In similar systems, the division of the endoclusters into the internal guest and external cage becomes uncertain. Calculations predict that the isolated “salt” molecules of the L n C20 and L n B20 type in which the C20 and B20 clusters function as anions surrounded by the L atoms of alkali metals (n = 1–6) should be stable to stepwise dissociation accompanied by elimination of separate L atoms and L2 molecules.

Partial geometry optimization with FMO-MP2 gradient: Application to TrpCage

The reliability of protein structure is a critical concern to grasp the insights with respect to residue–residue and residue–ligand interactions by computational methods. In such calculations, the molecular geometries are usually prepared by the optimization of experimental structure with empirical molecular mechanics (MM) parameters. As an alternative to MM methods, we have developed a partial geometry optimization with the fragment molecular orbital (FMO) scheme at the second-order Møller–Plesset perturbation (MP2) level. The TrpCage miniprotein was used as a demonstrative example. The geometries of the central region were partially optimized at the FMO-MP2 and Hartree–Fock (FMO-HF) levels, and the former with the correlation correction showed reasonable agreement with the experimental structure.

Multiconfigurational study on the synchronous mechanisms of the ClO self-reaction leading to Cl or Cl2

For studying the adiabatic and nonadiabatic mechanisms of the ClO (X 2Π) + ClO (X 2Π) → ClOOCl → 2Cl (2 P u) + O2 (X 3Σ − ) reaction (1) and the ClO (X 2Π) + ClO (X 2Π) → ClOOCl → Cl2 (X 1Σ + ) + O2 (X 3Σ − ) reaction (2), we calculated, by partial geometry optimizations under the C2 constraint, the O–O and O–Cl dissociation potential energy curves (PECs) from the five low-lying states of ClOOCl at the CASPT2 level. The CASSCF minimum-energy crossing point (MECP) between the potential energy surfaces of the 1 1A ground state [correlating with the product of reaction (1)] and the 1 3B state [correlating with the product of reaction (2)] states was also determined. Based on the CAS calculation results (PECs, energies, and spin–orbit coupling at the MECP), we predict that reaction (1) occurs along pathway 1: ClO (X 2Π) + ClO (X 2Π) → ClOOCl (1 1A) → 2Cl (2 P u) + O2 (X 3Σ − ) and that reaction (2) occurs along pathway 2: ClO (X 2Π) + ClO (X 2Π) → ClOOCl (1 1A) → 1 1A/1 3B MECP (142.4 cm−1) → ClOOCl (1 3B) → Cl2 (X 1Σ + ) + O2 (X 3Σ − ). The needed energies (relative to the reactant) for pathways 1 and 2 are predicted to be 5.3 and 11.1 kcal/mol, respectively, which indicates that reaction (1) is more favorable than reaction (2). The present work supports the traditional photochemical model for ozone degradation: ClOOCl (1 1A), formed by two ClO (X 2Π), can directly produce O2 plus two Cl atoms.

Correction of Vibrational Broadening in Molecular Dynamics Clusters with the Normal Mode Optimization Method

Vibrational properties of solutions are frequently simulated with clusters of a solute and a few solvent molecules obtained during molecular dynamics (MD) simulations. The raw cluster geometries, however, often provide unrealistic vibrational band broadening, for both ab initio and empirical force fields. In this work, partial optimization in normal-mode coordinates is used on empirical basis to reduce the broadening. The origin of the error is discussed on a simplified two-dimensional system, which indicates that the problem is caused by the anharmonic MD potential, mode coupling, and neglect of quantum effects. Then the procedure of partial geometry optimization on Raman and Raman optical activity (ROA) spectra is applied and analyzed for the solvated lactamide molecule. Comparison to experiment demonstrates that the normal-mode partial optimization technique with a suitable frequency limit can significantly reduce the broadening error. For lactamide, experimental and simulated vibrational bandwidths are compared; the most realistic theoretical spectra are obtained for partially optimized clusters with the vibrational wavenumber cutoff of about 200 cm(-1).

