Minimization of the energy of a molecule with respect to nonlinear parameters of the basis set

We study characteristic features of minimization of the Hartree-Fock-Roothaan energy with respect to nonlinear parameters of the Gaussian basis set. We describe and apply regularization of the discrete Newton-Raphson method based on the analysis of eigenvalues of the Hessian matrix. We discuss results of groundstate energy calculations for the molecules LiH, CH⁺, CH^–, He₃ ²⁺, BH₂ ⁺, and H₂O in optimal ls-Gaussian basis sets. We find that, for molecules with four to six electrons, good accuracy is obtained with small basis sets consisting of ls-functions only.Translated from Teoreticheskaya i Éxperimental'naya Khimiya, Vol. 24, No. 2, pp. 215–218, March–April, 1988.     

Ethene loss kinetics of methyl 2-methyl butanoate ions studied by threshold photoelectron-photoion coincidence: The enol ion of methyl propionate heat of formation

Threshold photoelectron-photoion coincidence (TPEPICO) spectroscopy has been used to investigate the unimolecular chemistry of gas-phase methyl 2-methyl butanoate ions [CH₃CH₂CH(CH₃)COOCH₃^·+]. This ester ion isomerizes to a lower energy distonic ion [CH₂CH₂CH(CH₃)COHOCH₃^·+] prior to dissociating by the loss of C₂H₄. The asymmetric time of flight distributions, which arise from the slow rate of dissociation at low ion energies, provide information about the ion dissociation rates. By modeling these rates with assumed k(E) functions, the thermal energy distribution for room temperature sample, and the analyzer function for threshold electrons, it was possible to extract the dissociative photoionization threshold for methyl 2-methyl butanoate which at 0 K is 9.80 ± 0.01 eV as well as the dissociation barrier of the distonic ion of 0.86 ± 0.01 eV. By combining these with an estimated heat of formation of methyl 2-methyl butanoate, we derive a 0 K heat of formation of the distonic ion CH₂CH₂CH(CH₃)COHOCH₃^·+ of 101.0 ± 2.0 kcal/mol. The product ion is the enol of methyl propionate, CH₃CHCOHOCH₃^·+, which has a derived heat of formation at 0 K of 106.0 ± 2.0 kcal/mol.     

Jahn-teller effects in the MNDO approximation: structures of the molecular cations of some simple organoberyllium compounds

The MNDO method gives geometries for the molecular cations of organoberyllium compounds of types BeR₂ and HBeR (R = CH₃, CHCH₂, CCH, CN, C₅H₅), of C₄H₄Be and CH₃BeBeH₃ and of the series CH_4?n(BeH)_n (n = 0–4) which have symmetries in precise accord with the predictions of the Jahn-Teller theorem. In the series CH_4?n(BeH)_n and CH_4?n(BeH)_n⁺, the barriers to inversion via a planar intermediate decrease with increasing n, are significantly smaller for the cations than for the neutral molecules, and are zero for CH(BeH)₃⁺ and C(BeH)₄⁺, both of which have their minimum energy when strictly planar at carbon.     

Mass spectrometric investigation of stereosomeric 1,2-dimethyl-4-substituted decahydroquinol-4-ol N-oxides. Concerning the configuration of the asymmetric nitrogen atom

The main fragmentation pathways of the N-1, C-2 and C-4 stereoisomers of the 1,2-dimethyl-4-R-transdecahydroquinoline-4-ol N-oxides (R=C?CH, CH?CH₂ and C₂H₅) under electron impact are discussed. The correlation between the mass spectrometric chromatographic behaviour and the configuration of polar groups in the N-oxides examined is discussed. The mass spectra of the N-1 stereoisomers may be subdivided into two groups, depending only on the orientation of N→O group and not of the 4-OH group. The spectra of N-oxides with the axial N-oxide group reveal less intense ions and much more intense [M? CH₃]⁺, [M? O]⁺, [M? OH]⁺ and ions, whereas in the spectra of their equatorial epimers the abundance of the ions exceeds the intensities of the latter ions.     

Fluorescence of dissociating fragments from supersonic jet-electron collisions

Supersonically cooled jets of nitrogen, methane, ethane, cyclopropane, and azomethane are crossed with collimated streams of electrons. The CH (B²Σ^? → X²Π) spectra resulting from the electron-induced dissociation of CH₄, C₂H₆, and CH₂)₃ can be fit with rotation temperatures between 4000 and 6000 K for an electron energy of 100 eV. Flourescence spectra of N₂⁺ (B²Σ_w⁺ → X²Π) from the dissociative ionization of azomethane yield a rotational temperature of =8×10³ K; from ionization of molecular nitrogen the rotational temperature of B²Σ_w⁺ N₂⁺ is 45 K. Mechanisms for these various processes are discussed.     

