Equilibrium Geometry Parameters Research Articles

Calculation of spectroscopic parameters of hydrogen and halogen bounded CH3CHO···HF and CH3COH···FH complexes

In this work, equilibrium geometry, bond energy, harmonic and anharmonic spectral parameters of the monomers of CH3CHO, HF molecules and CH3CHO···HF, CH3COH···FH complexes were calculated using the set of bases MP2/6-311++G(3df, 3pd). Anharmonic calculations were performed using second-order vibration theory. The binding energies of CH3CHO ··· HF and CH3COH ··· FH complexes are 10.1 kcal/mol and 1.7 kcal/mol, respectively.

Origin of the π-stacking induced shifts in absorption spectral bands of the green fluorescent protein chromophore

We present the results of computational studies of the shifts in absorption bands in the 4-hydroxybenzylidene-1,2-dimethylimidazolinone (HBDI), a synthetic analogue of the green fluorescent protein chromophore, induced by its π-stacking interaction with aromatic compounds. The set of model systems composed of HBDI in the anionic form π-stacked with the substituted derivatives of benzene is considered. Ground state equilibrium geometry parameters are obtained at the MP2/cc-pvdz level of theory and the vertical S0,min-S1 excitation energies are estimated using the XMCQDPT2/sa2-CASSCF(12/12) approach. It is shown that the bathochromic shifts are obtained for systems with smaller values of the dipole moment variation while the hypsochromic shifts correlate with larger values of this quantity. We also demonstrate that absolute values of the S0,min-S1 transition energy shift well correlate with the calculated bond interaction energy parameter of π-stacked complexes.

Internal Rotation and Equilibrium Structure of the Bromonitromethane Molecule According to Gas Electron Diffraction Data and Quantum Chemical Calculations

The structure and internal rotation of the bromonitromethane molecule are studied using electron diffraction analysis and quantum chemical calculations. The electron diffraction data are analyzed within the models of a general intramolecular anharmonic force field and quantum chemical pseudoconformers to account for the adiabatic separation of a large amplitude motion associated with the internal rotation of the NO2 group. The following experimental bond lengths and valence angles are obtained for the equilibrium orthogonal configuration of the molecule with Cs symmetry: re(N=O) = 1.217(5) A, re(C–N) = 1.48(2) A, re(C–Br) = 1.919(5) A, ∠еBr–C–N = 109.6(9)°, ∠еO=N=O = 125.9(9)°. The equilibrium geometry parameters are in good agreement with CCSD(T)/cc-pVTZ calculations. Thermally averaged parameters are calculated using the equilibrium geometry and quadratic and cubic quantum chemical force constants. The barrier to internal rotation cannot be determined reliably based on the electron diffraction data used in this work. There is a 82% probability that the equilibrium configuration with orthogonal C–Br and N=O bonds is most preferable, and internal rotation barrier does not exceed 280 cm-1, which agrees with CCSD(T)/cc-pVTZ calculations.

Conformational analysis of N-methylacetamide molecule in the ground and excited electronic states

Equilibrium geometry parameters, harmonic vibrational frequencies and barriers to conformational transitions and conformer energy differences for N-methylacetamide (CH3CONHCH3) molecule in S0, S1 and T1 electronic states were calculated in MP2 (S0) and CASPT2 (S1, T1) levels of theory. It is known that there are two planar (or effectively planar) conformers of N-methylacetamide in the ground electronic state. It is proved that the electronic excitation to aforementioned electronic states resulted in both CCON and HNCC fragments becoming pyramidal and rotated around «central» CN bond. One-, two- and three-dimensional potential energy surface (PES) sections by different large amplitude motions (LAM) coordinates were obtained by MP2 (S0) and CASPT2 (S1, T1) methods with cc-pVTZ basis set. On 2D PES sections by «central» torsion (CN) and one of the CCON or HNCC fragments’ inversion coordinates there are six different minima. Using PES sections as the potentials in model Hamiltonians, different anharmonic vibrational problems were solved and the frequencies of large amplitude vibrations were estimated variationally.

