Perturbative calculation of intermolecular interactions in orthogonalized or biorthogonal basis sets

Two versions of a many-body perturbation theory for the computation of molecular interaction energies are investigated. The methods are based on the partitioning of the second-quantized form of the dimer Hamiltonian written either in the orthogonalized basis of the monomer MOs, or, alternatively, in the original non-orthogonal dimer basis set handling the overlap by the biorthogonal formalism. The zeroth-order Hamiltonian H ⁰ is the sum of effective monomer Fockians and the zeroth-order wave functions are exact eigenfunctions of H ⁰. Full antisymmetry is ensured by the second-quantized formalism. Basis set superposition error is accounted for by the counterpoise correction recipe. Results for He₂, (H₂)₂ and (H₂O)₂ indicate the reliability of the biorthogonal technique.     

Electronic quantum motions in hydrogen molecule ion

The hydrogen molecule ion is a two‐center force system expressed under the prolate spheroidal coordinates, whose quantum motions and quantum trajectories have never been addressed in the literature before. The momentum operators in this coordinate system are derived for the first time from the Hamilton equations of motion and used to construct the Hamiltonian operator. The resulting Hamiltonian comprises a kinetic energy T and a total potential V_Total consisting of the Coulomb potential and a quantum potential. It is shown that the participation of the quantum potential and the accompanied quantum forces in the force interaction within H₂⁺ is essential to develop an electronic motion consistent with the prediction of the probability density function |Ψ|². The motion of the electron in H₂⁺ can be either described by the Hamilton equations derived from the Hamiltonian H = T_K + V_Total or by the Lagrange equations derived from the Lagrangian H = T_K ? V_Total. Solving the equations of motion with different initial positions, we show that the solutions yield an assembly of electronic quantum trajectories whose distribution and concentration reconstruct the σ and π molecular orbitals in H₂⁺. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Spin–orbit corrections to the indirect nuclear spin–spin coupling constants in XH4 (X=C, Si, Ge, and Sn)

Summary.  Using the quadratic response function at the ab initio SCF level of approximation we have calculated the relativistic corrections from the spin–orbit Hamiltonian, H ^SO, to the indirect nuclear spin–spin coupling constants of XH₄ (X=C, Si, Ge, and Sn). We find that the spin–orbit contributions to J _X–H are small, amounting only to about 1% for J _Sn–H. For the geminal H–H coupling constants the relativistic corrections are numerically smaller than for J _X–H, but in some cases relatively larger compared to the actual magnitude of J _H–H. We also investigate the use of an effective one-electron spin–orbit Hamiltonian rather than the full H ^SO in the calculation of these corrections. Received July 12, 1996 / Final revision received September 12, 1996 / Accepted September 17, 1996     

A new oxamido-bridged dinuclear copper(II) complex with large antiferromagnetic exchange interactions

A new oxamido-bridged dinuclear compound [Cu₂(µ-pmox)(DMF)₄]?·?2ClO₄ (1) (H₂pmox?=?N,N′-bis-(2-methylpyridyl)oxalamide, DMF?=?dimethylformamide) was synthesized and structurally characterized. The five-coordinate Cu(II) is bridged by oxamido groups and further cross-linked by C–H···O hydrogen bonds between the uncoordinated oxygen of perchlorate and methyl of DMF. The complex was also characterized by infrared spectroscopy and magnetic measurement. The copper complex exhibits strong antiferromagnetic interactions via the trans oxamido bridge with J of ?414?cm^?1, where J is the exchange parameter in the isotropic Hamiltonian H?=??JS₁S₂.     

Spin-orbit corrections to the indirect nuclear spin-spin coupling constants in XH4 (X = C, Si, Ge, and Sn)

Summary Using the quadratic response function at theab initio SCF level of approximation we have calculated the relativistic corrections from the spin-orbit Hamiltonian,H ^SO, to the indirect nuclear spin-spin coupling constants of XH₄ (X = C, Si, Ge, and Sn). We find that the spin-orbit contributions toJ _X-H are small, amounting only to about 1% forJ _Sn-H. For the geminal H-H coupling constants the relativistic corrections are numerically smaller than forJ _X-H, but in some cases relatively larger compared to the actual magnitude ofJ _H-H. We also investigate the use of an effective one-electron spin-orbit Hamiltonian rather than the fullH ^SO in the calculation of these corrections.     

