Analytical optimization of exponent values in protonic and deuteronic Gaussian‐type functions by elimination of translational and rotational motions from multi‐component molecular orbital scheme

To optimize the exponent values in protonic and deuteronic Gaussian‐type functions (GTF) by the elimination of translational and rotational motions, we have proposed the new scheme of an analytical gradient formula with respect to the exponent values in the multi‐component molecular orbital scheme, which can take into account the quantum effects of protons and deuterons, under the Hartree‐Fock level of theory. Numerical assessment of H₂ and D₂ molecules confirms that there is a clear difference between distributions of protonic and deuteronic orbitals following the elimination of translational and rotational motions. In particular, the d‐type GTF in the protonic orbital drastically improves the total energy. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

Full variational molecular orbital method: Application to the positron-molecule complexes

Optimal Gaussian-type orbital (GTO) basis sets of positron and electron in positron-molecule complexes are proposed by using the full variational treatment of molecular orbital (FVMO) method. The analytical expression for the energy gradient with respect to parameters of positronic and electronic GTO such as the orbital exponents, the orbital centers, and the linear combination of atomic orbital (LCAO) coefficients, is derived. Wave functions obtained by the FVMO method include the effect of electronic or positronic orbital relaxation explicitly and satisfy the virial and Hellmann–Feynman theorems completely. We have demonstrated the optimization of each orbital exponent in various positron-atomic and anion systems, and estimated the positron affinity (PA) as the difference between their energies. Our PA obtained with small basis set is in good agreement with the numerical Hartree–Fock result. We have calculated the OH⁻ and [OH⁻; e⁺] species as the positron-molecular system by the FVMO method. This result shows that the positronic basis set not only becomes more diffuse but also moves toward the oxygen atom. Moreover, we have applied this method to determine both the nuclear and electronic wave functions of LiH and LiD molecules simultaneously, and obtained the isotopic effect directly. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 70: 491–501, 1998     

Ab initio calculations on the barrier height for the hydrogen addition to ethylene and formaldehyde. The importance of spin projection

Heats of reaction and barrier heights have been computed for H + CH₂CH₂ → C₂H₅, H + CH₂O → CH₃O, and H + CH₂O → CH₂OH using unrestricted Hartree-Fock and Møller–Plesset perturbation theory up to fourth order (with and without spin annihilation), using single-reference configuration interaction, and using multiconfiguration self-consistent field methods with 3-21G, 6-31G(d), 6-31G(d,p), and 6-311G(d,p) basis sets. The barrier height in all three reactions appears to be relatively insensitive to the basis sets, but the heats of reaction are affected by p-type polarization functions on hydrogen. Computation of the harmonic vibrational frequencies and infrared intensities with two sets of polarization functions on heavy atoms [6-31G(2d)] improves the agreement with experiment. The experimental barrier height for H + C₂H₄ (2.04 ± 0.08 kcal/mol) is overestimated by 7?9 kcal/mol at the MP2, MP3, and MP4 levels. MCSCF and CISD calculations lower the barrier height by approximately 4 kcal/mol relative to the MP4 calculations but are still almost 4 kcal/mol too high compared to experiment. Annihilation of the largest spin contaminant lowers the MP4SDTQ computed barrier height by 8?9 kcal/mol. For the hydrogen addition to formaldehyde, the same trends are observed. The overestimation of the barrier height with Møller-Plesset perdicted barrier heights for H + C₂H₄ → C₂H₅, H + CH₂O → CH₃O, and H + CH₂O → CH₂OH at the MP4SDTQ /6-31G(d) after spin annihilation are respectively 1.8, 4.6, and 10.5 kcal/mol.     

In cation interactions with some organics: ab initio molecular orbital and density functional theory

Ab initio molecular orbital and density functional theory studies were undertaken to investigate the structural and energetic characteristics of complexes of In⁺ with several different organic molecules for the first time. HF, MP2, QCISD, and CCD levels of theory in ab initio MO as well as B3LYP, B3PW91 hybrid functionals in density functional theory were used. A valence TZ+P basis set with relativistic effective core potentials was used for the In atom while the 6-311++G(3d, 2p) basis set was utilized for all other atoms. Both closed-shell (H₂O, CH₄, CH₃OH, and C₆H₆) and open-shell (CH₃ and C₂H₃) molecules were considered for complexation with In⁺. In⁺ affinities of 21.5, 24.8, 28.6, 18.4, and 23.0 kcal/mol were obtained with the B3PW91 hybrid functional for H₂O, CH₃OH, C₆H₆, CH₃, and C₂H₃, respectively. The large values for the calculated affinities indicate the validity of our recent experimental detection of In⁺ ion attachment to some organic molecules.     

