SCF MO Research Articles

State of ions and water molecules in the water salt solutions of polyacrylamide and co-polymer of “acrylamide–acrylic acid Na/k salt”

Geometrical and electronic parameters of the microstates of the molecular models of polyacrylamide and co-polymers of acrylamide-acrylic acid in aqueous solutions of sodium and potassium chlorides were computed by the non-empirical SCF MO LCAO method with the use of the basis MINI Huzinaga. The models contained four monomeric units of the polymer, including two metal carboxylate groups, 80 water molecules and two pairs of ions Na+ and Cl– or K+ and Cl–. It follows from the calculation results that there is a principal difference in the hydration of Na+ and K+: the Na+‧‧‧О2– bond is shorter than the sum of the radii of the interacting ions, while the k+‧‧‧O2– bond is equal or longer. This indicates that in the first case, the bonds are partially covalent, while in the second one they are pure electrostatic. All elements of the molecular models in the both cases are combined by the intermolecular bonds forming a spatial net. The polymer molecules have a flexible chain with oxygen containing functional groups that are built into the structure of the salt solutions without distorting it. We assume that this is the main reason for the good solubility of the studied polymers in the aqueous salt solutions.

Hydration of ion exchangers: Thermodynamics and quantum chemistry calculations. IV. The state of ions and water molecules in alkali forms of sulfostyrene resins

New information on the state of water molecules and ions in the alkali ion forms of sulfostyrene resins have been obtained by joint application of thermodynamic and quantum chemistry methods to treatment of experimental water sorption isotherms taken from the literature. The theoretical water sorption isotherms have been computed from suggested earlier model of Predominant Hydrates. The model parameters were obtained with the help of quantum chemical calculations of structures of the swollen ion exchangers. Ab initio non-empirical SCF MO LCAO method has been used. The molecular models included fragments of the polystyrene chain with two sulfonic groups and the number of water molecules identical to that in the resins with 10% divinylbenzene. The theoretical water sorption isotherms for all alkali metal forms accurately describe the experimental data in the assumption of presence in the resin three (Li+ and Na+) or two (K+, Rb+ and Cs+) predominant hydrates. The calculations allowed obtaining the following characteristics of the molecular models: binding energy of the water molecules to the swollen ion exchanger, Gibbs' energy of the hydrates formation, distances between the water molecules and ions, lengths of the hydrogen bonds and some other parameters. These data allowed explaining physical reasons for the difference in properties of the alkali ions related to the water “structure forming” and “structure breaking” subgroups. The results of the quantum chemistry calculations clearly indicate separation of water molecules in the resin into several groups differing in the binding energy and the distances to the cations. The number of hydrogen bonds per water molecule in the ion exchanger is about 25% less than in the bulk water, but the total number of intermolecular bonds (hydrogen and ion-molecular) is approximately the same as in the bulk water. Intermolecular bonds in the ion exchanger form an integrated net in which the mobile and the fixed ions function as the knots.

Calculation of Vibrational Spectra of p-Ethylbenzenesulfonic Acid Hydrates

Quantum-chemical calculations of vibrational spectra of the sulfonated ion-exchanger model p-ethylbenzenesulfonic acid hydrated by 1–10 water molecules and its dimer were calculated by the non-empirical SCF MO LCAO method with the 6-31G(d) basis set. The calculated results were compared with experimental IR and Raman spectra of sulfonated ion exchangers. The infl uence of hydration on the vibrational frequencies of functional groups in the ion exchangers was analyzed. It was shown that the sulfonic acid was completely dissociated if three and more water molecules per functional group were present. Bands near 1130 cm–1 were due to S–O–H bending vibrations in the absence of water molecules and C–S–O–H3O combination vibrations with 3–6 water molecules per sulfonic acid.

Mathematical aspects of the LCAO MO first order density function (5): centroid shifting of MO shape functions basis set, properties and applications

In MO SCF theory and related computational levels, the first order density function (DF) can be considered as a linear combination of the MO shape functions (ShF) set. This work studies the possibility of constructing a centroid function from the ShF set elements using it to perform a ShF set origin shift, while permitting the DF decomposition in two well defined function terms. The properties and consequences of such a simple operation are analyzed in deep.

