Prediction of geometries and interaction energies of complexes formed by small molecules using semiempirical and ab initio methods

The accuracy of the semiempirical quantum mechanics methods (AM1 and PM3), and the ab initio methods (6-31G^** and MP2/6-31G^**) in predicting intermolecular geometries and interaction energies have been evaluated by detailed studies of 17 bimolecular complexes formed by small molecules. Comparisons between calculated and experimental geometries for 12 complexes are presented. It was found that AM1 gave reasonably good predictions of the geometries of complexes such as CH₄ · CH₄, which have very weak interactions, but it is not as good as other methods in predicting intermolecular geometry for complexes where hydrogen bonding interactions play an important role. This is consistent with its inability to reproduce the charge transfer in the formation of hydrogen bonds in these complexes.

PM3 is able to predict intermolecular geometries for most complexes, including those with hydrogen bonding; its major flaw is its tendency to overestimate the strength of the interactions between hydrogen atoms. Care should be taken therefore in using PM3 to study complicated molecular systems with multiple hydrogen atom interactions and the method's weakness in handling complexes in which electrostatic forces are important should also be noted.

Among ab initio methods, both the 6-31G^** and the MP2/6-31G^** were found to outperform AM1 and PM3 in prediction of intermolecular geometry. Both of these ab initio methods showed excellent consistency in geometry prediction for most of the complexes studied, although MP2/6-31G^** is better than 6-31G^**. It is noted that the MP2/6-31G^** did not produce the correct geometry for the CO₂· HF complex.

For 12 complexes for which experimental geometry data are available, AM1, PM3, 6-31G^**, and MP2/6-31G^** successfully predicted the geometry in 10, 12, 12, and 11 cases, respectively. The average errors given by AM1 in the predicted intermolecular distances were 0.264, 0.272, 0.091, and 0.061 Å, respectively. In comparison to the ab initio methods, AM1 and PM3 commonly underestimated the molecular interaction energy in such complexes by ˜ 1–2 kcal mol⁻¹.     

Theoretical studies of carbenes and carbenoids. 5. Intramolecular reactions of cyclopropylcarbene

Intramolecular reactions of cyclopropylcarbene in singlet ground state have been studied using HF/3-21G- gradient methods. Relative energies are estimated with 6–31G^**. The “super-conjugation” between the cyclopropyl and the p AO at the carbene site stabilizes the carbene and retards its exo-endo isomerization with a barrier of 13.7 kcal/mol. The ring expansion occurs preferably from the exo conformation with a barrier of 12.9 kcal/mol. Two terminals disrotate in different rotation directions before and after the transition state. The ring expansion from the endo conformation is a more energetic pathway. The 1,2 H shift is not competitive to the ring expansion for its much higher barrier.     

Ab initio calculations of minimum-energy pathways of the nucleophilic addition of the H anion, LiH molecule and Li/H ion pair to acetylene and methylacetylene

Ab initio calculations were performed for special points of the minimal energy pathways (MEP) of the nucleophilic addition reactions of the isolated H⁻ anion, LiH molecule and Li⁺/H⁻ ion pair to acetylene (A) and methylacetylene (MA) molecules, proceeding in accordance (M) and against (aM) the Markovnikov's rule. All structural parameters were optimized using the restricted Hartree–Fock (RHF) method. For the addition of H⁻, the 6-31++G^* basis set was used and for the reactions of LiH and Li⁺/H⁻ the 6-31G^* basis set with the subsequent recalculation of single point energies, taking into account of electron correlation energy by means of the second-order Möller–Plesset perturbation theory at the MP2/6-31++G^** level. The results of calculations demonstrate, that the energy characteristics of both M- and aM-additions with H⁻ do not differ sufficiently (0.1–1.2 kcal/mol for the activation energies (ΔE_a) and the reaction heats (ΔQ)). The substitution of the H atom by the CH₃ group in A molecule results in practically the same values of ΔQ and ΔE_a. On the contrary, for the LiH molecule and Li⁺/H⁻ ionic pair, the M-addition is favorable (charge control). It is found that the presence of electrophile decreases the activation energy by 3–5 kcal/mol as compared with the addition of the isolated hydride ion H⁻.     