The epitaxial growth of gaas using alkylarsine: Part 2. molecular orbital calculation

Semi-empirical molecular orbital calculations were carried out for the compounds (C₂H₅)₃As, (C₂H₅)₃Ga and RAsH₂ (R = C₂H₅, i-C₃H₇, i-C₄H₉, and t-C₄H₉) by using the CNDO/2-U program, and their capability of β-elimination reaction is compared on the basis of the torsion energy to the transition state, electrostatic interactions and orbital overlapping between the central atom and the β-hydrogen, and bond order of the metal-carbon, and carbon-hydrogen bond. In the comparison of (C₂H₅)₃As with (C₂H₅)₃Ga, we found that the β-elimination of (C₂H₅)₃As could hardly be expected to take place in the thermal decomposition. The capability of β-elimination would be smaller in C₂H₅AsH₂ than that in (C₂H₅)₃As. Moreover when the ethyl group is replaced by a t-butyl group in RAsH₂, the β-elimination reaction appears to become more difficult and a large possibility for a radical process is suggested.     

Ab initio molecular orbital calculations for 3,6-dihydro-1,2-dithiin and 3,6-dihydro-1,2-dioxin

Optimized geometries and total energies for the conformers of 3,6-dihydro-1,2-dithiin ( 2 ) and 3,6-dihydro-1,2-dioxin ( 3 ) were calculated at several ab initio MO levels: RHF/3-21G(*), RHF/6-31G*, MP2/6-31G*, and MP2/6-31G*/ /RHF/3-21G(*). For the dioxin, in addition to the above levels the corresponding nonextended basis sets ab initio methods were also carried out. The dithiin results are compared with those of simple disulfanes, HSSH and (CH₃)₂S₂, whose optimized geometries agree closely with the observed structures, which is the gauche (C₂ symmetry). For the disulfanes, the gauche geometries from RHF/3-21G(*) are in good agreement with the observed structure while the RHF/3-21G results best fit the dioxin. Pertinent structural data at the RHF/3-21G(*) for the half-chair (C₂) dithiin are: bond lengths, ? SS? , ? CS? , ? CC?, and ? C?C? , 2.050, 1.817, 1.515, and 1.317 Å, respectively; bond angles, CSS, ?CCS, and C?CS, 98.0, 114.2, and 127.8°, respectively; CSSC dihedral angle of 63.2°; and twist angle of 36.5°. The total energy for half-chair dithiin at MP2/6-31G*//RHF/3-21G(*) is less than the planar (C_2v) and the half-boat (C_s) structures by 69.67 and 29.05 kJ/mol, respectively. The calculated structural data (vs. observed) at RHF/3-21G for the half-chair dioxin are: bond lengths, ? OO? , ? CO? , ? CC?, and C?C, 1.464 (1.463), 1.454, 1.509, and 1.313 Å (1.338 Å), respectively; bond angles, COO, ?CCO, and C?CO, 105.0, 109.8 (110.3), and 120.7° (119.9°), respectively; COOC dihedral angle of 79.7° (80 ± 2°); and twist angle of 39.0 (38.3°). The total energy for half-chair dioxin at MP2/6-31G//RHF/3-21G is less than the planar and the half-boat structures by 70.35 and 42.85 kJ/mol, respectively. The total energies calculated at the extended basis sets (*) ab initio levels for the C₂ symmetry dioxin are much lower than those of the nonextended basis sets. © John Wiley & Sons, Inc.     

The use of population localised orbitals to interpret molecular orbital calculations

An efficient and general method is derived to calculate population localised molecular orbitals (LMO's) from a given SCF eigenvector matrix, by reduction to an eigenvalue problem. Applications to both localised molecules (NH₃ and C₂H₂) and delocalised ones (B₂H₆, C₆H₆ and butadiene) are discussed in some detail. It is shown that unequal occupation of atomic energy levels leads to non-orthogonal LMO's. The consequences of non-orthogonal atomic hybrid orbitals are discussed, formulas for their overlap in terms of atomic occupation numbers are derived and it is shown that the occupation numbers are connected to LMO atomic orbital coefficients by various sum rules.     