Basis set dependence of molecular information channels and their entropic bond descriptors

Information channels from SCF MO calculations using different basis sets and their entropic bond descriptors are compared within the orbital communication theory. In this information-theoretic (IT) treatment of communications between basis functions the overall covalency and ionicity bond components reflect the average communication noise and information flow, respectively, in the resolution level specified by the adopted set of basis functions. The basis-set dependence of the orbital conditional probabilities and their entropic descriptors of the information covalency/ionicity content is explored. Compared to the minimum set \({{\bf \chi}}\) of the occupied atomic orbitals of the separated constituent atoms, the extended basis sets of Gaussian orbitals and/or their formal contractions generally give rise to a higher IT-covalency and lower IT-ionicity descriptors of the system chemical bonds. In the augmented set case, \({{\bf \chi}^{aug.} = ({\bf \chi},{\bf \psi})}\) , containing the polarization function complement \({{\bf \psi}}\) of \({{\bf \chi}}\) , the use of only \({{\bf \chi} \rightarrow {\bf \chi}}\) communications is advocated in a semi-quantitative chemical interpretation of the IT bond indices. The maximum-overlap criterion is used to transform the general (orthonormal) extended basis \({{\bf \xi}}\) to its semi-augmented form \({\widetilde{\bf \chi}^{aug.} = \widetilde{\bf \xi}=(\widetilde{\bf \chi}, \widetilde{\bf \psi}),}\) in which \({\widetilde {\bf \chi} \approx {\bf \chi}}\) and \({\widetilde {\bf \psi} \approx{\bf \psi}}\), which facilitates the near minimum basis set interpretation of bond descriptors and extraction of communications involving the polarization functions \({{\widetilde {\mathbf \psi}}}\) . A similar transformation using the minimum information distance criterion can be also envisaged. The effect of the atomic reduction of the molecular channels, which misses the effect of the “internal” communications (bonds) on constituent atoms, is also examined. As intuitively expected, the IT descriptors of such reduced channels are found to be less sensitive to the basis set enlargement.

Periodic calculations of excited state properties for solids using a semiempirical approach

The semiempirical SCF MO method MSINDO (modified symmetrically orthogonalized intermediate neglect of differential overlap) [T. Bredow and K. Jug, Electronic Encyclopedia of Computational Chemistry, 2004] is extended to the calculation of excited state properties through implementation of the configuration interaction singles (CIS) approach. MSINDO allows the calculation of periodic systems via the cyclic cluster model (CCM) [T. Bredow et al., J. Comput. Chem., 2001, 22, 89] which is a direct-space approach and therefore can be in principle combined with all molecular quantum-chemical techniques. The CIS equations are solved for a cluster with periodic boundary conditions using the Davidson-Liu iterative block diagonalization approach. As a proof-of-principle, MSINDO-CCM-CIS is applied for the calculation of optical spectra of ZnO and TiO(2), oxygen-defective rutile, and F-centers in NaCl. The calculated spectra are compared to available experimental and theoretical literature data. After re-adjustment of the empirical parameters the quantitative agreement with experiment is satisfactory. The present approximate approach is one of the first examples of a quantum-chemical methodology for solids where excited states are correctly described as n-electron state functions. After careful benchmark testing it will allow calculation of photophysical and photochemical processes relevant to materials science and catalysis.

Interionic Interactions in Carboxylic Acid Cation Exchangers on the Base of Polyacrylic Acid. Ab Initio Calculations

Ab initio calculations of the structure of representative fragments of carboxylic acid cation exchangers on the base of polyacrylic acid in forms of alkali, alkali earth, and some heavy metal ions (Cu2+, Ni2+, Co2+, Cd2+, Mn2+, Pb2+) have been made by the RHF SCF MO LCAO method. In the case Ni2+ and Cu2+ in the main valence state, the calculations were made by the ROHF SCF MO LCAO method. The calculated fragments contained up to nine repeating units of the polymer chain, the counterions and 0–10 water molecules per carboxylate group. The geometry and electronic characteristics of the Me–O bonds with carboxylic groups and water molecules in the hydration systems were analyzed. The ionic hydration in these systems was characterized by the number of water molecules directly bound only to the carboxylic groups, only to the counterion both to the carboxylate group and the counterion, and only to the other water molecules. It appeared that in all cases the counterions are strongly bound with carboxylate groups forming rigid structures in which one univalent counterion can be directly bound to two carboxylate groups. The bivalent cations are mainly bound to three carboxylate groups. The electroneutrality of the polymer fragment is provided through the group binding of the counterion and the carboxylic groups. The significant degree of covalence of the bonds between the cations and carboxylic group dependent on the atomic mass and number of water molecules in the system is mainly responsible for the selectivity series of the alkali and alkali earth metals. These series are opposite to those for sulfonic cation exchangers. The high selectivity of sorption of the heavy metal ions is due to the fact that the Me–O bonds with oxygen atoms of both carboxylate groups and water molecules have a high degree of covalence. These interactions are competitive and their balance is individual for any pair of fixed and counterion.