Internal rotation and equilibrium structure of the 2-methyl-2-nitropropane molecule from joint processing of gas phase electron diffraction data, vibrational and microwave spectroscopy data, and quantum chemical calculation results

The structure and internal rotation of the 2-methyl-2-nitropropane molecule is studied by electron diffraction and quantum chemical calculations with the use of microwave and vibrational spectroscopy data. The electron diffraction data are analyzed within the general intramolecular anharmonic force field model and the quantum chemical pseudoconformer model, considering the adiabatic separation of the degree of freedom of large amplitude motion, i.e., the internal rotation of the NO2 group. The equilibrium eclipsed configuration of the C s symmetry molecule has the following experimental bond lengths and valence angles: r e(N=O) = 1.226//1.226(8) A, r e(C–N)//r e(C–C) = 1.520//1.515/1,521(4) A, ∠еC–C–N = = 109.1/106,1(8)°, ∠еO=N=O = 124.2(6)°, ∠eC–C–Havg = 110(3)°. The equilibrium geometry parameters are well consistent with MP2/cc-pVTZ quantum chemical calculations and microwave spectroscopy data. The thermally average parameters previously obtained within the small vibration model show a satisfactory agreement with the new results. The electron diffraction data used in this work do not allow a reliable determination of the barrier to internal rotation. However, at a barrier of 203(2) cal/mol, which is derived from the microwave study, it follows from the electron diffraction data that the equilibrium configuration must correspond to an eclipsed arrangement of C–C and N=O bonds, which is also consistent with the results of quantum chemical calculations of various levels.

Conformational analysis of acetamide in the ground and lowest excited electronic states

For acetamide molecule (CH3CONH2) in the ground (S0) and lowest excited singlet (S1) and triplet (T1) electronic states calculations of equilibrium geometry parameters, harmonic vibrational frequencies and barriers to conformational transitions (also conformer energy differences in excited states) using following ab initio methods: MP2, CCSD(T), CASSCF, CASPT2 and MRCI were performed. One-, two- and three-dimensional potential energy surface (PES) sections by different large amplitude motions (LAM) coordinates were calculated by means of MP2/aug-cc-pVTZ (S0) and CASPT2/cc-pVTZ (S1, T1). As a result of electronic excitation, both CCON and CNH2 fragments become pyramidal. On 2D PES sections by torsion (CN) and inversion coordinates there are six minima forming three pairs of enantiomers. Using PES sections different anharmonic vibrational problems were solved and the frequencies of large amplitude vibrations were estimated.

On large amplitude motions of simplest amides in the ground and excited electronic states

For the formamide, acetamide, N-methylformamide and N-methylacetamide molecules in the ground (S0 ) and lowest excited singlet (S1 ) and triplet (T1 ) electronic states equilibrium geometry parameters, harmonic vibrational frequencies, barriers to conformational transitions and conformer energy differences were estimated by means of MP2, CCSD(T), CASSCF, CASPT2 and MRCI ab initio methods. One-, two- and three-dimensional potential energy surface (PES) sections corresponding to different large amplitude motions (LAM) were calculated by means of MP2/aug-cc-pVTZ (S0 ) and CASPT2/cc-pVTZ (S1 ,T1 ). For these molecules, in each excited electronic state six minima were found on 2D PES sections. Using PES sections, different anharmonic vibrational problems were solved and the frequencies of large amplitude vibrations were determined.

Conformational analysis of N-methylformamide in ground S0 and excited S1 and T1 electronic states

For conformers of the N-methylformamide (HCONHCH3) molecule, calculations of equilibrium geometry parameters, harmonic vibration frequencies, energy differences and potential barriers to conformational transitions were performed in the ground (S0) and lowest excited singlet (S1) and triplet (T1) electronic states. In the S0 state, the molecule exists in trans and cis stable conformations (having Cs symmetry). Our calculations show that the electronic excitations T1←S0 and S1←S0 cause changes in the structure of conformers: both HCON and HNCC fragments become pyramidal and rotate around the CN bond. As a result, in each excited electronic state under consideration, there are 12 minima forming six pairs of equivalent conformers separated by relatively small potential barriers. One- and two-dimensional potential energy surface sections corresponding to different intramolecular large-amplitude motions were calculated using the MP2/aug-cc-pVTZ (S0) and CASPT2/cc-pVTZ (S1 and T1) methods. Anharmonic vibrational problems for large-amplitude motions were solved, and the corresponding frequencies were estimated.

Structure and conformational dynamics of formamide molecule in the ground and lowest excited electronic states

Electronic state calculations, such as equilibrium geometry parameters, harmonic vibrational frequencies and potential barriers to conformational transitions (as well as conformer energy differences in excited states), using ab initio methods, such as MP2, CCSD(T), CASSCF, CASPT2 and MRCI, were carried out on the formamide molecule in the ground (S0) and the lowest excited singlet (S1) and triplet (T1) states. One-, two- and three-dimensional PES sections corresponding to different large amplitude motions (LAMs) were calculated using the MP2/aug-cc-pVTZ (S0) and CASPT2/cc-pVTZ (S1, T1) methods. In each excited electronic state, six minima with comparatively small potential barriers to internal rotation (less than 15kJ/mol) between them were discovered. Using PES sections, the anharmonic vibrational problem was solved, and the frequencies of the LAMs were determined.

