Calculated Equilibrium Geometries Research Articles

On the effect of the BSSE on intermolecular potential energy surfaces. Comparison of a priori and a posteriori BSSE correction schemes

AbstractA comparative study of geometrical parameters is performed on the complexes HF–HF, H2O–H2O, and HF–H2O using 12 different basis sets at the RHF, MP2, and DFT (BLYP and B3LYP) levels of theory. The equilibrium geometries were obtained from uncorrected, a posteriori (counterpoise, CP) and a priori (Chemical Hamiltonian Approach, CHA) BSSE‐corrected potential energy surfaces. The calculation of equilibrium geometries using the CP and CHA schemes is described in details. The effect of the BSSE on various intermolecular parameters is discussed and the performance of the applied theoretical models is critically evaluated from the BSSE point of view. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 765–786, 2001

Electrostatic potential profiles may guide cation–pi interaction in antimalarials chloroquine and mefloquine: an ab initio quantum chemical study

The electrostatic potential profiles beyond the van der Waals surface of uncomplexed molecular fragments are used to guide the cation–pi interaction and equilibrium geometry for metal–aromatic complexes in antimalarials such as chloroquine (CQ), 1; 6-chloro CQ, 2; CQ without a chlorine atom, 3; and mefloquine, 4. The binding energies of sodium ion with the pi-electrons of the aromatic ring were calculated and compared with the published results in simple aromatics using the ab initio 6-31G ∗∗ quantum chemical method. A significant difference in binding energy, geometry and site of interaction is observed between the 1–Na + and 4–Na + complexes implying two different mechanistic paths for this type of noncovalent interaction. The relative binding affinity and equilibrium geometry of complexes of some commonly found mammalian biometals such as zinc, calcium, magnesium and iron with the aromatic pi-electrons in 1 and 4 are calculated using the 3-21G ∗ basis set. The calculated affinity orders are Zn(II)>Fe(II)>Mg(II)>Ca(II) for 1 and Mg(II)>Ca(II)>Zn(II)>Fe(II) for 4, respectively. In all these calculated equilibrium geometries, the electrostatic potential profile of the uncomplexed molecule appears to play a major role in determining the cation–pi noncovalent interaction.

Molecular geometries and vibrational spectra of SnCl 4− n(OH) n

We present calculated equilibrium geometries and vibrational spectra for SnCl 4− n (OH) n , n=0,1,…4. We also predicted energies of reaction for successive replacement of chlorine atoms with OH groups, and we found all reactions to be slightly endothermic. We obtained these results using ab initio Hartree–Fock theory with electron correlation in a series of approximations; for SnCl 4, we obtain good agreement with experiment.

Totally symmetric vibrational modes of fullerene C60

Semiempirical molecular orbital calculations are carried out for the totally symmetric vibrations of the C60 molecule. The calculated equilibrium geometry coincides with the precision experimental data to within measurement error. The ratio of force constants calculated for the two different types of C-C bonds in fullerene is equal to 1.389. A comparison of the computational results with the Raman scattering data indicates that there may be Fermi resonance between the totally symmetric vibrations.

Rotational isomerism of 1,2-dichlorotetramethyldisilane studied by Raman spectroscopy and ab initio quantum chemical calculations

The Raman vibrational spectra of 1,2-dichlorotetramethyldisilane recorded at various temperatures prove that two rotamers, gauche and anti, are present in the liquid state due to restricted rotation of the SiMe 2Cl groups. The solid is composed of the anti rotamer exclusively. From a van’t Hoff plot, the enthalpy difference Δ H= H gauche− H anti has been determined as 1.01±0.2 kJ mol −1, the anti rotamer being more stable. Ab initio SCF-HF calculations of equilibrium geometries, harmonic vibrations and harmonic force fields have been performed for both rotamers and the vibrational spectra have been assigned employing these results.