Crystal-field splittings and optical spectra of transition-metal mixed-ligand complexes by effective Hamiltonian method

Many of the important properties of transition-metal complexes depend on the low-energy excitation spectrum formed by d-electrons of the central transition-metal atom. The spectra of this type are usually fit to the well-known crystal field theory or to the angular overlap model. The result of the fitting is a set of parameters which are considered as characteristics of the electronic structure of the complex such as strength of the ligand field or types and extent of metal-ligand bonding. We present here a short account of the effective Hamiltonian method recently developed to calculate the splitting of the d-levels by the ligands and the resulting d-d spectra of transition-metal complexes together with some results of its application to the mixed-ligand complexes with the general formula ML₄Z₂, where M = V, Co, Ni; L = H₂O, NH₃, Py; and Z = H₂O, NCS−,C −l. Particular attention is paid to the V(H₂O)₄Cl₂ and Co(H₂O)₄Cl₂ compounds. The former seems to have tetragonal structure, whereas for the latter, our method predicts a spatially degenerate ground state for the tetragonal arrangement of the ligands. That must lead to the Jahn-Teller distortion, which is actually observed. © 1996 John Wiley & Sons, Inc.     

Hydrothermal synthesis,crystal structure and magnetic properties of a copper(II) phosphonate

The treatment of 3-ammonium-1-hydroxypropylidene-1,1′-bisphosphonate (H₇ahdp) and 4,4′-bipy with CuCl₂?·?2H₂O resulted in a metal phosphonate [Cu(H₅ahdp)?·?H₂O] _n . Its crystal structure has been characterized by single X-ray crystallography. Although there is no 4,4′-bipy in the lattice structure, it plays a very important role in forming the one-dimensional chain of the polymer. Hydrogen bonds link the chains into a 3D network. The dinuclear secondary building units are observed in the compound. The determination of variable-temperature magnetic susceptibilities (5?～?300?K) shows weak intrachain antiferromagnetic coupling between copper(II) centers. The magnetic data were fitted to the appropriate equations derived from the Hamiltonian H?=??2JS ₁ S ₂, giving the parameter J?=??25.78?cm^?1. Its thermal properties were also investigated.     

Separation of the vibrational,rotational, and translational motions of polyatomic molecules using curvilinear vibrational coordinates

A new method is suggested for separating the vibrational, rotational, and translational motions of polyatomic molecules using curvilinear vibrational coordinates that are linear with respect to the natural vibrational coordinates. It is shown that, in this case, Coriolis interactions between the vibrational and rotational motions are absent. The solutions of the anharmonic vibrational-rotational problems in the curvilinear and linear vibrational coordinates are compared. The absence of Coriolis interactions between the vibrational and rotational motions in the curvilinear vibrational coordinates is proved numerically. The same conclusion is additionally supported by calculations of the anharmonic vibrational energy levels for the H₂O, H₂S, NO₂, SO₂, and ClO₂ molecules in the linear and curvilinear vibrational coordinates using the Hamiltonian designed in the curvilinear vibrational coordinates with and without Coriolis vibrational-rotational interactions. Volgograd Pedagogical University. Translated fromZhurnal Strukturnoi Khimii, Vol. 36, No. 2, pp. 239–254, March–April, 1995. Translated by I. Izvekova     

Cyano-bridged Heterotrinuclear Molybdenum(IV)-Nickel(II) Complexes: Synthesis,Crystal Structure and Magnetic Properties

Two novel cyano-bridged heterotrinuclear molybdenum(IV)-nickel(II) complexes ([Ni(en)₂(H₂O)]_2-[Mo(CN)₈]·2H₂O, 1, and [NiL(H₂O)]₂[Mo(CN)₈]·4H₂O, 2), where en=1,2-diaminoethane and L= 1,3,6,9, 11,14-hexaazacyclo[12,2,1,1^6,9]octodecanne were synthesized and characterized. The crystal structure of 1 was determined. The structure consists of trinuclear units, space group C2/c, with unit cell dimensions a=17.178(9), b=11.032(5), c=17.629(8) Å, α=108.484(8)°. The temperature dependence of the magnetic susceptibilities for 1 and 2 was analyzed by means of a Hamiltonian expression leading to J=-0.87cm^-1, ZJ'=0.65cm^-1, D=0.02cm^-1, g _Ni=2.45 for complex 1, and J=-0.87cm^-1, ZJ'=0.56cm^-1, D=0.02cm^-1, g, _Ni=2.45 for complex 2.     