Structural stability and Lewis acidity of tetravalent Ti, Sn, or Zr-linked interlayer-expanded zeolite COE-4: A DFT study

Density functional theory (DFT) has been performed to characterize the structural stability and Lewis acidic properties of the T-COE-4 zeolites, in which the linked site between the layers is isomorphously substituted by the tetravalent Ti-, Sn-, or Zr- heteroatom. The effects of substitution energy and equilibrium geometry parameters on the stability of T-COE-4 are investigated. The computed Fukui function values and the adsorption of ammonia, pyridine, water and trimethylphosphine oxide molecules have been employed to predict the Lewis acid strength of the T-COE-4 zeolites. It is found that the smaller the O1-T-O2 bond angle is, the more difficult is to form the regular tetrahedral unit. The substitution energies at the linker position increase in the following sequence: Ti-COE-4 < Sn-COE-4 < Zr-COE-4. The incorporation of Ti-, Sn-, or Zr-heteroatom enhances the Lewis acidity of COE-4 zeolite. It is predicted that the Lewis acid strength increases in the order of Ti-COE-4 < Zr-COE-4 ≤ Sn-COE-4 by the adsorption of different base molecules. Six O-T-O bond angles are divided into different extent to form the analogous trigonal bipyramid structures in the optimized ligand adsorbed complexes. These findings could be beneficial for the structural design and catalytic function modification of the interlayer-expanded zeolites.

High-level theoretical spectroscopic parameters for three ions of astrochemical interest

The equilibrium geometry and rovibrational spectroscopic parameters of the three astrochemical ions l-C3H+, l-SiC2H+, and C3N− and some of their isotopologues are obtained from high-level quantum chemical calculations. A composite approach based on the explicitly correlated coupled-cluster method CCSD(T)-F12b, that further includes core correlation, scalar-relativistic effects and most importantly higher order correlation beyond CCSD(T) is used to set-up the near-equilibrium potential energy surface (PES). The spectroscopic parameters of these linear tetra-atomic ions are then extracted from these PESs by vibrational perturbation theory of second order (VPT2). Calculation of absolute intensities is also carried out for the stretching frequencies of the cations in order to identify the bands that are most likely to be detected. The importance of the accurate calculation of the rotational constants B0 and D0 for astrochemistry is discussed as well as the limits of VPT2 in this context and reasons for these limitations.

Electron diffraction analysis for the molecules with multiple large-amplitude motions. 3-nitrostyrene--a molecule with two internal rotors.

Dynamic structural analysis of the molecules possessing large-amplitude degrees of freedom has been attempted by many researchers; however, so far, electron diffraction investigations involved only one large-amplitude coordinate (internal rotation or bending). The current state of computational facilities allows extending of the general dynamic approach to the systems possessing two or more large-amplitude motions. This paper presents the first practical implementation of the theoretical method developed previously by the authors for solving the dynamic-structural problem with two or more large-amplitude coordinates; the procedure is applied to a molecule of 3-nitrostyrene. The molecule is represented as a set of pseudoconformers built on a two-dimensional grid corresponding to both internal rotation coordinates present in the molecule (with 10-30° steps by each angle); altogether, up to 342 pseudoconformers were used. Structural analysis was based on the experimental electron diffraction data supported by quantum chemical calculations (at the MP2 and B3LYP levels of theory) and molecular spectroscopy data. Quantum chemistry predicts the planar structure of both syn- and anti- stable conformations with close energies and weak interaction between internal rotations of nitro and vinyl groups. The gas-phase electron diffraction experimental data are compatible with the quantum chemical predictions. The principal equilibrium geometry parameters of the molecule (syn- conformation) have been determined as follows: r(e)(C-C)(ring, avg.) = 1.391(1) Å, r(e)(C-C) = 1.477(5) Å, r(e)(C═C) = 1.333(7) Å, r(e)(C-N) = 1.463(5) Å, r(e)(N═O) = 1.227(3) Å, ∠e(O═N═O) = 124.3 (4)°. Experimental data for this molecule are insufficient to make estimates of the barrier heights of internal rotation; the population ratio of syn- and anti- conformations is evaluated as 50 ± 20%. Results of our investigation confirm the presence of significant internal rotations in the 3-nitrostyrene molecule.