Binding Site Influence on the Electronic Structure and Electron Paramagnetic Resonance Properties of the Phyllosemiquinone Free Radical of Photosystem I

Electronic structure calculations are performed on models of the phyllosemiquinone (PhSQ) free radical in the A(1A) and A(1B) sites of photo system I. Partial geometry optimization of each site is performed, and from the resultant geometry spin densities and hyperfine couplings are calculated. We exploit the ONIOM methodology to progressively build up a model of the A(1A) site and monitor the effect on the spin density distribution of the PhSQ and its hyperfine couplings. For the A(1A) site, we show that while the O1 atom of the PhSQ is not involved in direct hydrogen bonding, the (17)O anisotropic hyperfine coupling for this position is sensitive to interactions with neighboring groups, especially Trp A697 and Phe A689. The results obtained are in agreement with experimental determinations which indicate small differences in (17)O hyperfine couplings for both oxygen atoms. Good agreement between calculated and experimental (1)H and (13)C hyperfine couplings is also found. In addition, we find that a significant (14)N isotropic coupling of 1.4 MHz is calculated for the peptide NH group of Leu A722. The (14)N isotropic hyperfine coupling obtained for the indole nitrogen atom of Trp A697 is calculated to be zero in disagreement with a previous experimental assignment. The spin density distribution of the PhSQ in the A(1B) site is calculated to be very similar to that in the A(1A) site. The presence of just one relatively weak hydrogen bond to the photo system I quinone is proposed to contribute substantially to its relatively low redox potential when compared with the more strongly hydrogen bonded quinone acceptors present in type II reaction centers.

Ab Initio calculations of 3-(trichlorogermyl)propanoylamide structure and nature of its Ge←O coordination bond

Calculations of 3-(trichlorogermyl)propanoylamide molecule containing a Ge←O coordination bond were performed by RHF/6-31G(d) method with full and partial geometry optimization. Its total energy 2.22 kcal mol−1 is lower than that of the molecule with tetracoordinated germanium atoms. Germanium and oxygen atoms initiate the formation of a coordination Ge←O bond in this molecule and are conductors of the electron density transfer from the atoms nearest to the oxygen on the atoms of the germanium coordination polyhedron. No electron density transfer occurs from the oxygen atom to germanium. Upon decrease in the Ge...O distance the axial Ge-Cl bond is polarized much stronger than the equatorial bonds. In the crystalline state of the substance these molecules are fixed in an energetically unfavorable structure.

Quantum-chemical study of chlorophosphoranes: I. Structure of the (C6H5)2PCl3 molecule in gaseous and crystalline states

The quantum-chemical calculations of the (C6H5)2PCl3 molecule were performed by the methods RHF/6-31G(d) and MP2/6-31G(d) with complete and partial optimization of its geometry. The results of calculations were used for evaluating the NQR frequencies of 35Cl and the parameters of asymmetry of the of electric field gradient on the 35Cl nuclei of this molecule. According to the results of calculations with the partial optimization of geometry and to the experimental data of 35Cl NQR the bond lengths were found of central atom P in the solid state of this compound. The mutual influence of its axial and equatorial bonds was studied. It is shown that in chlorophosphoranes the 35Cl NQR frequencies of the axial and equatorial chlorine atoms decrease with the decrease in the bond lengths of phosphorus atom.

Quantum-chemical study of chlorophosphoranes: III. Structure of the molecules of the series (X,X′) a P(Cl3) e . Mutual influence of axial and equatorial substituents

Quantum-chemical calculations by the methods RHF/6-31G(d) and MR2/6-31G(d) of a series of chlorophosphoranes (X,X′)aP(Cl3)e with complete optimization of their geometry were performed. The results of the calculations were used to estimate 35Cl NQR frequencies and asymmetry parameters of the electric field gradient at the 35Cl nuclei of these molecules. From the results of calculations using RHF/6-31G(d) method with partial geometry optimization and experimental data on 35Cl NQR the lengths of the bonds of central P atom of the compounds in solid state were found. Mutual influence of axial and equatorial substituents was revealed. As in other chlorophosphoranes, the decrease in the length of axial or equatorial P-Cl bonds leads to the decrease in NQR frequencies of axial and equatorial chlorine atoms, respectively.

Quantum-chemical study of chlorophosphoranes: II. Structure of molecules of (Cl2) a P(Cl n X3−n ) e series, and mutual influence of axial and equatorial substituents

The quantum-chemical calculations by the methods RHF/6-31G(d) and MP2/6-31G(d) of chlorophosphoranes of a series (Cl2)aP(ClnX3−n)e with complete and partial optimization of their geometry were performed. The results of calculations were used for evaluation of the frequencies of 35Cl NQR and the asymmetry parameters of the electric field gradient on the 35Cl nuclei of these molecules. According to the results of calculations with the partial geometry optimization and the experimental data on 35Cl NQR the bond lengths of central atom P in the solid state of the corresponding compounds were used. A substantial change in the NQR frequencies of the axial chlorine atoms and a weak change in the frequencies of the equatorial ones at a change in the number of the latter was explained.