Structure and formation of gaseous [C4H6O]+˙ ions: 1—The enolic ions [CH2C(OH)?CHCH2]+˙ and [CH2CH?CHCH(OH)]+˙ and their relationship with their keto counterparts

The [C₄H₆O]^+˙ ion of structure [CH₂?CHCH?CHOH]^+˙ (a) is generated by loss of C₄H₈ from ionized 6,6-dimethyl-2-cyclohexen-1-ol. The heat of formation ΔH_f of [CH₂?CHCH?CHOH]^+˙ was estimated to be 736 kJ mol^?1. The isomeric ion [CH₂?C(OH)CH?CH₂]^+˙ (b) was shown to have ΔH_f, ? 761 kJ mol^?1, 54 kJ mol^?1 less than that of its keto analogue [CH₃COCH?CH₂]^+˙. Ion [CH₂?C(OH)CH?CH₂]^+˙ may be generated by loss of C₂H₄ from ionized hex-1-en-3-one or by loss of C₄H₈ from ionized 4,4-dimethyl-2-cyclohexen-1-ol. The [C₄H₆O]^+˙ ion generated by loss of C₂H₄ from ionized 2-cyclohexen-1-ol was shown to consist of a mixture of the above enol ions by comparing the metastable ion and collisional activation mass spectra of [CH₂?CHCH?CHOH]^+˙ and [CH₂?C(OH)CH?CH₂]^+˙ ions with that of the above daughter ion. It is further concluded that prior to their major fragmentations by loss of CH₃˙ and CO, [CH₂?CHCH?CHOH]⁺˙ and [CH₂?C(OH)CH?CH₂]^+˙ do not rearrange to their keto counterparts. The metastable ion and collisional activation characteristics of the isomeric allenic [C₄H₆O]^+˙ ion [CH₂?C?CHCH₂OH]^+˙ are also reported.     

Quadrupole mass spectrometric study of positive ions from RF plasmas of pure CH4, CH4/H2, and CH4/Ar systems

Quadrupole mass spectrometry has been employed to characterize the ionic species in the discharges of pure CH₄, CH₄/H₂, and CH₄/Ar systems. For pure methane, the major positive ions in the discharge at low pressure (e.g., 0.15 torr) are CH ₃ ⁺ , C₂H ₃ ⁺ , CH ₂ ⁺ , C₂H ₂ ⁺ , CH ₄ ⁺ , C₂H ₄ ⁺ , and C₂H ₅ ⁺ at high pressure (e.g., 0.5 torr) the major ions are CH ₃ ⁺ , C₂H ₃ ⁺ , C₂H ₅ ⁺ , C₃H ₃ ⁺ , C H₃H ₇ ⁺ , C₄H ₇ ⁺ , C₅H ₇ ⁺ , C₆H ₅ ⁺ , and C₇H ₇ ⁺ . The relative abundances of C₁ ions decrease with increasing pressure, whereas those of higher-order ions increase with pressure. For 5% CH₄ + 95% H₂ mixture, in addition to those sampling from the pure methane plasma at the lower pressure, H _n ⁺ ions have also been detected. For 5% CH₄ +95% Ar mixture, the principal ions are CH ₃ ⁺ , CH ₂ ⁺ , CH⁺, CH ₅ ⁺ , Ar⁺, and ArH⁺; the ions containing more than two carbon atoms are negligible. In these discharges, the CH ₃ ⁺ and C₂H ₃ ⁺ are the most important positive ions in C₁ and C₂ ions, respectively. The ions detected are believed to come from the sheath between the electrode and the luminous plasma, and have high kinetic energy. An ion-molecule reaction mechanism is proposed which can well explain the observed main features of ionic products.Died June 1, 1991.     

Vibrational analysis of l-alanine and deuterated analogs

Raman spectra of the polycrystalline l-alanine analogs CH₃CH(NH⁺₃)COO^?, CH₃CH(ND⁺₃)-COO^?, CD₃CD(NH⁺₃)COO^?, and CD₃CD(ND⁺₃)COO^? have been obtained. A normal coordinate analysis is carried out based on the experimental frequencies of the four isotopic analogs and a 34 parameter valence-type force field defined in terms of local symmetry coordinates. The final refinement, in which five stretching force constants are constrained to fixed values obtained from bond length data, results in an average error of 7 cm^?1 (0.9%) for the observed frequencies of the four isotopically substituted molecules. Band assignments are given in terms of the potential energy distribution for local symmetry coordinates. For non-deuterated l-alanine, the vibrations above 1420 cm^?1 and below 950 cm^?1 may be described as localized group vibrations. By contrast, the eight modes in the middle frequency range, viz. the three skeletal stretching, the COO^? symmetric stretching, one NH⁺₃ rocking, the symmetric CH₃ deformation, and the two methyne CH deformation vibrations, are very strongly coupled to one another. Some decoupling appears to take place in the perdeutero molecule, and all but five modes can be described as localized group vibrations.     