Ab Initio Cluster Model Study of the Chemisorption of CO on Low-Index Platinum Surfaces

A systematic theoretical study of the adsorption of CO on the Pt{100}, Pt{110}, and Pt{111} surfaces is presented. The calculated equilibrium geometries and vibrational frequencies have been found to be rather independent of the cluster model chosen to represent the surface. However, calculated interaction energies are found to be very sensitive to the surface cluster model. The analysis of the chemisorption bond has been carried out by means of the constrained space orbital variation, CSOV, and of projection operator techniques. These analysis reveal that the bonding interactions are dominated by the π-back-donation although σ-donation plays a significant role. It is also clearly shown that all bonding mechanisms, other than Pauli repulsion, but specially π-back-donation, contribute to the observed red shift. However, the π-back-donation contribution to the red shift is very similar for CO on different sites. Hence, π-back-donation cannot be the mechanism responsible for the observed difference for the CO vibrational frequency on on-top and bridge sites. The CSOV decomposition reveals that the leading term contributing to this difference in vibrational frequency of chemisorbed CO is the initial Pauli repulsion or “wall effect”; this is a new, important and unexpected conclusion.

Ab initio study of structural and cohesive properties of polymers: Polyiminoborane and polyaminoborane

Results of Wannier orbital-based Hartree–Fock and various correlated ab initio calculations using 6–31G** basis sets are reported for the two boron–nitrogen polymer systems polyaminoborane [BNH4]∞ and polyiminoborane [BNH2]∞. At the Hartree–Fock level the calculated equilibrium geometries, cohesive energies, polymerization energies, and band structures are virtually identical with those obtained from the standard Bloch orbital-based approach. Electron correlation effects on the investigated ground state properties are discussed within Mo/ller–Plesset second-order perturbation theory and coupled-cluster singles, doubles, and triples theory. For polyaminoborane no bond alternation is found in contrast to previous studies. Correlation corrections to the band structures are considered in second-order Mo/ller–Plesset perturbation theory with third-order localization diagrams included. They lead to a decrease of the fundamental gap of polyaminoborane and polyiminoborane by 40% and 51%, respectively, and reduce the band dispersions.

Displacement and distortion of the ammonium ion in rotational transition states in ammonium fluoride and ammonium chloride

Ab initio density functional calculations have been carried out on ammonium fluoride to determine the equilibrium structure and the transition state for rotation of the ammonium ion. The calculated equilibrium geometry agrees satisfactorily with crystallographic data. Optimization of the crystal geometry in the transition state for rotation results in significant distortion and displacement of the ammonium ion within the unit cell. Upon reexamination of the rotational transition states in ammonium chloride, similar distortion and displacement of the ammonium ion are found. The rotation process is similar to a carousel motion, in which the ion moves along the rotation axis and changes shape as it rotates. These results show that rigid ion models for ammonium ion rotational dynamics in crystals are, at best, incomplete.

Analytical energy gradients of a self-consistent reaction-field solvation model based on CM2 atomic charges

Analytical energy gradients have been derived for an SM5-type solvation model based on Hartree–Fock self-consistent reaction-field theory and CM2 atomic charges. The method is combined with an analytic treatment of the first derivatives of nonelectrostatic first-solvation-shell contributions to the free energy and implemented in the General Atomic and Molecular Electronic Structure System (GAMESS). The resulting equations allow one to use accurate class IV charges to calculate equilibrium geometries of solutes in liquid-phase solutions. The algorithm is illustrated by calculations of optimized geometries and solvation free energies for water, methanol, dimethyl disulfide, and 9-methyladenine in water and 1-octanol.

