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.     

Calculation of excited-state properties of some small molecules: Comparative study of the CNDO/S and CNDO/2-vn−1 potential methods

The transition energy and geometry of the lowest excited (nπ*) singlet and triplet states of CO, CS, HNO, H₂CO, HFCO, and F₂CO molecules are calculated by CNDO /S and CNDO /2-V_N?1 potential methods, and the results are compared with those of experimental and ab initio theoretical studies, wherever available. In the calculation of the vertical transition energy, the performance of the CNDO /S method is seen to be generally more satisfactory than that of the CNDO /2-V_N?1 potential method, while the reverse is true for the excited-state geometry. The CNDO /S method as such fails to describe the geometry of the excited state, but a combined version (CNDO /S-2) of CNDO /S and CNDO /2, as well as the CNDO /2-V_N?1 potential method is fairly successful in this regard.     

Semiempirical quantum-chemical calculations on the conformations of methyl formate and methyl thiolformate

The cis, trans, and gauche conformations of the methyl esters of formic and thiolformic acids have been investigated by different semiempirical methods. Total geometry optimization (CNDO/2, MINDO/3) and bond angle optimization (PCILO, NDDO) have been performed for the O-alkyl ester. The S-alkyl ester has been studied by the MINDO/3 method at the total geometry optimization level and by CNDO/2 and PCILO methods at the bond angle optimization level. The influence of sulphur d orbitals on the optimized molecular geometry as well as on the magnitude and direction of the dipole moment vector has been investigated in the CNDO/2 framework. The total energy differences of the conformers are compared to the experimental and ab initio results. CNDO/2 and NDDO energy partitioning have been performed to obtain information on the origin of the cis—trans energy difference and of the rotation barrier. The extent of the lone-pair delocalization has been studied in the different conformations using localized molecular orbitals. Calculations have been performed on the staggered and eclipsed positions of the methyl group in the planar conformations of both esters.     

Calculation of periodic molecular systems with perturbed periodicity within the PCILO framework. II. Model systems

The energetic behavior of one-dimensional (HF)_n and (H₂O)_n chains with added or inserted H₂O or HF was studied by means of the PCILOPSI method presented in Part I. The results were compared with the ones by the original PCILO method. The stabilization energies are in good qualitative agreement; energy differences due to impurity effects even quantitatively agree. The results show that the PCILOPSI method is well suited for the study of perturbed periodic molecular systems.     

Preferential conformation of the carbon-fluorine bond and electronic interactions in substituted benzyl fluorides

CNDO/2 and PCILO calculations have been used to study the preferential conformations and relative stabilities of six para-substituted, three ortho-substituted and two diortho-substituted benzyl fluorides. In non-ortho-substituted compounds, the C-F bond of the CH₂F group lies preferentially in the plane of the phenyl ring. The HOMO energies show that conjugation exists between the substituent and the fluorine atom. Some experimental evidence has been obtained through the use of Raman spectroscopy on the crystalline state. For ortho-substituted compounds the calculations are in agreement with several previous studies which show that steric hindrance can lead to a change in the preferential conformation in the phenyl ring plane as occurs in 2,6-dichlorobenzyl fluoride.     

A modified PCILO framework using the CNDO/Boyd–Whitehead parametrization

The CNDO /BW modification of the CNDO /2 approximation was used within the PCILO framework. It was shown on some significant examples that all the good results of the original PCILO -CNDO /2 method can be reproduced by the modified version PCILO -CNDO /BW at least. Thus, preserving the quality of its results a computer-expense-reduced PCILO method is proposed for calculations on large molecular systems.     

Electronic and molecular structures of (HCN)n polymers

The CNDO/2 method, using the tight-binding approximation, for polymers, has been applied to several constituents of (HCN)_n polymers. Contributions of the intrasegment and intersegment energies to the total energy are discussed in connection with the relative stabilities of these various constituents. The stabilities of the (NCN)_n polymers as protein ancestors are discussed on the basis of the calculations. Band structures of the typical polymer constituents are very briefly discussed.     

On the correlation between photoelectron and electronic spectra in trans- azomethane

A possibility of correlating electronic and photoelectron spectra is discussed, using trans-azomethane as an example. The Coulomb and exchange integrals required were obtained by three semi-empirical SCF-methods: MINDO/2, CNDO/2, and a modified CNDO method. The orbital energies were taken as minus the corresponding experimental ionization potentials. The sequence of the transition energies ΔE (n_s → π*) Δ E (n_a → π*) < ΔE (π → π*) is found to be different from the ionization potential sequence IP (n_s) < IP (π) < IP (n_a), in agreement with previous spectroscopic studies; the results support the latest view that the π → π* transition of the azo group occurs at around 12 eV.     