Vibrational spectra and density functional study of propylgermane

Raman and infrared spectra of propylgermane, CH₃CH₂CH₂GeH₃, and its Ge-deuterated analog, CH₃CH₂CH₂GeD₃, were investigated in their gaseous, liquid and solid states. The normal coordinate treatment was carried out by density functional theory (DFT) calculation, using B3LYP/6-31G^* and 6-311++G^** basis sets, and the corresponding fundamental vibrations were assigned. The trans (T) and gauche (G) forms around the central C–C bond coexisted in the gaseous and liquid states and only the T form existed in the solid state. From the temperature dependent measurements of the Raman spectra in the liquid state, the enthalpy difference was found to be ΔH(T−G)=−0.36±0.02 kcalmol⁻¹ with the T form being more stable. The energy differences between the isomers obtained by DFT calculations were ΔE(T−G)=−0.46 kcalmol⁻¹ and ΔE(T−G)=−0.87 kcalmol⁻¹ by the 6-31G^* basis set and 6-311++G^** basis set, respectively.     

A theoretical investigation on the potential energy surface of CN2H rotation of the encapsulated 1-bicyclo[2.2.1]heptyldiazirine

The potential energy surface (PES) of CN₂H rotation of the encapsulated 1-bicyclo[2.2.1]heptyldiazirine (BHD) inside a molecular container: Cram’s hemicarcerand (CH) was explored using two different DFT involved ONIOM methods: B3LYP/6-31G^**//ONIOM(B3LYP/6-31G^*: AM1) and B971/6-31G^**//ONIOM(B971/6-31G^*: AM1). The free-state PES of CN₂H rotation was also calculated, respectively by B3LYP/6-31G^**//B3LYP/6-31G^* and B971/6-31G^**//B971/6-31G^* methods for comparison. The findings in this study have shown that the PES profiles differ from each other notably in the two states. In the encapsulated state the rotation barrier corresponding to the free-state conversion with the largest rotation barrier increases by about 2 kcal/mol, which has exceeded the largest rotation barrier in the free-state. The conformational preference behavior towards certain BHD isomers, which might be in better conformational compatibility with the container, has been demonstrated.     

Benzooxirene. Ab initio calculations

Ab initio calculations have been performed on benzooxirene, the corresponding oxo carbene (“ketocarbene”), and the transition state linking the two. At the highest level used, QCISD(T)/6-31G^*//MP2(FULL)/6-1G^* with MP2(FULL)/ 6-31G^* zero point energy corrections, the relative energies of the oxirene, the transition state and the carbene are 0, 24.6, and −17.8 kJ mol⁻¹. Correlation energy effects are very important in this system: at the QCISD(T) level the oxirene lies above the carbene, as at the MP4 and HF levels, but at the MP2 level the ordering is reversed. Benzooxirene is probably slightly nonplanar: the HF/6-31G^* geometry is C_2v but the MP2(Fermi contact)/6-31G^* geometry is C_s with a 6-/3-ring coplanarity deviation of about 6.9 °, although in the MP2(FULL)/6-31G^* geometry this is reduced to about 3.1 °.     

Investigation of the use of B3LYP zero-point energies and geometries in the calculation of enthalpies of formation

The use of B3LYP/6–31G^* zero-point energies and geometries in the calculation of enthalpies of formation has been investigated for the enlarged G2 test set of 148 molecules [J. Chem. Phys. 106 (1997) 1063]. A scale factor of 0.96 for the B3LYP zero-point energies gives an average absolute deviation nearly the same as scaled HF/6–31G^* zero-point energies for G2, G2(MP2), and B3LYP/6–311 + G(3df,2p) enthalpies. A scale factor of 0.98, which has been recommended in some studies, increases the average absolute deviation by about 0.2 kcal/mol. Geometries from B3LYP/6–31G^* are found to do as well as MP2/6–31G^* geometries in the calculation of the enthalpies of formation.     

Electronic spectrum of a photochromic diarylethene derivative in a supersonic free jet. Internal conversion from S2(1B) to S1(2A)

The fluorescence excitation and dispersed fluorescence spectra of the open-ring isomer of 1,2-bis(3-methyl-2-thienyl)perfluorocyclopentene have been measured in a supersonic free jet. No vibronic structure has been observed in the excitation spectrum. The intensity of fluorescence gradually increases with the excitation energy in the 25,500–28,700 cm⁻¹ region, indicating that the geometry of the molecule substantially changes upon photoexcitation. The dispersed fluorescence spectrum is anomaly Stokes-shifted with respect to the excitation energy, suggesting that the S₂(1B) state is initially excited followed by rapid internal conversion from the S₂(1B) to S₁(2A) state. The fluorescence is due to the S₁(2A)–S₀(1A) transition. Density functional theory calculations at the B3LYP/6-31G^** level have been carried out to investigate stable conformations responsible for the observed spectra.     