ChemInform Abstract: Nucleophilic Displacement in Polyhalogenoaromatic Compounds. Part 14. Chloroazulenes.

Methoxydechlorination of 5,6-dichloroazulene in NaOMe–MeOH shows second-order kinetics, apparently proceeding by the SNAr mechanism in which the attack of the nucleophile, and not the loss of chloride ion, is rate-determining. No evidence of a Meisenheimer-type intermediate is found. The rate of the reaction is not affected by light, nor by the presence of nitrobenzene; radical contributions to the process are therefore unlikely. The corresponding reactions of 4,5,6,7- and 1,3,5,6-tetrachloroazulene, and of 1- and 3-nitro-5,6-dichloroazulene all show second-order kinetics and are all accelerated compared to the parent compound; 1,3,4,5,6,7-hexachloroazulene reacted too rapidly for measurement. As expected, the extent of such acceleration is conditioned not only by the nature of the substituent but also by its position. Unexpectedly, chlorine substituent effects are clearly greater from the five-membered ring than from the ring undergoing attack.Semi-empirical all-valence-electron SCF–MO calculations are presented which rationalise the orientation of attack and describe the observed substituent effects.

ChemInform Abstract: Oxidation of 3-Hydroxythiophenes (Thiophen-3(2H)-ones): An EPR Study of Monomeric and Dimeric Intermediates.

Hydrogen abstraction from thiophen-3(2H)-ones gives 3-oxothiophen-2-yl radicals which have been observed by EPR spectroscopy at temperatures below ambient. The structures, enthalpies of formation, and spin densities of these species have been investigated by semiempirical SCF MO methods. The radicals readily couple to give dimers which (except for 2-substituted 3-hydroxythiophenes) are susceptible to a second hydrogen abstraction step to give extensively delocalized dimeric radicals; EPR spectroscopy showed the 5,5′-disubstituted dimeric radicals to be significantly persistent even at higher temperatures. A mechanism for the oxidation of thiophen-3(2H)-ones by air and one-electron oxidants is proposed and justified.

Quantum chemical calculations of vibrational spectra of para-ethylbenzenesulfonic acid

Quantum chemical calculations of vibrational spectra of para-ethylbenzenesulfonic acid have been conducted by means of a non-empirical SCF MO LCAO method with the use of the 6-31G(d) basis set. Calculated IR and Raman frequencies are assigned to vibrations of specific atomic groups. It is shown that para-ethylbenzenesulfonic acid can serve as a reasonable quantum chemical model in calculations of vibrational spectra for polystyrene sulfonic resins of various degrees of hydration.

Theoretical Mass Spectra of PE, PP, PS and PET Polymers by QMD Methods Using the Model Molecules

We used a quantum molecular dynamics {QMD (MD with MO)} due to the force function of MO with the velocity Verlet algorithm using the model oligomers of PE, PP, PS, and PET polymers to obtain theoretical mass spectra of the polymers. The QMD calculation was performed in the thermal energy range of 0.69 - 0.95 eV, and the sampling position data by a time step of 0.5 fs were performed up to 5000 steps. The fragments at the final step of 60 trajectories in the QMD were obtained as positive, negative, and neutral charged ones from the net atomic charge analysis at geometry-optimization of the MO SCF calculations. We can compare the positive ion fragments of polymer models with the experimental distribution of polymers in mass spectra and secondary ionization mass spectra after a few tens of keV of primary heavy metal ion bombardment. We also showed the chemical structures of fragments for PE, PP, PS, and PET polymers in positive ion spectra, unavailable from experimental methods.

Theoretical studies on the cycloaddition reaction of ethylene and formaldehyde

The potential energy surface of cycloaddition (H2CCH2 + H2CO) has been investigated by using the ab initio SCF MO method at extended (3–21G) level. All the critical points were optimized by energy gradient technique and characterized by computing the Hessian matrices with analytic method. The results of computations indicate that: (i) Stepwise reactions involving diradicaloid intermediates and transition states are more favorable than the concerted ones. (ii) There are two compatible stepwise reaction mechanism, one is to form C—C bond firstly, while the other is to form C—O bond at first. (iii) For the reverse reaction-thermolysis of oxetane, the cleavage of C—O bond is preferred over that of C—C bond.

Catalytic activity of the first solvation shell in the CO2 hydration reaction

The catalytic activity of the first solvation shell for the CO2 hydration reaction has been studied within the ab initio LCAO MO SCF supermolecular approach to determine the significance of the specific solvation sites in lowering the activation barrier. The role of OH- ion replacing some solvent molecules has also been investigated suggesting alternative mechanism of CO2 hydration in alkaline solutions. In addition, the basis set dependence of the activation barrier and basis set superposition effect on barrier lowerings were examined.