Molecular orbital studies of polyethylene deformation

Young's modulus E for polyethylene in the chain direction is calculated with molecular orbital theory applied to n-alkanes C₃H₈ through n-C₁₃H₂₈ and analyzed with the cluster-difference method. Semiempirical CNDO, MNDO, and AM1 models and ab initio HF/STO-3G, HF/6-31G, HF/6-31G*, and MP2/6-31G* models are used. Cluster-difference results, when extrapolated to infinite chain length, give E in good agreement with moduli evaluated with molecular cluster or crystal orbital methods, provided minimal basis sets are employed. E decreases from 495 GPa (CNDO) to 336 GPa (MP2/6-31G*) as the level of theory is improved, consistent with established behaviors of the various models. Our calculations do not reproduce earlier molecular cluster or crystal orbital results, which gave E < 330 GPa. The most rigorous MP2/6-31G* model is known to overestimate force constants by ∼ 11%; the scaled modulus E = 299 GPa is in good accord with E = 306 GPa from recent calculations based on experimental vibration frequencies. © 1996 John Wiley & Sons, Inc.     

An ab initio molecular orbital study of the deprotonation of amines

The geometries of the amines NH₂X and amido anions NHX^?, where X = H, CH₃, NH₂, OH, F, C₂H, CHO, and CN have been optimized using ab initio molecular orbital calculations with a 4-31G basis set. The profiles to rotation about the N? X bonds in CH₃NH^?, NH₂NH^?, and HONH^? are very similar to those for the isoprotic and isoelectronic neutral compounds CH₃OH, NH₂OH, and HOOH. The amines with unsaturated bonds adjacent to the nitrogen atoms undergo considerable skeletal rearrangement on deprotonation such that most of the negative charge of the anion is on the substituent. The computed order of acidity for the amines NH₂X is X = CN > HCO > F ≈ C₂H > OH > NH₂ > CH₃ > H and for the reaction NHX^? + H⁺ → NH₂X the computed energies vary over the range 373–438 kcal/mol.     

An ab initio molecular orbital study of the trimethylgallium-arsine adduct: (CH3)3Ga:AsH3

The structure, harmonic frequencies, and binding energy of the trimethylgallium-arsine adduct, (CH₃)₃Ga: AsH₃, have been computed using ab initio molecular orbital methods, and, where possible, compared with experimental results. The structures and frequencies of the precursors trimethylgallium and arsine are perturbed to only a small extent upon adduct formation. The binding energy of (CH₃)₃Ga: AsH₃ is found to be 5.2 kcal/mol lower than that for H₃Ga:AsH₃ at the MP2/HUZSP^*//RHF/HUZSP^* level of computation.     

Structures and stabilities of [C3H3O]+ ions in the gas phase: A molecular orbital study

The relative energies of 11 [C₃H₃O]⁺ ions are calculated by different molecular orbital methods (MINDO/3, MNDO, ab initio with 3-21G and 4-31G* basis set and configuration interaction). The four most stable structures are: a ([CH₂?CH? CO]⁺), b c ([CH?C? CHOH]⁺) and d ([CH₂?C?COH]⁺); their relative energies at the CI/4-31G*//3-21G level are 0, 117, 171 and 218 kJ mol^?1, respectively. The isomerizations c→[CH?CH? CHO]⁺→[CH₂?C? CHO]⁺→ a and dissociations into [C₂H₃]⁺+CO and [HCO]⁺+C₂H₂ are explored. The calculated potential energy profile reveals that the energy-determining step is the 1,3-H migration c→[CH?CH? CHO]⁺. This explains the value of unity of the branching ratio and the spread of kinetic energy released for the two dissociation channels.     