Molecular structure and conformational stability of allylisocyanate—post-Hartree–Fock and density functional theory studies

The molecular structure and conformational stability of allylisocyanate (CH₂CHCH₂NCO) molecule was studied using the ab initio and DFT methods. The geometries of possible conformers, C-gauche (δ=120°, θ=0°) (δ=C=C–C–N and θ=C–C–N=C) and C-cis N-trans (δ=0° and θ=180°) were optimized employing HF/6-31G^*, MP2/6-31G^* levels of theory of ab initio and BLYP, B3LYP, BPW91 and B3PW91 methods of DFT implementing the atomic basis set 6-311+G(d,p). The structural and physical parameters of the above conformers were discussed with the experimental and theoretical values of the related molecules, methylisocyanate and 3-fluoropropene. It has been found that the N=C=O bond angle is not linear as the experimental result for both the conformers and the theoretical bond angle is 173°. The rotational potential energy surfaces have been performed at the HF/6-31G^*, and MP2/6-31G^* levels of theory. The Fourier decomposition potentials were analysed at the HF/6-31G^*, and MP2/6-31G^* levels of theory. The HF/6-31G^* level of theory predicted that the C-gauche conformer is more stable than the C-cis N-trans conformer by 0.41 kJ/mol, but the MP2 and DFT methods predicted the C-cis N-trans conformer is found to be more stable than the C-gauche conformer. The calculated chemical hardness value at the HF/6-31G^* level of theory predicted the C-cis N-trans form is more stable than C-gauche form, whereas the chemical hardness value at the MP2/6-31G^* level of theory favours the slight preference towards the C-gauge conformer.     

Conformational stability of 1-bromo-2-fluoroethane from temperature dependent FT-IR spectra of rare gas solutions

Variable temperature (−55 to −135°C) studies of the infrared spectra (3500–400 cm⁻¹) of 1-bromo-2-fluoroethane, BrCH₂CH₂F, dissolved in liquid krypton and xenon have been recorded. From these data, the enthalpy difference has been determined to be 108±9 cm⁻¹ (1.296±0.113 kJ/mol) and 112±8 cm⁻¹ (1.346±0.098 kJ/mol) from the krypton and xenon solutions, respectively, with the trans conformer the more stable rotamer. Complete vibrational assignments are presented for both conformers which are consistent with the predicted frequencies obtained from the ab initio MP2/6-31G^* calculations. The optimized geometries, conformational stabilities, harmonic force fields, infrared intensities, Raman activities, and depolarization ratios have been obtained from RHF/6-31G^* and/or MP2/6-31G^* ab initio calculations. These quantities are compared to the corresponding experimental quantities when appropriate. Structural parameters and conformational stability have also been obtained from MP2/6-311+G^** calculations. Combining the ab initio predicted structural parameters with the microwave rotational constants, r_o parameters have been obtained for the gauche conformer.     

Further studies on the rotational barriers of Carbamates. An NMR and DFT analysis of the solvent effect for Cyclohexyl N,N-dimethylcarbamate

The solvent effect on the Gibbs energy of activation for rotation around the (C=O)–N bond in cyclohexyl N,N-dimethylcarbamate was investigated by dynamic NMR spectroscopy and density-functional theory at the B3LYP/6-311+G^** level. The experimental barriers were about 15 kcal mol⁻¹ with no appreciable variation when the solvent polarity was changed. A reaction field model was applied to theoretically mediate the solvent effect and the results were comparable to the experimental data. An analysis, based on the Onsager solvation theory, showed that the solvent effect on rotational barriers can be understood employing the total molecular dipole moment, the difference between the dipole moments of the ground and the transition state structures, or both, as appropriate.     

An ab initio study on the geometries and vibrational frequencies of hydrazoic acid and methyl azide

The geometric parameters for hydrazoic acid and methyl azide were optimized at the HF/6-31G^** and MP2/6-31G^** levels and the vibrational frequencies of the compounds were calculated by use of these optimized geometries. The experimental frequencies are assigned on the basis of the calculated results. The effects of deutero-substitution and substitution of hydrogen in HN₃ by a methyl group are also discussed.     