Ion association of alkali and alkaline earth metal azides in dimethylsulfoxide. Infrared spectrometry and ab initio calculations

The 1:1 species formed in dimethylsulfoxide (DMSO) solution between the azide anion and alkaline and alkaline earth metal cations Mz+ are investigated by infrared spectrometry. The ν3 vibration of N3- at 2000 cm-1 is shifted to higher wavenumbers by ion pairing. Shift values are not significantly different from those observed in MNCO(z-1)+ although azide ion pairs are less stable. The forbidden ν1 vibration of N3- at 1315 cm-1 becomes allowed in ion pairs. Δν3 and Δν1 wavenumber shifts are both proportional to the polarizing power of the cation. Longitudinal force constants are calculated by assuming that in an N1N2N3M ion pair the force constant of the N2N3 bond is insensitive to ion pairing. The mean polarizability of N3- and the anisotropy of polarizability are measured by refractive index and by Rayleigh diffusion measurements. From these results the integrated intensity of the ν1 band is interpreted by calculating the variation of dipole moments induced by the Mz+ in N3-. Theoretical calculations of equilibrium geometry, polarizability, wavenumbers and IR intensity are made by the DFT (Density Functional Theory) method on some typical azide species: free N3-, unsolvated ion pairs LiN3, NaN3 and KN3, solvent shared ion pair LiN3.3H2O and triple anion N3LiF-.

Part II—1,1,1,2,2,3-Hexamethyltrisilanes X2MeSiSiMe2SiMe3 with X=H, F, Cl, Br, I, C6H5 and OCH3

The Raman vibrational spectra of the hexamethyltrisilanes X2MeSiSiMe2SiMe3 with X=H, F, Cl, Br, I, C6H5 and OCH3, recorded at various temperatures, prove the simultaneous presence of two rotamers, anti and gauche, in the liquid state. Enthalpy differences between the rotamers were determined as described previously. Ab initio calculations of equilibrium geometries and harmonic force constants were performed for anti and gauche X2MeSiSiMe2SiMe3 with X=H, F, Cl, Br, I and OCH3. Fundamental vibrations were assigned with the help of normal coordinate analyses and potential energy distributions were calculated. The preferred conformations of these trisilanes are gauche (CSiSiSi torsional angle near 180°) for X=H, Br, I, OCH3 and C6H5, and anti for X=F and Cl with enthalpy differences ranging from 0.25 to 2.2 kJ mol-1. © 1998 John Wiley & Sons Ltd.

The cyclic MO 2 (M=Al, Ga) systems: CCSD(T) and DFT studies of their structures, harmonic vibrational frequencies, and dissociation energies

The AlO 2 and GaO 2 superoxides are the primary products of the reaction of Al, or Ga, with O 2 in cryogenic matrices. CCSD(T) and DFT calculations using 6-311+G(3df) and 6-311+G(2df) basis for AlO 2 and GaO 2, respectively, have been performed. The calculated equilibrium geometries, harmonic frequencies, and dissociation energies are presented. Each system possesses a 2A 2 ground state. The CCSD(T) calculations yield dissociation energies of 65 and 51 kcal/mol, respectively. DFT yields similar results. Comparison with existing experimental and theoretical data are made. Both the DFT and the single reference CCSD(T) methods overcome the symmetry breaking problems encountered in previous theoretical studies.

Cis- and trans-3-hexene: infrared spectrum in liquid argon solution, ab initio calculations of equilibrium geometry, normal coordinate analysis, and vibrational assignments

The infrared spectra of cis-3-hexene and trans-3-hexene dissolved in liquid argon have been obtained at temperatures from 93 to 120 K. The absorptions were observed with a low-temperature cell and a Fourier transform infrared spectrophotometer. Ab initio molecular orbital calculations were performed to obtain the equilibrium geometry, vibrational frequencies, force fields, and infrared intensities. The calculations were done at the Hartree-Fock level using 6-31G basis set. The Cartesian force fields from ab initio calculations have been converted to the force field in symmetry coordinates. The scale factors of ab initio calculated force fields were determined. Normal coordinate calculations were performed using a scaled quantum mechanical (SQM) force field. Vibrational normal modes calculated for the lowest energy rotamers of cis- and trans-3-hexene have been assigned to infrared absorption bands observed in liquid argon solution. The assignments were based on calculated frequencies and potential energy distributions. The equilibrium geometries of the two lowest energy rotamers (symmetry C 2 and C s ) of cis-3-hexene and of the three lowest energy rotamers (symmetry C i , C 2, and C 1) of trans-3-hexene were calculated. Variable temperature studies of the infrared spectrum of cis- and trans-3-hexenes dissolved in liquid argon were done to obtain the ΔH of conversion between the rotamers C 2 and C s of cis-3-hexene and between the rotamers C i , C 2, and C 1 of trans-3-hexene.