Theoretical Investigations on Fluorine-Substituted Ethylene Dications C2HnF4-n 2+(n = 0–4)

The optimized geometries and energies of fluorine-substituted ethylene dications C₂H_nF_4-n ²⁺ (n = 0–4) have been investigated by means of ab initio methods. At the MP3/6-31G**//6-31G* + zero-point energy level of theory, the results predict that C₂F₄²⁺ and C₂HF₃²⁺ are planar, while C₂H₄²⁺, C₂H₃F²⁺ and 1,1—C₂H₂F₂²⁺ prefer a perpendicular geometry. For 1,2—C₂H₂F₂²⁺ an energy difference of only 0.3 kcal/mol is found between the (trans) planar and perpendicular structure. The stabilizations attributed to hyperconjugation, fluorine lone-pair donation, and (C? F) double-bond conjugation are discussed. A comparison is made for the C? C and C? F stretching frequencies determined at 6-31G*//6-31G* between the neutral and dicationic species. The theoretically determined ionization energies for the vertical process N⁺ → N²⁺ at the MP3/6-31G*//3-21G level are compared with experimental Q_min values.     

Semiempirical molecular orbital calculations on boranes

Traditional Pariser-Parr-Pople and variable electronegativity calculations have been carried out on C₆H₅B(OR)₂ and p-CH₃OC₆H₄B(OR)₂, and the results compared with calculations for C₆H₅BR₂. It is concluded that the VE-SCF method offers a real advantage over the simple PPP method for predicting percent charge transfer and transition intensity in cases where excited states possess substantial C.T. character. The restriction that empirically chosen parameters fit the observed transition energies and intensities of both triarylboranes and ArB(OR)₂ requires the choice of a boron VSIP greater than 2.0 eV in the fixed parameter procedure of the usual PPP-SCF-CI method for these molecules. Observed transitions in C₆H₅B(OR)₂ correlate with ¹ L _b, ¹ L _a, ¹ B _b, whereas the first absorption maximum of (C₆H₅)₃B is assigned to C.T. (¹ A ₁¹ A ₁) local C _2v symmetry.

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Zusammenfassung PPP- und VE SCF-Rechnungen wurden für C₆H₅B(OR)₂ und p-CH₃OC₆H₄(OR)₂ durch- geführt, und die Ergebnisse wurden mit denjenigen für C₆H₅BR₂ verglichen. Es kann der Schluß gezogen werden, daß die VE SCF-Methode einen Vorteil gegenüber der einfachen PPP-Methode bietet, um den prozentualen Charge Transfer und Übergangsintensitäten in Fällen zu bestimmen, in denen die angeregten Zustände einen wesentlichen C.T.-Charakter besitzen. Die Bedingung, daß die empirisch gewählten Parameter den beobachteten Übergangsenergien und -intensitäten von sowohl Triarylboranen als auch ArB(OR)₂ angepaßt sein sollen, erfordert die Wahl eines Bor-VSIP größer als 2,0 eV im Rahmen der üblichen Parametrisierung der PPP-SCF-CI-Methode. Beobachtete Über-gänge in C₆H₅B(OR)₂ korrelieren mit ¹ L _b, ¹ L _a, ¹ B _b, wogegen das erste Absorptionsmaximum des (C₆H₅)₃B einem C.T.-Übergang (¹ A ₁¹ A ₁) lokaler C_2v -Symmetrie zugeordnet wird.

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Résumé Des calculs traditionnels Pariser-Parr-Pople et des calculs d'électronégativité variable ont été effectués sur C₆H₅B(OR)₂ et p-CH₃OC₆H₄B(OR)₂ avec comparison aux résultats obtenus pour C₆H₅BR₂. La conclusion est que la méthode VE-SCF offre un réel avantage sur la méthode PPP simple en ce qui concerne la prédiction du transfert de charge et de l'intensité de transition pour les états excités possédant un net caractère de transfert de charge. La restriction selon laquelle les paramètres empiriques doivent permettre de reproduire les énergies de transition et les intensités des deux triarylboranes et de ArB(OR)₂, nécessite le choix d'un potential d'ionisation de l'état de valence du bore supérieur de 2 eV à celui employé dans les méthodes ordinaires. Les transitions observées dans C₆H₅B(OR)₂ sont reliées à ¹ L _b, ¹ L _a, ¹ B _b, tandis que la première absorption de (C₆H₅)₃B est attribuée à un transfert de charge (¹ A ₁¹ A ₁) de symétrie locale C_2v.