Decomposition Mechanism of 5,5′-Bis(tetrazole)-1,1′-dioIate(TKX-50) Anion Initiated by Intramolecular Oxygen Transfer

Density functional theory calculations at the B3LYP/6-31+G^** and B3LYP/6-311++G ^** levels were perfonned on thermal decomposition of 5,5′-bis(tetrazole)-1 ,r-diolate(TKX-50) anion with an intramolecular oxygen transfer being an initial step. Tlie results show that the intramolecular oxygen transfers are the rate-limiting steps for the decomposition of title anion with activation energies being in the range of 287-328 kJ/mol. Judged by the nucleus- independent chemical shift values, the formation of antiaromatic ring in transition state or the decrease of aromaticity of the tetrazole ring of the reactant makes somewhat contribution to the high potential energies of the rate-limiting transition states. However, the activation energies of the following N2 elimination tlirough various pathways are in a low range of 136-166 kJ/mol. The tetrazole ring acts as an electron donor or acceptor in difierent pathways to assist the bond nipture or group elimination. The rate constants in a temperature range of 500-2000 K for all the intramolecular oxygen transferring reactions were obtained. The corresponding linear relationships between InA and 1/T were established.     

DFT B3-LYP/3-21G geometry optimisation and effective charge values calculations for azodiazaphenanthrenes and acylaminodiazaphenanthrenes

For four azodiazaphenanthrenes 1–4 and three acylaminodiazaphenanthrenes 5–7 the geometry was optimised and their effective charge and dipole moment values were calculated using DFT B3-LYP/3-21G method. For 5–7 the results have been compared with those obtained by AM1 method. The UV experimental values of 1–4 are presented. With the use of DFT B3-LYP/6-31G^** optimised geometry the simulation of UV spectra of 5–7 by AM1 and ZINDO/S methods was made and correlations with experimental UV values have been performed.     

Ab initio study of some peroxides. HOOH, CH3OOH and, CH3OOCH3

The geometries of HOOH, CH₃OOH, and CH₃OOCH₃, were optimized with different basis sets (3-21G, 6-31G^*(*) and D95^**) at different levels of theory (HF, MP2, MP4, and CI). HF/3-21G optimizations result in planar trans conformations for all three peroxides. HF/6-31G^** calculations predict skew conformations for HOOH and CH₃OOH, but a planar trans struture for CH₃OOCH₃. For the larger basis set the calculated bond lengths, especially the O-O bonds, are too short. Optimizations for HOOH including electron correlation at the MP2, MP3, MP4, CI, and CCD level improve the agreement for bond lengths and the OOH angle, but result in dihedral angles Which are too large by 3– 8°. In the case of CH₃OOCH₃, similar calculations at the MP2 and CI level predict planar trans structures instead of the experimentally observed skew conformation. On the other hand, MP4 single point calculations at MP2 optimized parameters result in a correct skew structure. For all three peroxides a computationally “economic” method, i.e., single point calculations at MP2 or MP4 level with HF/3-21G optimized parameters, result in close agreement between calculated and experimental structures.     

Ab initio studies of methanol, methanethiol and methylamine dimer

Quantum chemical calculations are used to provide structural, vibrational and energetical information on the dimers of the methanol, methylamine and methanethiol systems. These systems were studied employing the DFT(B3LYP) and MP2 methods together with the 6-31+G^** and 6-311+G^** basis sets. We found two distinct potential minima for methylamine (one of them is a transition structure) and methanethiol, and one for the methanol dimer. The properties of these dimers are compared with those of the dimers (H₂O)₂, (NH₃)₂ and (CH₃SH)₂. The interactions in these dimers were analyzed using electron density properties at the bond critical point.     

Ab initio studies of molecules with N-C-C=O units Part 1. 2-Aminoethanal

A complete conformational analysis of 2-aminoethanal (2AE) has been carried out using the 6-31G^** basis set. The curve corresponding to the barrier of rotation of the N-C-C=O torsion was obtained and compared with the MM392 and the previously reported 4-21 G curves. Geometrical trends relating to intramolecular hydrogen bonding were found and quantitatively discussed. Full geometry optimization MP2/6-31G^**//6-31G^** was performed for the stable conformers found along the N-C-C=O curve with different arrangements of the NH₂ group.