Determination of one-centre core integrals from the average energies of atomic configurations

One-center core integrals for valence orbitals are determined from the experimental average energies of neutral atomic configurations from Li through Zn. These values are compared with those estimated from CNDO /1, “INDO /1”, CNDO /2, “INDO /2” and with theoretical values calculated from a pseudo-potential method. The agreement is good between values obtained from neutral atoms and from the psuedo-potential calculation except for the 3d orbitals of the transition elements where the theoretically calculated integrals over single ξ functions are not realistic. These two methods reproduce both term and average configuration energies for the first two rows of atoms; the semiempirical method reliably reproduces them for the third row. The CNDO /1 and INDO /1 methods underestimate atomic energies, while the CNDO /2 and INDO /2 procedures fail rather poorly. The propriety of using core integrals estimated semiempirically in molecular orbital calculations is discussed.     

Theoretical studies on structures and electronic spectra of linear carbon chains C2nH+ (n = 1−5)

The density functional theory (DFT) and the complete active space self‐consistent‐field (CASSCF) method have been used for full geometry optimization of carbon chains C_2nH⁺ (n = 1–5) in their ground states and selected excited states, respectively. Calculations show that C_2nH⁺ (n = 1–5) have stable linear structures with the ground state of X³Π for C₂H⁺ or X³Σ^? for other species. The excited‐state properties of C_2nH⁺ have been investigated by the multiconfigurational second‐order perturbation theory (CASPT2), and predicted vertical excitation energies show good agreement with the available experimental values. On the basis of our calculations, the unsolved observed bands in previous experiments have been interpreted. CASSCF/CASPT2 calculations also have been used to explore the vertical emission energy of selected low‐lying states in C_2nH⁺ (n = 1–5). Present results indicate that the predicted vertical excitation and emission energies of C_2nH⁺ have similar size dependences, and they gradually decrease as the chain size increases. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009     

线性BC2nB (n＝1～12)的结构特征和电子光谱的理论研究

应用密度泛函理论, 在B3LYP/6-31G^*水平上优化得到了线性簇合物BC_2nB (n＝1～12, D_(h)的平衡几何构型, 并计算了它们的谐振动频率. 在优化平衡几何构型下, 通过TD-B3LYP/cc-pvDZ和TD-B3LYP/cc-pvTZ计算, 分别得到了n＝1～12和n＝1～7的电子跃迁的垂直激发能和对应的振子强度. 在B3LYP/6-311＋G^*水平上计算得到了簇合物BC_2nB (n＝1～12, D_(h)的电离能. 基于计算结果, 导出了BC_2nB体系电子跃迁能以及第一电离能与体系大小n的解析表达式.     

Investigation of the electronic structure of the TCNQ-TTF system. I. TCNQ and TTF monomers and dimers in the all-valence-electron approximation

Closed-shell and DODS CNDO/2 calculations have been performed for neutral and charged TCNQ and TTF monomers and different dimers. For the sake of comparison the calculation have also performed for the corresponding TCNE molecules.The most important result obtained indicates a large splitting of the lowest unfilled level of TCNQ in going from the monomer to the stacked (TCNQ)₂ dimer. The same holds true for the HOMO level of the (TTF)₂ dimer. This indicates that one should expect a broad conduction band for the neutral poly (TCNQ) chain and a broad valence band for the neutral poly (TTF) chain. In order to test the quality of the CNDO/2 approximation scheme a comparison is attempted with existing experimental findings as well as with some MINDO results and available theoretical predictions within different approximation schemes.     

Intermolecular and intramolecular interactions calculated with ab initio perturbative configuration interaction method using strongly localized orbitals

We have applied the ab initio formulation of the perturbative configuration interaction using localized orbitals (PCILO ) method up to third order to calculate intermolecular and intramolecular interaction energies going beyond the ab initio Hartree–Fock calculation. For the rotational barrier in ethane our results agree well with the experimental value and the cis- and even the trans-barriers in HOOH are at least qualitatively reproduced with the aid of the STO -3G basis set. In the case of the water dimer we obtain an equilibrium intermolecular distance and interaction energy which are confirmed by other calculations. We can further conclude from our studies that one has to include higher orders in the perturbation expansion as the system becomes more complicated. It is especially the last aspect which hinders the application of the ab initio PCILO to estimate the major part of the electron correlation energy for large molecules.     