Electronic Structure and Unimolecular Reactions of Cyclopropenone Carbonyl Oxide. A Theoretical Study.

A theoretical investigation on the lowest singlet and triplet potential energy surfaces of cyclopropenone carbonyl oxide 1 is presented. The calculated equilibrium geometry and dipole moment suggest that 1 possesses a strong zwitterionic character. The energy barrier for the isomerization of 1 to the cyclic isomer dioxirane 2 is computed to be 9.4 kcal/mol. The singlet state of 1 dissociates into cyclopropenone and excited singlet oxygen atom ((1)D), while the triplet state of 1 dissociates yielding oxygen atom in its ground state ((3)P). The dissociation process is endothermic for the singlet state but highly exothermic for the triplet.

Deviations from idealised geometries part 3: approximately tetrahedral molecules of form MX 2Y 2 studied by SCF and MP2 calculations

The relatively minor deviations from true tetrahedral geometry for molecules of type MX 2Y 2 where M is tetravalent, and X, Y are either H, Me or halogen are discussed, in the light of ab initio calculations of equilibrium geometry with a large (triple zeta valence + polarisation) basis, at both the SCF and MP2 levels. The results are compared with known experimental structural and dipole moment data; in most cases a very close correlation with experiment is found, with slight improvements in the MP2 data. The study is coupled with a localised orbital study of relevance to Bent's Rule.

Isomerization of SiOH +, HSiOH and H 2SiO: a density functional study

Density functional theory (DFT) is used to investigate the isomerization reactions of SiOH +, and of HSiOH. Linear SiOH + is predicted to be more stable than linear HSiO + by 65.1 kcal mol −1. This energy difference becomes 63.5 kcal mol −1 after zero-point vibrational energy (ZPVE) correction. The barrier height for the endothermic isomerization is predicted to be 96.7 kcal mol −1 (93.1 kcal mol −1 after ZPVE correction). The calculated total energies for HSiOH (cis), HSiOH (trans) and H 2SiO are very close to each other. HSiOH (trans) is predicted to be more stable than the cis-isomer by 0.2 kcal mol −1. HSiOH (trans) is predicted to be more stable than H 2SiO by 2.0 kcal mol −1. Zero-point vibrational energy correction changes the relative stability of HSiOH (cis) and HSiOH (trans) by making the cis-isomer to be more stable than the trans-isomer (0.02 kcal mol −1). ZPVE correction decreases the energy difference between HSiOH (trans) and H 2SiO but does not lead to a reversal of relative stabilities. The predicted barrier height for HSiOH (cis) → HSiOH (trans) reaction is 8.1 kcal mol −1. A much larger barrier height (56.3 kcal mol −1) is predicted for the reaction H 2SiO → HSiOH (trans). Calculated equilibrium geometries, activation energies and vibrational frequencies are shown to be in good agreement with the results of high quality ab initio studies.

The covalently bound N 3O 2 molecule: Two possible isomers

Density functional theory has been applied to investigate the possibility of the existence of the neutral N 3O 2 molecule. Two isomers (cyclic and open ONNNO) are found to be minima on the potential energy hypersurface at the local level of theory. The cyclic structure represents a minimum with the nonlocal functionals as well, while the open form is predicted to be a transition state with one of the applied nonlocal functionals. The open isomer lies about 20 kcal/mol lower in energy than the cyclic molecule, but both isomers are thermodynamically unstable with respect to NO + N 2O and N 2 + NO 2. The calculated equilibrium geometries, vibrational frequencies and bond orders suggest that both isomers are covalently bound structures.