Some properties of the bivariational Hartree–Fock scheme for complex symmetric many-particle operators

The bivariational Hartree–Fock scheme for a general many-body operator T is discussed with particular reference to the complex symmetric case: T^? = T*. It shown that, even in the case when the complex symmetric operator T is real and hence also self-adjoint, the complex symmetric Hartree–Fock scheme does not reduce to the conventional real form, unless one introduces the constraint that the N-dimensional space spanned by the Hartree–Fock functions ? should be stable under complex conjugation, so that ?* = ?α. If one omits this constraint, one gets a complex symmetric formulation of the Hartree–Fock scheme for a real N-electron Hamiltonian having the properties H = H* = H^?, in which the effective Hamiltonian H_eff (1) may have complex eigenvalues ε_k. By using the method of complex scaling, it is indicated that these complex eigenvalues—at least for certain systems—may be related to the existence of so-called physical resonance states, and a simple example is given. Full details will be given elsewhere.     

Mode Selective Stereomutation and Parity Violation in Disulfane Isotopomers H2S2, D2S2, T2S2

We report quantitative calculations of stereomutation tunneling in the disulfane isotopomers H₂S₂, D₂S₂, and T₂S₂, which are chiral in their equilibrium geometry. The quasi‐adiabatic channel, quasi‐harmonic reaction path Hamiltonian approach used here treats stereomutation including all internal degrees of freedom. The torsional motion is handled as an anharmonic reaction coordinate in detail, whereas all the remaining degrees of freedom are taken into account approximately. We predict how stereomutation is catalyzed or inhibited by excitation of the various vibrational modes. The agreement of our theoretical results with spectroscopic data from the literature on H₂S₂ and D₂S₂ is excellent. We furthermore predict the influence of parity violation on stereomutation as characterized approximately by the ratio (ΔE_pv/ΔE_±) of the (local or vibrationally averaged) parity violating potential ΔE_pv and the tunneling splittings ΔE_± in the symmetrical case. This ratio is exceedingly small for the reference molecules H₂O₂ and D₂O₂, and still very small (2⋅10⁻⁶ cm⁻¹) for H₂S₂, which, thus, all exhibit essentially parity conservation in the dynamics. However, for D₂S₂ it is ca. 0.002, and for T₂S₂ it is ca. 1, which seems to be the first case where such intermediate mixing through parity violation is quantitatively predicted for spectroscopically accessible molecules. The consequences for the spectroscopic detection of molecular parity violation are discussed briefly also in relation to other molecules.     

Theory of Stereomutation Dynamics and Parity Violation in Hydrogen Thioperoxide Isotopomers 1,2,3HSO1,2,3H

We present quantitative calculations of the mode‐selective stereomutation tunneling and parity violation in chiral hydrogen thioperoxide (‘oxadisulfane') isotopomers XSOY with X, Y=H, D, and T. The torsional tunneling stereomutation dynamics are investigated with a quasi‐adiabatic channel quasi‐harmonic reaction path Hamiltonian approach, which treats the torsional motion anharmonically in detail and all remaining coordinates as harmonic (but anharmonically coupled to the reaction coordinate). We predict how stereomutation is catalyzed or inhibited by excitation of various vibrational modes compared to the corresponding stereomutation dynamics of the vibrational ground state. Parity‐violating potentials were calculated with our recent multiconfiguration linear response (MC‐LR) approach in the random phase approximation (RPA). We find that, in agreement with general scaling expectations, the parity‐violating energy difference for the equilibrium structures of the two HSOH enantiomers (ca. 5×10^?12J mol^?1) is situated intermediate between HOOH and HSSH. Our results on the stereomutation dynamics and the influence of parity violation on these are discussed in relation to investigations for the analogous molecules H₂O₂, H₂S₂, and Cl₂S₂. As expected in XSOY (X, Y=H, D, and T), this influence is much larger than in the corresponding H₂O₂ isotopomers, but smaller than in H₂S₂ or Cl₂S₂.     