Excited state properties,fluorescence energies,and lifetimes of a poly(fluorene‐phenylene), based on TD‐DFT investigation

The structural and electronic properties of fluorene‐phenylene copolymer (FP)_n, n = 1–4 were studied by means of quantum chemical calculations based on density functional theory (DFT) and time dependent density functional theory (TD‐DFT) using B3LYP functional. Geometry optimizations of these oligomers were performed for the ground state and the lowest singlet excited state. It was found that (FP)_n is nonplanar in its ground state while the electronic excitations lead to planarity in its S₁ state. Absorption and fluorescence energies were calculated using TD‐B3LYP/SVP and TD‐B3LYP/SVP+ methods. Vertical excitation energies and fluorescence energies were obtained by extrapolating these values to infinite chain length, resulting in extrapolated values for vertical excitation energy of 2.89 and 2.87 eV, respectively. The S₁ ← S₀ electronic excitation is characterized as a highest occupied molecular orbital to lowest unoccupied molecular orbital transition and is distinguishing in terms of oscillator strength. Fluorescence energies of (FP)_n calculated from TD‐B3LYP/SVP and TD‐B3LYP/SVP+ methods are 2.27 and 2.26 eV, respectively. Radiative lifetimes are predicted to be 0.55 and 0.51 ns for TD‐B3LYP/SVP and TD‐B3LYP/SVP+ calculations, respectively. These fundamental information are valuable data in designing and making of promising materials for LED materials. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

Zur theoretischen Interpretation von NMR-chemischen Verschiebungen tetrakoordinierter zentralatome. IV—CNDO/2-Berechnungen von 29Si-NMR-chemischen Verschiebungen. Der Einfluß der ΔE-Näherung

On the basis of the CNDO/2 method paramagnetic screening constants of the central atom of tetrasubstituted silicon compounds of the type Me_4–nSiX_n (X = F, OMe, NMe₂, C1) are calculated, both with and without ΔE approximation. The results are compared with the experimental ²⁹Si n.m.r. chemical shifts. The ‘averaged excitation energies’ ΔE obtained from the comparison of calculated values depend on the charge of the central atom and cannot be considered to be constant for quantitative studies.     

Optimization of molecular geometries in the PCILO and CNDO/2 formalism. The barrier to internal rotation in thioacetaldehyde

The barrier to internal rotation in thioacetaldehyde was investigated within the PCILO and CNDO/2 framework using standard and optimized geometries. The optimized geometries give for the barrier of PCILO a value closer to the experimental one (1.06 kcal mol^?1) whereas the CNDO/2 results yield a qualitatively wrong conformational behavior.     

Theoretical investigation of the structures and spectroscopic properties of (H2O4)n (n = 1–4) clusters

Density functional theory and ab initio calculations were performed to elucidate the hydrogen interactions in (H₂O₄)_n (n = 1–4) clusters. The optimized geometries, binding energies, and harmonic vibrational frequencies were predicted at various levels of theory. The trans conformer of the H₂O₄ monomer was predicted to be the most stable structure at the CCSD(T)/aug‐cc‐pVTZ level of theory. The binding energies per H₂O₄ monomer increased in absolute value by 9.0, 10.1, and 11.8 kcal/mol from n = 2 to n = 4 at the MP2/cc‐pVTZ level of theory (after the zero‐point vibrational energy and basis set superposition error corrections). This result implies that the intermolecular hydrogen bonds were stronger in the long‐chain clusters, that is, the formation of the longer chain in the (H₂O₄)_n clusters was more energetically favorable.     

A pair-excitation MCSCF calculation based on CNDO/INDO approximation I

Second-order multiconfigurational self-consistent field (MCSCF ) calculation has been programmed on the basis of CNDO /INDO molecular orbital bases, in which the configuration space employed is restricted within pair-excitations. Test calculations have been carried out for 17 small molecules. All the MCSCF ground states of these molecules have been successfully converged to their respective optimal states by employing a simple weighting scheme. This procedure provides a great savings in computer time. The MCSCF calculation on azetidine required only 27 min on a HITAC M-680H. The MCSCF energies of HF, F₂, and BH show improved behaviors up to large atomic distances (～7au).