A density functional study of borane and alane monoammoniate (BH3NH3,AlH3NH3)

Molecular structures, harmonic vibrational frequencies, dissociation energies, and barriers to internal rotation have been determined using a Gaussian density functional method. Both local and nonlocal levels of theory have been employed. The calculated equilibrium geometry and harmonic vibrational frequencies for BH3NH3 compare well with those determined by microwave and infrared experiments. The rotational barrier is found to be 2.09 kcal/mol in very good agreement with the experimental data. The calculated properties for ammonia-alane (AlH3NH3) are compared with those obtained previously from high level correlated methods.

Influence of polarization functions on atomic properties of bridge N and H atoms of HCN … HCN

The effect of different types of core and valence polarization functions on the equilibrium geometry, electric fields, Cioslowsky and Mulliken atomic charges, dissociation energy and CH stretching frequency changes for HCN … HCN was investigated. Basis sets for C, N and H were constructed (6-GCM) from the 6-31G basis sets to improve the Hellmann-Feynman forces and to describe adequately the asymptotic behavior of the wavefunction in the valence region. This new procedure provided accurate basis sets. Calculations of equilibrium geometry, total energies, harmonic frequencies and electric fields of some test molecules showed excellent agreement with accurate results. The resulting basis sets were considerably large in size and the need for reliable calculations of the hydrogen bonds of the HCN dimer with a 6-31G basis set using different procedures to include polarization functions was investigated. The properties calculated at the Hartree-Fock level of theory (SCF) for the HCN dimer using the 6-GCM basis sets were taken as reference. Three sets of polarization functions derived from the original 6-31G basis set were used with the original 6-31G basis set at the SCF level of theory for the HCN dimer. The agreement between the properties calculated with the polarized 6-31G basis set and the standard 6-GCM basis was analyzed using the simple statistical Euclidean distance. Comparison of the Euclidean distances for molecular properties (electric field, Cioslowsky charges, bond lengths, change in CH stretching frequency and dissociation energies) suggests that 6-31G polarized with the Pople's original d type functions or mixing Pople's polarization function with polarization that improves the Hellmann-Feynman forces are in closer agreement with the calculations using the 6-GCM basis set. If molecular properties more directly related to the hydrogen bond are improved, other molecular properties are also better characterized. Euclidean distances for Mulliken charges have shown a different tendency. If only Mulliken charges are considered, the polarization of hydrogen is sufficient.

Resonance Raman spectra and quantum chemical vibrational analysis of the C7H7⋅ and C7D7⋅ benzyl radicals

Time-resolved resonance Raman (RR) spectra of the benzyl radical and its perdeutero isotopomer are presented. The radicals are created by laser flash photolysis (λ=266 nm) of benzylchloride in solution. The spectra are excited at a wavelength of 315 nm, in resonance with the intense D3(2 2A2)←D0(1 2B2) transition. Twenty Raman bands, both polarized and depolarized, are observed. The RR spectra are analyzed through quantum chemical force field for π electrons (QCFF/PI) and ab initio calculations of equilibrium geometries, vibrational frequencies, Franck–Condon factors, and vibronic interactions. Polarized intense bands are assigned to totally symmetric a1 modes, and a number of depolarized bands to fundamentals of b1 modes. The observed activity of b1 modes suggests vibronic coupling, which is confirmed theoretically by calculations of vibronic interactions between the D3(2 2A2) and D5(4 2B2) states. The results from semiempirical and ab initio calculations are compared with experiment. The contributions of the different internal coordinates to the normal modes are calculated together with the changes in the molecular structure upon electronic excitation from D0 to D3 and D5.