The DEPTQ+ Experiment: Leveling the DEPT Signal Intensities and Clean Spectral Editing for Determining CHn Multiplicities

We propose a new ¹³C DEPTQ⁺ NMR experiment, based on the improved DEPTQ experiment, which is designed to unequivocally identify all carbon multiplicities (Cq, CH, CH₂, and CH₃) in two experiments. Compared to this improved DEPTQ experiment, the DEPTQ⁺ is shorter and the different evolution delays are designed as spin echoes, which can be tuned to different ¹J_CH values; this is especially valuable when a large range of ¹J_CH coupling constants is to be expected. These modifications allow (i) a mutual leveling of the DEPT signal intensities, (ii) a reduction in J cross-talk in the Cq/CH spectrum, and (iii) more consistent and cleaner CH₂/CH₃ edited spectra. The new DEPTQ⁺ is expected to be attractive for fast ¹³C analysis of small-to medium sized molecules, especially in high-throughput laboratories. With concentrated samples and/or by exploiting the high sensitivity of cryogenically cooled ¹³C NMR probeheads, the efficacy of such investigations may be improved, as it is possible to unequivocally identify all carbon multiplicities, with only one scan, for each of the two independent DEPTQ⁺ experiments and without loss of quality.     

Ab-initio calculations on small hydrides including electron correlation

The ground state energies of CH ₃ ⁺ , CH₃, and CH ₃ ^– are calculated both in the SCF (near Hartree-Fock) approximation and in the IEPA-PNO scheme including correlation energy. Due to a more appropriate choice of the basis, our SCF-values for CH ₃ ^– are substantially better than previously published ones. Both CH ₃ ⁺ and CH₃ are planar whereas the equilibrium bond angles in CH ₃ ^– are nearly tetrahedral. The inversion barrier of CH ₃ ^– is 2kcal/mol. The force constants of the out-of-plane bending modes are changed by correlation in the case of CH₃ from 0.03–1.8 mdyn/Å. The localized MO's that correspond to the CH-bonds are bent in the non-equilibrium geometries. The dependence of the different pair correlation contributions on the angle that describes out-of-plane deformation is analyzed. The electron affinity of CH₃ is 0.3 eV. Finally the Pariser-Parr disproportionation reaction is analyzed in the light of the present results. Changes in correlation energy for this reaction amount to less than 1 eV.     

Compounds containing CSF4 and CS+F4

The preparations of CH₂SF₄ and CH₃CHSF₄ are presented and the structures are discussed. Addition reactions of polar species give a wide range of new compounds, like Hg(CH₂SF₅)₂, F₄AsCH₂SF₅, cisBrSF₄CH₃, cisF₅SeOSF₄CH₂Br, a.o. While CH₂SF₄ decomposes at room temperature slowly to CH₂CH₂ and SF₄, at high temperatures HF and CSF₂ are formed. CH₃CHSF₄ gives mainly CH₃CHF₂ at room temperature. The “saturated” compounds CH₃SF₅ and C₂H₅SF₅ have been prepared. They react with SbF₅ in SO₂ at low temperatures to form the cations CH₃SF₄⁺ and C₂H₅SF₄⁺. The CH₃SF₄⁺ ion has been investigated in detail by nmr methods at low temperatures. It decomposes to CH₃ and SF₄, which react further in the SO₂/SbF₅ system to CH₃OSO⁺ and SF₃⁺.     

Correlated polarization propagator calculations of static polarizabilities

We present a systematic comparison of the correlation contribution at the level of the second-order polarization propagator approximation (SOPPA ) and MP 2 to the static dipole polarizability of (1) Be, BeH^?, BH, CH⁺, MgH^?, AIH, SiH⁺, and GeH⁺; (2) BH₃, CH₄, NH₃, H₂O, HF, BF, and F₂; and (3) N₂, CO, CN^?, HCN, C₂H₂, and HCHO . Fairly extended basis sets were used in the calculations. We find that the agreement with experimental values is improved in SOPPA and MP .2 over the results at the SCF level. The signs and magnitudes of the correlation contribution in SOPPA are similar to those obtained in analytical derivative MP 2 calculations. However, it is not possible to say, in general, which method gives the largest correlation contribution or the best agreement with experiment, nor is it possible to make a priori prediction of the sign of the correlation contribution. For the first group of molecules, which have a quasi-degenerate ground state, additional CCDPPA and CCSDPPA calculations were performed and compared with polarizabilities obtained as analytical/numerical derivatives of the CCD and CCSD energies. The CCSDPPA results were found to be in better agreement with other calculations than were the SOPPA results, demonstrating the necessity of using methods based on infinite-order perturbation theory for these systems. © 1994 John Wiley & Sons, Inc.     