Theoretical insight into the magnetic circular dichroism of uranium N6,7-edge X-ray absorption

We use ligand-field density functional theory to determine the electronic structure and to model magnetic circular dichroism in the X-ray absorption spectroscopy (XAS) of uranium compounds. This study extends earlier work on tetravalent uranium ion, in which a model Hamiltonian was set up in order to study electronic structure with three nonequivalent 4f, 5f, and 6d electrons. In the earlier work, the model Hamiltonian took into consideration the interelectron repulsion, spin-orbit coupling interaction, and ligand-field splitting. Uranium N_6,7-edge XAS spectra were calculated on the basis of the 5f² → 4f¹³5f²6d¹ electron transition, showing spectral profiles that were mainly dominated by 4f electron spin-orbit coupling, as well as 6d ligand-field splitting. Fine structures were also observed due to the interelectronic repulsion between 4f-5f, 4f-6d, and 5f-6d electrons. Here, the theoretical study is extended to take into consideration the presence of an external magnetic field, incorporating into the model Hamiltonian for three-open-shell electron configuration a term for Zeeman interaction. Therefore, we are able to model spectra with a left-circularly and right-circularly polarized X-ray, demonstrating evidence of X-ray magnetic circular dichroism (XMCD) for a tetravalent U⁴⁺ ion in the molecular (U(η⁸-C₈H₈)₂) complex. The XMCD originates from a ground-state electronic structure with open-shell 5f electrons. Furthermore, the present calculation of uranium N_6,7-edge XAS and XMCD spectra also enables the ligand-field bonding analysis of the coordination compound.     

Ab initio CPHF calculations of the static polarizability and second hyperpolarizability of small molecules: Comparisons between standard and moderately large basis sets augmented with diffuse functions

Static polarizability and second hyperpolarizability have been calculated for a number of small molecules? CO₂, OCS, CS₂, C₂H₂, C₂H₆, C₃H₈, cyclo-C₃H₆, C₃H₄, C₃H₆, SiH₄, Si₂H₆? in the framework of the coupled-perturbed Hartree-Fock (CPHF ) theory. The linear and nonlinear coefficients have been calculated with standard Gaussian basis sets and 3-21G bases moderately enlarged with diffuse functions. It is shown that the parallel component of the polarizability saturates rapidly, which suggests that a 3-21G basis containing s and p diffuse functions is sufficient to reproduce α_zz. For the α_xx and α_yy components, a 3-21G basis with s, p, and d diffuse functions is required. In general, the concordance between α computed with this basis set and the experimental static polarizability is at least of the order of 80%. On the contrary, the computation of the second hyperpolarizability with the same basis set for CO₂, CS₂, and C₂H₂ gives values that are 30% too low, compared to the experimental value. Better results are observed for ethane, propane, and cyclopropane for which the error is lower than 50%. The better agreement observed for the saturated compounds can probably be explained by their saturated character.     

Dicretization to avoid singularities in vibration–rotation Hamiltonians: A bisector embedding for AB2 triatomics

A previously proposed [Sutcliffe and Tennyson, Int. J. Quantum Chem. 29 , 183 (1991)] body-fixed Hamiltonian is applied to AB₂ systems in Radau coordinates with the x-axis embedded along the bisector of the angle. It is shown that by using a discrete variable representation for the angular coordinate it is possible to avoid singular regions of the Hamiltonian. A two-step variational procedure is used to obtain rotationally excited states of the system. The results of test calculations H₂S and D₂S with J = 0, 1, 5, and 10 are discussed along with computer-usage characteristics.     

Thermal decomposition of hydrogen peroxide in the presence of sulfuric acid

Hydrogen peroxide (H₂O₂) is popularly employed as a reaction reagent in cleaning processes for the chemical industry and semiconductor plants. By using differential scanning calorimetry (DSC) and vent sizing package 2 (VSP2), this study focused on the thermal decomposition reaction of H₂O₂ mixed with sulfuric acid (H₂SO₄) with low (0.1, 0.5 and 1.0 N), and high concentrations of 96 mass%, respectively. Thermokinetic data, such as exothermic onset temperature (T ₀), heat of decomposition (ΔH _d), pressure rise rate (dP/dt), and self-heating rate (dT/dt), were obtained and assessed by the DSC and VSP2 experiments. From the thermal decomposition reaction on various concentrations of H₂SO₄, the experimental data of T ₀, ΔH, dP/dt, and dT/dt were obtained. Comparisons of the reactivity for H₂O₂ and H₂O₂ mixed with H₂SO₄ (lower and higher concentrations) were evaluated to corroborate the decomposition reaction in these systems.     