A benchmark study of molecular structure by experimental and theoretical methods: Equilibrium structure of thymine from microwave rotational constants and coupled-cluster computations

Accurate equilibrium, re, structures of thymine have been determined using two different, and to some extent complementary techniques. The composite ab initio Born–Oppenheimer, re(best ab initio), structural parameters are obtained from the all-electron CCSD(T) and MP2 geometry optimizations using Gaussian basis sets up to quadruple-zeta quality. The semi-experimental mixed estimation method, where internal coordinates are fitted concurrently to equilibrium rotational constants and geometry parameters obtained from a high level of electronic structure theory. The equilibrium rotational constants are derived from experimental effective ground-state rotational constants and rovibrational corrections based on a quantum-chemical cubic force field. Equilibrium molecular structures accurate to 0.002Å and 0.2° have been determined. This work is one of a few accurate equilibrium structure determinations for large molecules. The poor behavior of Kraitchman’s equations is discussed.

Framework Stability and Brønsted Acidity of Isomorphously Substituted Interlayer‐Expanded Zeolite COE‐4: A Density Functional Theory Study

COE-4 zeolites possess a unique two-dimensional ten-ring pore structure with the Si(OH)2 hydroxyl groups attached to the linker position between the ferrierite-type layers, which has been demonstrated through the interlayer-expansion approach in our previous work (H. Gies et al. Chem. Mater. 2012, 24, 1536). Herein, density functional theory is used to study the framework stability and Brønsted acidity of the zeolite T-COE-4, in which the tetravalent Si is isomorphously substituted by a trivalent Fe, B, Ga, or Al heteroatom at the linker position. The influences of substitution energy and equilibrium geometry parameters on the stability of T-COE-4 are investigated in detail. The relative acid strength of the linker position is revealed by the proton affinity, charge analysis, and NH3 adsorption. It is found that the range of the ⟨T-O-Si⟩ angles is widened to maintain the stability of isomorphously substituted T-COE-4 zeolites. The smaller the ⟨O1-T-O2⟩ bond angle is, the more difficult is to form the regular tetrahedral unit. Thus, the substitution energies at the linker positions increase in the following sequence: Al-COE-4 < Ga-COE-4 < Fe-COE-4 < B-COE-4. The adsorption of NH3 as a probe molecule indicates that the acidity can affect the hydrogen-bonding interaction between (N-H⋅⋅⋅O2) and (N⋅⋅⋅H-O2). The relative Brønsted-acid strength of the interlayer-expanded T-COE-4 zeolite decreases in the order of Al-COE-4 > Ga-COE-4 > Fe-COE-4 > B-COE-4. These findings may be helpful for the structural design and functional modification of interlayer-expanded zeolites.

Ab initio study and spectral simulation of the [formula omitted] photodetachment processe of dichlorocarbene anion

Combining ab initio molecular orbital calculations with Franck–Condon analysis to simulate vibrationally resolved photoelectron spectra have been carried out on the CCl2(X̃1A1)←CCl2-(X̃2B1) detachment process. By using CCSD/6-311+G(2d, p) values, the theoretical spectra obtained are in agreement with the observed one, and, the equilibrium geometry parameters, 1.890±0.002Å and 102.9±0.3° of the X̃2B1 state of CCl2− are acquired, by employing an iterative Franck–Condon (IF–C) analysis procedure. In addition, on different levels of theory, our best calculated electron affinity (EA) is in fair agreement with the experimental value.

A general analytical expression for the three-dimensional Franck–Condon integral and simulation of the photodetachment spectrum of the [formula omitted] anion

Calculations of Franck–Condon factors are crucial for interpreting vibronic spectra of molecules and studying nonradiative processes. We have derived straightforwardly a more general analytical expression for the calculation of the three-dimensional Franck–Condon overlap integrals on the basis of harmonic oscillator approximation under the influence of mode mixing effects. This new analytical expression was applied to study the photoelectron spectra of PO2-. The theoretical spectrum obtained by employing CCSD(T) values is in excellent agreement with the observed one. An ‘irregular spacing’ observed in the experimental photoelectron spectrum of PO2- is interpreted as contributing from a hot-band sequence of the bending vibration ω2 and combination bands of the stretching vibration ω1 and the bending vibration ω2. In addition, the equilibrium geometry parameters, r(O–P)=1.495±0.005Å and ∠(O–P–O)=119.5±0.5°, of theX∼1A1 state of PO2-, are derived by employing an iterative Franck–Condon analysis procedure in the spectral simulation.