Nonisothermal membrane phenomena across perfluorosulfonic acid-type membranes,Flemion S: part I. Thermoosmosis and transported entropy of water

Solvent transports across the perfluorosulfonic acid-type membrane Flemion S were measured for aqueous electrolyte solutions under a temperature difference and under an osmotic pressure difference. H⁺, Li⁺, Na⁺, K⁺, NH ₄ ⁺ , CH₃NH ₃ ⁺ , (CH₃)₂NH ₂ ⁺ , (CH₃)₃NH⁺, (CH₃)₄N⁺, (C₂H₅)₄N⁺, (n-C₃H₇)₄N⁺ and (n-C₄H₉)₄N⁺ were used as counterions. Water flux across the membrane in HCl solution is higher than that in the other electrolyte solutions because hydrogen ions can exchange with the hydrogen of the neighbor water molecules and contribute to the water transport across the membrane as a proton jump in conductivity. The direction of thermoosmosis across the membrane in HCl, NaCl, (CH₃)₄NCl and (C₂H₅)₄NCl solutions was from the cold side to the hot side and that in LiCl, KCl, NH₄Cl, CH₃NH₃Cl, (CH₃)₂NH₂Cl and (n-C₄H₉)₄NBr solutions was from the hot side to the cold side, although thermoosmosis across anion-exchange membranes always occurs toward the hot side.     

The site of ionization in the acetylation of aliphatic esters by [(CH3CO)3]+

A series of esters RCOOR′ (where R, R′ = CH₃, CH₃CH₂, (CH₃)₂CH, (CH₃)₃C) were reacted with the [(CH₃CO)₃]⁺ ion from biacetyl in an ion cyclotron resonance spectrometer. A steric effect influences the rate of formation of stable products [RCOOR′·CH₃CO]⁺ and is used to determine that either oxygen of the ester may be initially acylated by [(CH₃CO)₃]⁺.     

Solubilities and Gibbs transfer energies of thiolato,sulfenato, sulfinato and tris(ethylenediamine)cobalt(III) complexes,as well as of perchlorate,from acetonitrile into its mixtures with water

Information on the solvation of thiolato complex cations [Co(en)₂(SCH₂COO)]⁺ [Co(en)₂(SCH₂CH(COO)NH₂)]⁺, [Co(en)₂(SCH₂CH₂NH₂)]²⁺, sulfenato complexes [Co(en)₂(SOCH₂COO)]⁺ [Co(en)₂{SOCH₂CH(COO)NH₂}]⁺, [Co(en)₂(SOCH₂CH₂NH₂)]²⁺, the sulfinato [Co(en)₂{SO₂CH₂CH(COO)NH₂}]⁺, [Co(en)₂(SO₂CH₂CH₂NH₂)]²⁺ as well as of [Co(en)₃]³⁺ has been obtained from solubility measurements in MeCN–H₂O mixtures at 298.2 K. The single-ion Gibbs energies of transfer of the Co^III complexes were derived from the solubilities of picrate and perchlorate salts for the full range of MeCN–H₂O mixtures. Single-ion Gibbs energies of transfer for the perchlorate ion are given. The effects of the solvent mixtures were interpreted in the framework of chemical bond formation between the ions and the individual solvent molecules.     

Correlated and gauge origin independent calculations of magnetic properties

Summary We have applied a gauge origin invariant method for calculations of nuclear magnetic shielding constants to the singly bonded molecules BF, F₂, BH₃, CH₄, NH₃, H₂O, and HF as well as to the¹H shielding constants of HCN and C₂H₂. The calculations were performed at the RPA and second order polarization propagator (SOPPA) level of theory. For most molecules the correlation contribution in SOPPA is less diamagnetic than in the comparable MP2 calculations. For F₂, SOPPA gives a large paramagnetic correlation correction whereas the MP2 method gives a very small correlation contribution. For all molecules agreement with experimental results is generally improved at the SOPPA level compared to RPA. We have also demonstrated that second order gauge origin invariant, common and local origin (SOLO) methods do not necessarily give the same shielding even in the limit of a converged basis set.     