Variational calculation of vibrational energies of triatomic molecules using SCF optimized modes

A self-consistent field optimization of the vibrational coordinates for nonlinear triatomic molecules is presented. The optimal coordinates are obtained by making a three-dimensional rotational transformation of the normal modes and determining the rotation angles as those for which the SCF energy is stationary. The utility of the optimized coordinates in full variational calculations of vibrational energies is studied for the molecules of H₂O, O₃, H₂D⁺, H₂T⁺, and D₂T⁺. For H₂O and O₃, the optimization procedure leads to the local mode representation. It is shown that the use of the optimal coordinates in variational calculations allows a large reduction of the dimension of the Hamiltonian matrix to be diagonalized in order to reach convergence.     

Additivity of atomic static polarizabilities and dispersion coefficients

A new empirical method is proposed to evaluate the average molecular polarizabilities assuming the additivity of atomic static polarizability. Atomic static polarizability for each atom in a particular valence state is obtained. Calculated molecular polarizabilities of 94 non-halogenated compounds and of the bases in nucleic acids show the excellent agreement with experimental data.To check the further validity of this method, dispersion coefficients for CH₄, C₂H₆, C₃H₈,n–C₄H₁₀,n–C₅H₁₂,n–C₆H₁₄,n–C₇H₁₆,n–C₈H₁₈, H₂, H₂O and NH₃ are obtained from a sum of atomic terms using a London-type formula, and are compared with the accurate values of dipole oscillator strength distribution (DOSD) method. The results show the excellent agreement between theory and experiment.     

Gas-chromatographic determination of impurities of organic and chlorinated organic compounds and carbon monoxide and dioxide in high-purity hydrogen chloride

A gas-chromatographic procedure was developed for determining impurities (CH₄, C₂H₆, C₃H₈, C₄H₁₀, iso-C₄H₁₀, C₅H₁₂, iso-C₅H₁₂, neo-C₅H₁₂, CH₃Cl, C₂H₅Cl, CH₂Cl₂, CHCl₃, CO, and CO₂) in hydrogen chloride using two columns and a column switching technique in an isothermal mode with a flame ionization detector; the detection limits were 0.01–0.1 ppm. The matrix was separated in a precolumn packed with urea. CO and CO₂ were determined by reaction gas chromatography with their conversion into methane.     

Post‐Synthetic Reversible Incorporation of Organic Linkers into Porous Metal–Organic Frameworks through Single‐Crystal‐to‐Single‐Crystal Transformations and Modification of Gas‐Sorption Properties

The porous metal–organic framework (MOF) {[Zn₂(TCPBDA)(H₂O)₂]?30 DMF?6 H₂O}_n ( SNU‐30 ; DMF=N,N‐dimethylformamide) has been prepared by the solvothermal reaction of N,N,N′,N′‐tetrakis(4‐carboxyphenyl)biphenyl‐4,4′‐diamine (H₄TCPBDA) and Zn(NO₃)₂?6 H₂O in DMF/tBuOH. The post‐synthetic modification of SNU‐30 by the insertion of 3,6‐di(4‐pyridyl)‐1,2,4,5‐tetrazine (bpta) affords single‐crystalline {[Zn₂(TCPBDA)(bpta)]?23 DMF?4 H₂O}_n ( SNU‐31 SC ), in which channels are divided by the bpta linkers. Interestingly, unlike its pristine form, the bridging bpta ligand in the MOF is bent due to steric constraints. SNU‐31 can be also prepared through a one‐pot solvothermal synthesis from Zn^II, TCPBDA^4?, and bpta. The bpta linker can be liberated from this MOF by immersion in N,N‐diethylformamide (DEF) to afford the single‐crystalline SNU‐30 SC , which is structurally similar to SNU‐30 . This phenomenon of reversible insertion and removal of the bridging ligand while preserving the single crystallinity is unprecedented in MOFs. Desolvated solid SNU‐30′ adsorbs N₂, O₂, H₂, CO₂, and CH₄ gases, whereas desolvated SNU‐31′ exhibits selective adsorption of CO₂ over N₂, O₂, H₂, and CH₄, thus demonstrating that the gas adsorption properties of MOF can be modified by post‐synthetic insertion/removal of a bridging ligand.