Dynamic treatment of vibrational energy relaxation in a heterogeneous and fluctuating environment

A computational approach to describe the energy relaxation of a high-frequency vibrational mode in a fluctuating heterogeneous environment is outlined. Extending previous work [H. Fujisaki, Y. Zhang, and J. E. Straub, J. Chem. Phys. 124, 144910 (2006)], second-order time-dependent perturbation theory is employed which includes the fluctuations of the parameters in the Hamiltonian within the vibrational adiabatic approximation. This means that the time-dependent vibrational frequencies along a molecular dynamics trajectory are obtained via a partial geometry optimization of the solute with fixed solvent and a subsequent normal mode calculation. Adopting the amide I mode of N-methylacetamide in heavy water as a test problem, it is shown that the inclusion of dynamic fluctuations may significantly change the vibrational energy relaxation. In particular, it is found that relaxation occurs in two phases, because for short times (approximately < 200 fs) the spectral density appears continuous due to the frequency-time uncertainty relation, while at longer times the discrete nature of the bath becomes apparent. Considering the excellent agreement between theory and experiment, it is speculated if this behavior can explain the experimentally obtained biphasic relaxation the amide I mode of N-methylacetamide.

CASPT2 investigation of ethane dissociation and methyl recombination using canonical variational transition state theory

AbstractEthane dissociation and the reverse recombination reactions were investigated based on CASPT2 and CASSCF calculations. The CASPT2 (partial) geometry optimization calculations and the CASSCF frequency calculations provided geometrical parameters, potential energies, and vibrational frequencies along the reaction pathway. For determining dissociation and recombination rate constants at a temperature range from 200 to 2000 K, two models (models 1 and 2) were used on the basis of the canonical variational transition state theory. The different methods for accounting for the five transitional modes were proposed in the two models. Dissociation activation parameters evaluated using the two models are in good agreement with the data available in the literature. Model 1 predicts reasonable rate constant values for methyl recombination at high temperature, and model 2 predicts reasonable values in both high‐ and low‐temperature ranges. © 2008 Wiley Periodicals, Inc. Int J Chem Kinet 40: 161–173, 2008

H−ZSM-5 Modified Zeolite: Quantum Chemical Models of Acidic Sites

A ZSM-5 fragment, containing 52 tetrahedral moieties, each of them formed by one silicon or one aluminum atom surrounded by four oxygen atoms, was employed to model (52T systems) by quantum chemical calculations (i) the influence of the positions of the acidic sites on the energetics of 22 aluminum monosubstituted and bisubstituted 52T acidic zeolite (H−ZSM-5) systems and (ii) the local adsorption properties and acidic strength of the corresponding −OH sites. The energetics and the structural properties of simpler acid H−ZSM-5 systems containing only five tetrahedral moieties (5T systems) were also modeled for comparison. B3LYP/6-31G(d,p) partial geometry optimization routines were performed on the 5T and 52T systems. On the latter, ONIOM(B3LYP/6-31G(d,p)|AM1) calculations and an alternative approach, i.e., the ONIOM method followed by a single-point at the above B3LYP/6-31G(d,p) level, aimed to decrease the need of computational resources, were also employed to analyze the properties of the different H−ZSM-5 models. The whole results showed that the orientation and the position of the acidic hydrogen atoms within the zeolite channel strongly affect the stability of the model systems, irrespective of the starting local topology characterizing the Al ↔ Si substitution site. Brönsted gas-phase acidity strength and adsorption-ability were evaluated through the analysis of the energy involved in (i) the proton dissociation from the acidic sites and (ii) the cis-but-2-ene and trans-but-2-ene adsorption on the same acidic sites. Both were affected, although to a very different extent, by the location and number of the considered −OH acidic groups. In particular, 2 among the 12 modeled acidic sites resulted in a highly stabilized zeolite structure, pointing out that the Al ↔ Si substitutions in the synthesis of aluminated ZSM-5 zeolites, and hence the corresponding catalytic activity, could preferentially occur on special sites. The choice of the computational method along with the size and the cutoff of the mimicked structures influenced the reliability of the calculations. The suggested alternative approach (that is, the ONIOM followed by the DFT single-point calculation) provided reasonable findings at very low computational cost.