     

Structure and stability of X4Y4H4 (XY=CC,BN)

Ab initio calculations have been carried out to study the structures and relative stabilities of the planar eight‐membered ring B₄N₄H₄ and its isoelectronic species C₈H₄ at the HF/6‐31G*, MP2/6‐31G*, MP2/6‐311G**, and MP4SDQ/6‐31G* levels. The analyses of Milliken population, vibration frequencies, π‐molecular orbital components, and orbital energy levels were used to evaluate the relative stabilities of these two similar systems. The homodesmotic reactions were also taken to be a useful index of relative stability for X₄Y₄H₄ (XY=CC, BN) and gave the resonance energies with MP4SDQ/6‐31G* of C₈H₄ (?37.2 kcal/mol) < B₄N₄H₄ (?29.2 kcal/mol). Furthermore, we calculated the thermodynamic functions of these reactions to discuss the influence of temperature. It is concluded that B₄N₄H₄ may exist in theory and could be a little more stable than C₈H₄. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 82: 293–298, 2001     

The geometric and electronic structures of oxocarbons. An ab initio molecular orbital study

Ab initio molecular orbital calculations with the STO-3G and 4-31G basis sets have been carried out for the neutral oxocarbons C_nO_n (n = 3, 4, 5, 6 and 7), the dianions C_nO_n^2- (n = 3, 4, 5, 6 and 7), the monoanions C_nO_nH^? (n = 3 and 4) and the related acids C_nO_nH₂ (n = 3 and 4). Fully optimised geometries have been obtained for all species. The geometries, stabilities and acidities are discussed.     

Über Chalkogenolate. 127. Diester der Cyaniminodiameisensäure NC?N(CO?OR)2 mit R = CH3, C2H5 und C6H5. Thiolyse der Diester

On Chalcogenolates. 127. Diesters of Cyanimino Diformic Acid NC? N(CO? OR)₂, where R = CH₃, C₂H₅, and C₆H₅. Thiolysis of these Diesters The diesters NC? N(CO? OR)₂ have been prepared by reaction of the sodium salt of cyanamide with the corresponding chloroformic acid ester. The thiolysis of these esters yields H₂N? CS? NH? CO? OR. The compounds with R = CH₃, C₂H₅, and C₆H₅ have been characterized by means of diverse methods.     

AB Initio molecular orbital calculations on the si2h4molecule

Ab initio molecular orbital calculations using an extended Gaussian basis set have been performed on C₂H₄, CH₂SiH₂ and Si₂H₄. The species CH₂ and SiH₂ have also been examined. Geometries were partially optimized and the energy difference between the planar singlet and orthogonal or twist triplet geometries of Si₂H₄ was studied in order to provide a measure of the strength of the Si-Si bond in this molecule. Mulliken population analyses were carried out on CH₂CH₂ and SiH₂SiH₂, to further study the nature of the Si-Si double bond in comparison with the C—C double bond.     

Probing the exohedral magnetic properties of C20 derivatives by through space NMR shieldings (TSNMRS)

The through space NMR shieldings (TSNMRS) of dodecahedrane C₂₀H₂₀, of the isomeric hydrocarbons C₂₀H₁₂, of the ions C₂₀H₁₂²⁺ and C₂₀H₁₂^2?, of the fluxional fullerene C₂₀ and of its dication C₂₀²⁺ have been ab initio calculated employing the NICS concept on basis of MP2/6-31G1 geometries and visualized as iso-chemical-shielding/deshielding surfaces (ICSSs). TSNMRS values were employed to study the exohedral magnetic properties of the compounds studied. Hereby, the curved π-conjugation in the compounds studied could be quantified.     

Quantum chemical studies of propene,ethylene, acetylene and dihydrogen reactivity in the insertion reaction into the titanium-alkyl bond

Using the ab initio method of SCF MO LCAO

1 SCF MO LCAO: Self-consistent field molecular orbital linear combination of atomic orbitals.

in a valency-splitted basis of the Gaussian functions we have studied the addition of various monomers (C₃H₈, C₂H₄, C₂H₂) and dihydrogen to the titanium-alkyl bond in the complex H₂TiCH₃. The structure of transition states in the insertion reaction, heats of π-complex formation and activation energies for the insertion of the coordinated monomers have been calculated. The calculation results show that the reactivity decreases in the order C₂H₂ > C₂H₄ > C₃H₈ > H₂. According to the results obtained, the energy of the π^*-antibonding orbital of monomers can serve as an index of relative reactivity in the insertion reaction into the metal-alkyl bond.