Ionization and appearance potentials in organic chemistry. I—energetic aspects of the mass spectra of stereoisomeric 4-substituted N-alkyl-2-methyldecahydroquinol-4-ols

The ionization potentials for the stereoisomers of trans-fused 1,2-dimethyl- and 1-ethyl-2-methyl-4-R-decahydroquinol-4-ols (R?C?CH, CH?CH₂ or C₂H₅) and the appearance potentials for the [M–CH₃]⁺ and [M–C₂H₅]⁺ ions (loss of 2-CH₃ and 4-C₂H₅ groups potential, respectively) were measured by using the electron impact method. The ionization and appearance potential for [M–CH₃]⁺ are always lower for the isomers with the axial 2-CH₃ group. For the C-2 epimers, the difference between the appearance potentials for the [M–CH₃]⁺ ion values is likely to be equal to the enthalpy differences between the ground states of the epimers and the dissociation energy differences between the axial and equatorial C₂–CH₃ bonds. The appearance potentials for [M–C₂H₅]⁺ for the C-4 epimers possessing the 4-C₂H₅ group were very similar. At the same time, the appearance potentials for the [M–CH₃]⁺ ions were lower for less stable epimers which had an axial 4-C₂H₅ group.     

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.     

A modified PCILO method

The perturbative configuration interaction using strictly localized molecular orbitals, called the modified PCILO method, for which the use of the Rayleigh-Schrödinger many-body perturbation theory with the Moller-Plesset Hamiltonian partitioning is characteristic, has been proposed in this communication. On the CNDO/2 and INDO levels of Hamiltonian approximations strictly localized molecular orbitals have been constructed by solving modified Roothaan equations. From the zero and second order energy interatomic distances and harmonic force constants for some diatomic molecules have been calculated. The linear dependence of the correlation energy on the number of valence electrons in the series of the molecules CH₄, CH₃F, CH₂F₂, CHF₃ and CF₄ is perfect.     

Formation and hydrolysis of gas‐phase [UO2(R)]+: R═CH3, CH2CH3, CH═CH2, and C6H5

The goals of the present study were (a) to create positively charged organo‐uranyl complexes with general formula [UO₂(R)]⁺ (eg, R═CH₃ and CH₂CH₃) by decarboxylation of [UO₂(O₂C─R)]⁺ precursors and (b) to identify the pathways by which the complexes, if formed, dissociate by collisional activation or otherwise react when exposed to gas‐phase H₂O. Collision‐induced dissociation (CID) of both [UO₂(O₂C─CH₃)]⁺ and [UO₂(O₂C─CH₂CH₃)]⁺ causes H⁺ transfer and elimination of a ketene to leave [UO₂(OH)]⁺. However, CID of the alkoxides [UO₂(OCH₂CH₃)]⁺ and [UO₂(OCH₂CH₂CH₃)]⁺ produced [UO₂(CH₃)]⁺ and [UO₂(CH₂CH₃)]⁺, respectively. Isolation of [UO₂(CH₃)]⁺ and [UO₂(CH₂CH₃)]⁺ for reaction with H₂O caused formation of [UO₂(H₂O)]⁺ by elimination of ·CH₃ and ·CH₂CH₃: Hydrolysis was not observed. CID of the acrylate and benzoate versions of the complexes, [UO₂(O₂C─CH═CH₂)]⁺ and [UO₂(O₂C─C₆H₅)]⁺, caused decarboxylation to leave [UO₂(CH═CH₂)]⁺ and [UO₂(C₆H₅)]⁺, respectively. These organometallic species do react with H₂O to produce [UO₂(OH)]⁺, and loss of the respective radicals to leave [UO₂(H₂O)]⁺ was not detected. Density functional theory calculations suggest that formation of [UO₂(OH)]⁺, rather than the hydrated U^VO₂⁺, cation is energetically favored regardless of the precursor ion. However, for the [UO₂(CH₃)]⁺ and [UO₂(CH₂CH₃)]⁺ precursors, the transition state energy for proton transfer to generate [UO₂(OH)]⁺ and the associated neutral alkanes is higher than the path involving direct elimination of the organic neutral to form [UO₂(H₂O)]⁺. The situation is reversed for the [UO₂(CH═CH₂)]⁺ and [UO₂(C₆H₅)]⁺ precursors: The transition state for proton transfer is lower than the energy required for creation of [UO₂(H₂O)]⁺ by elimination of CH═CH₂ or C₆H₅ radical.