First-Principle Calculation of Reduced Masses in Vibrational Analysis Using Generalized Internal Coordinates: Some Crucial Aspects and Examples

In this paper we present and analyze the most essential aspects of reduced masses along generalized internal coordinates. The definition of reduced masses in the internal coordinate formalism is established through the Wilson G-matrix concept and includes sophisticated relations between internal and Cartesian coordinates. Moreover, reduced masses in internal coordinates are, in general, no longer constant but coordinate-dependent. Based on the approach presented earlier [Stare, J.; Balint-Kurti, G. G. J. Phys. Chem. A 2003, 107, 7204-7214] and on our experience with reduced masses discussed in this paper, we have developed a robust program for the calculation of Wilson G-matrix elements and their functional coordinate dependence. The approach is based on the first principles and can be used in virtually any (internal) coordinate set. Since the program allows for projection of any kind of nuclear motion on the selected internal coordinates, the method is particularly suitable for ab initio or DFT potential energy functions calculated by partial geometry optimization. Moreover, reduced masses obtained by this program can be used as a decision tool for selecting the most appropriate internal coordinates for the considered vibrational problem and for the inclusion or omission of the kinetic coupling terms in the vibrational Hamiltonian.

Geminal interactions in ClZ(CH3)2X molecules (Z = C, Si, Ge) according to ab initio calculations

The structure and electronic parameters of ClZ(CH3)2X molecules (Z = C, Si, Ge, X = CH3, OCH3) were calculated by the RHF/6–31G(d) and RHF/6–311G(d,p) methods with full geometry optimization; calculations of ClZ(CH3)2OCH3 molecules were also performed by the RHF/6–31G(d) method with partial geometry optimization. The 35Cl NQR frequencies calculated from the populations of less diffuse 3p constituents of valence p orbitals of chlorine [RHF/6–31G(d)] were in agreement with the experimental values. The 35Cl NQR frequencies for molecules with X = OCH3 are lower than those for molecules with X = CH3 (the Z atom being the same), due mainly to direct through-field polarization of the Z-Cl bond, induced by the effect of unshared electron pair of the oxygen atom in the trans position with respect to that bond. The difference in the 35Cl NQR frequencies decreases in going from Z = C to Z = Si, Ge, in parallel with variation of the Z-Cl bond polarization as the size of Z increases.

Influence of N−H···O and C−H···O Hydrogen Bonds on the 17O NMR Tensors in Crystalline Uracil: Computational Study

We report a computational study for the 17O NMR tensors (electric field gradient and chemical shielding tensors) in crystalline uracil. We found that N-H...O and C-H...O hydrogen bonds around the uracil molecule in the crystal lattice have quite different influences on the 17O NMR tensors for the two C=O groups. The computed 17O NMR tensors on O4, which is involved in two strong N-H...O hydrogen bonds, show remarkable sensitivity toward the choice of cluster model, whereas the 17O NMR tensors on O2, which is involved in two weak C-H...O hydrogen bonds, show much smaller improvement when the cluster model includes the C-H...O hydrogen bonds. Our results demonstrate that it is important to have accurate hydrogen atom positions in the molecular models used for 17O NMR tensor calculations. In the absence of low-temperature neutron diffraction data, an effective way to generate reliable hydrogen atom positions in the molecular cluster model is to employ partial geometry optimization for hydrogen atom positions using a cluster model that includes all neighboring hydrogen-bonded molecules. Using an optimized seven-molecule model (a total of 84 atoms), we were able to reproduce the experimental 17O NMR tensors to a reasonably good degree of accuracy. However, we also found that the accuracy for the calculated 17O NMR tensors at O2 is not as good as that found for the corresponding tensors at O4. In particular, at the B3LYP/6-311++G(d,p) level of theory, the individual 17O chemical shielding tensor components differ by less than 10 and 30 ppm from the experimental values for O4 and O2, respectively. For the 17O quadrupole coupling constant, the calculated values differ by 0.30 and 0.87 MHz from the experimental values for O4 and O2, respectively.