Franck–Condon analysis of the photoelectron spectra of HCCl−: Considering Duschinsky effects

Franck–Condon analysis and spectral simulations were carried out on the HCCl (X˜1A′)←HCCl-(X˜2A″) photo-detachment process. The theoretical spectra obtained by using CCSD/6-311+G(2p,d) values are in agreement with the observed one. Otherwise, the equilibrium geometry parameters, r(CCl)=1.950±0.002Å of the X˜2A″ state of HCCl− are derived, by using the spectral simulation and employing an iterative Franck–Condon (IF–C) analysis procedure. Furthermore, through the different methods, our best calculated electron affinity is 1.2106eV, which is in fair agreement with the experimental value.

A combined ab initio and Franck–Condon simulation study of the photodetachment spectrum of the [formula omitted] anion

A general analytical expression for the calculation of the two-dimensional four-mode Franck–Condon overlap integrals was presented and applied to scrutinize the photoelectron spectroscopy of ClO 2 - . Geometry optimization and harmonic vibrational frequency calculations have been performed on the X ∼ 2B 1 state of ClO 2 and X ∼ 1A 1 state of ClO 2 - by using the density functional theory (B2PLYP functional) and the coupled cluster singles and doubles with perturbative triples [CCSD(T)] methods with various basis sets up to aug-cc-pVQZ. The adiabatic electron affinity of ClO 2 was computed by using the CCSD(T) method extrapolated to the complete basis set limit with aug-cc-pVXZ (X = D, T, Q). Franck–Condon analyses and spectral simulation were carried out on the ClO 2( X ∼ 2B 1)–( ClO 2 - X ∼ 1A 1) photodetachment process. The simulated photoelectron spectrum of ClO 2 - are in accord with the experiment. While the Duschinsky effect plays a minor role and can be neglected. In addition, the equilibrium geometry parameters, R(Cl–O) = 1.572 ± 0.005 Å and ∠ (O–Cl–O) = 112.5 ± 0.5°, of the X ∼ 1A 1 state of ClO 2 - , are obtained by employing an iterative Franck–Condon analysis procedure in the spectral simulations.

Theoretical study of the models of Ca2+ and Mg2+ ions binding by the methylidene rhodanine neutral and anionic forms

The equilibrium geometry and energy parameters of the complexes of Ca2+ and Mg2+ with 5-methyl-2-thioxotiazolidin-4-one (methylidene rhodanine) and its anion in a 1:1 ratio in different conformations were calculated by the quantum-chemical method with the density functional theory on the level of hybrid functional B3LYP in the basis of atomic orbitals 6–31+G(d). The influence of metal ion size on the number of possible isomeric coordinations was indicated. The principles of stabilization and destabilization of the structures depending on their conformations al structure were described. Based on the calculated equilibrium geometry parameters of the complexes conformations the effect of complexation on the structure of rhodanine ligand was elucidated. In the framework of a polarizable continuum the relative stability of the possible tautomeric forms of methylidene rhodanine in water was investigated. A new structure of the methylidene rhodanine anion distinquished by a specific distribution of negative charge is suggested.

Ab initio adiabatic and quasidiabatic potential energy surfaces of lowest four electronic states of the H++O2 system

Ab initio global adiabatic and quasidiabatic potential energy surfaces of lowest four electronic (1-4 (3)A(")) states of the H(+)+O(2) system have been computed in the Jacobi coordinates (R,r,γ) using Dunning's cc-pVTZ basis set at the internally contracted multireference (single and double) configuration interaction level of accuracy, which are relevant to the dynamics studies of inelastic vibrational and charge transfer processes observed in the scattering experiments. The computed equilibrium geometry parameters of the bound [HO(2)](+) ion in the ground electronic state and other parameters for the transition state for the isomerization process, HOO(+)⇌OOH(+) are in good quantitative agreement with those available from the high level ab initio calculations, thus lending credence to the accuracy of the potential energy surfaces. The nonadiabatic couplings between the electronic states have been analyzed in both the adiabatic and quasidiabatic frameworks by computing the nonadiabatic coupling matrix elements and the coupling potentials, respectively. It is inferred that the dynamics of energy transfer processes in the scattering experiments carried out in the range of 9.5-23 eV would involve all the four electronic states.