Optimum geometries and relative energies for guanine, the imino-enol tautomer of guanine, the enol tautomer of guanine, adenine, and the imino tautomer of adenine as found by the MINDO/2 SCF MO method

A MINDO/2 SCF MO geometry optimization of guanine (G), the imino-enol tautomer of guanine (G*), the enol tautomer of guanine (G**), adenine (A), and the imino tautomer of adenine (A*) was made. The optimized geometries for guanine and adenine agree well with crystallographic data. The optimized geometries for the tautomers show the correct trends in bond lengthening and bond angle adjustment. The energies of all five molecules were lowered relative to the initial assumed geometry by the optimization procedure. The energies of tautomerization were found to be 0.4, − 18.7, and 12.5 kcal for G ⇌ G*, G ⇌ G**, and A ⇌ A*, respectively. When solvent effects are included the energies of tautomerization are 5.2, − 10.0, and 8.7 kcal for G ⇌ G*, G ⇌ G**, and A ⇌ A*, respectively.

Aspects of oxopyridine-water interactions

The hydration schemes of the lactam and lactim tautomers of 2- and 4-hydroxypyridines have been established by appropriate electrostatic calculations. It is shown that hydration stabilizes more of the lactam than the lactim tautomers of these molecules. Ab initio SCF MO calculations performed for the complex of 4-pyridone with water show that the binding energies for water situated out of the plane of pyridone are smaller than when water is placed in the plane of the molecule. The comparison of the ab initio results with earlier CNDO/2 ones shows that the latter greatly overestimate the stability of the nonplanar complexes.

On invariant procedures in approximate SCF MO theories

The CNDO and subsequent methods by Pople are analyzed with regard to a possible refinement. It is emphasized that the invariance requirements for atomic integrals under local rotations and local hybridization are not essential for the theory, but that the SCF equations have to be invariant under unitary transformations of the atomic basis set. The removal of this restriction yields the possibility of introducing different scale factors for the various 2s- and 2p-orbitals at the same center. For aromatic systems it is predicted that little improvement will result for ground state properties which are average values of the σ- and π-part, e.g. total dipole moments. The neccessity of the application of the more recent scale factors for calculations on spectra is pointed out.

Theoretical prediction of g tensors and hyperfine coupling tensors of triplet molecules

This is the first time that all-valence-electron SCF MO calculations of g tensors and hyperfine coupling (HFC) tensors of some triplet molecules have been carried out. The molecular orbital spin density is partitioned into the σ and π-electron spin delocalization (SD) terms and the remaining terms of spin polarization (SP) which arise from the CI effect. The g tensors for CH2 and some other carbenes which have ground triplet states and the excited triplet formaldehyde are evaluated. The origin of HFC in CH2 is analyzed in detail by using the partitioning method for spin density matrices. The absolute values of the isotropic and anisotropic 13C HFC tensors of CH2 calculated by taking into account the SD terms only are in good agreement with those observed for CD2. The contribution of the SP terms to the isotropic HFC tensors is fairly large, while the contribution to the anisotropic HFC tensors is negligibly small.

Self-consistent molecular orbital calculations by least-squares projection of 2-center charge distributions

A method for approximating hybrid and exchange integrals over atomic orbitals is discussed and examined in detail for the case of Slater-type orbitals (STO'S). The crux of the approximation is the least-squares projection of 2-center charge distributions onto suitably chosen 1-center charge distributions. The approximate integrals are thus linear combinations of Coulomb-type integrals, and are generated at a rate of ∼150/sec on a CDC 1604A computer. The method is employed in an SCF MO study of benzene and several of its ions.

The lowest excited states of BH

Digital computer calculations in SCF MO approximation on the two lowest excited states of BH, 1σ22σ23σ4σ, 3Σ+ and 1Σ+, from 2.0 a.u. out to dissociation are reported. As shown previously by Grimaldi and coworkers [1], these are stable Rydberg states, but it is now shown that the 3Σ+ potential curve on increasing the interatomic distance R goes over a maximum and then becomes a repulsion curve dissociating to normal atoms. The changing characteristics of the 2σ, 3σ and 4σ orbitals as a function of R are described and discussed.

An approximate SCF MO theory of molecules based on slater's Xα method

A new approximate SCF MO theory is constructed for molecular systems based on the Xα method. The proposed theory is suited especially for potential surface calculations. Atomic “core” is separated and no adjustable parameters appear in the theory. Many quantities in the theory can be determined by the undistorted atomic electron densities. Explicit expressions for the separation energy and the model potential are given.