Ab initio prediction of the low-temperature phase diagrams in the systems CsX–LiX (X = F, Cl, Br, I)

We have calculated the low-temperature phase diagrams for the ternary alkali halides CsX–LiX (X = F, Cl, Br, I) at an ab initio level without any recourse to experimental information. The starting point of our general approach is the global exploration of the enthalpy landscapes for many different compositions in these systems. Candidates for both ordered stoichiometric modifications and crystalline solid-solution phases are identified, and their free enthalpies are computed at an ab initio level. From this the low-temperature phase diagrams are derived. We find that in all systems under investigation only crystalline ordered phases should be present, in agreement with available experimental data. Furthermore, we predict several new thermodynamically stable and metastable phases in these systems.     

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     

Use of the normal coordinates in variational and perturbative ab initio handling of the vibronic and spin–orbit couplings in Π electronic states of linear tetra‐atomic molecules

Avariational and a perturbative approach are developed to handle the combined effect of the vibronic and spin–orbit couplings in Π electronic states of tetra‐atomic molecules with linear equilibrium geometry. Both of them are based on the use of the normal vibrational bending coordinates. The perturbative treatment is carried out via two schemes for partition of the model Hamiltonian: In the first, the spin–orbit coupling term is treated as a perturbation; in the second, it is included in the zeroth‐order Hamiltonian. It is demonstrated that both perturbative approaches lead to the same second‐order formulae when the spin–orbit coupling constant is small compared to the bending frequency, but much larger than the splitting of potential surfaces upon bending. These approaches are used to calculate the vibronic and spin–orbit structure in the X²Π electronic state of HCCS by employing the ab initio‐computed potential energy surfaces. Complete numerical equivalence of the results obtained with the present variational approach and those generated by the algorithms employing internal vibrational coordinates is demonstrated. The restrictions concerning the applicability of the perturbative approaches are discussed in terms of the agreement between the results obtained by means of them with those generated in the corresponding variational computations. The general reliability of the model employed is checked by comparing the theoretical results with the available experimental data. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2003     

All‐electron relativistic computations on the low‐lying electronic states,bond length,and vibrational frequency of CeF diatomic molecule with spin–orbit coupling effects

Ab initio all‐electron computations have been carried out for Ce⁺ and CeF, including the electron correlation, scalar relativistic, and spin–orbit coupling effects in a quantitative manner. First, the n‐electron valence state second‐order multireference perturbation theory (NEVPT2) and spin–orbit configuration interaction (SOCI) based on the state‐averaged restricted active space multiconfigurational self‐consistent field (SA‐RASSCF) and state‐averaged complete active space multiconfigurational self‐consistent field (SA‐CASSCF) wavefunctions have been applied to evaluations of the low‐lying energy levels of Ce⁺ with [Xe]4f¹5d¹6s¹ and [Xe]4f¹5d² configurations, to test the accuracy of several all‐electron relativistic basis sets. It is shown that the mixing of quartet and doublet states is essential to reproduce the excitation energies. Then, SA‐RASSCF(CASSCF)/NEVPT2 + SOCI computations with the Sapporo(‐DKH3)‐2012‐QZP basis set were carried out to determine the energy levels of the low‐lying electronic states of CeF. The calculated excitation energies, bond length, and vibrational frequency are shown to be in good agreement with the available experimental data. © 2018 Wiley Periodicals, Inc.     

A study on the stability,chirality, and theoretical spectra of the heterofullerenes C69X (X = N,P, As,B, Si,Ge)

There are two chiral and three achiral C₆₉X isomers possible. The achiral structures belong to the C_S group of symmetry while the chiral ones possess no symmetry elements. The stability of all five C₆₉X heterofullerenes for each of the X heteroatoms (X = N, P, As, B, Si, Ge) was determined at the (U)B3LYP/6-31G¹ level. The isomer population in an equilibrium mixture varies with the heteroatom type: the highest content of the chiral isomers was predicted for boron (92%) and nitrogen (47% plus 48%), while for the other heteroatoms studied the achiral isomers significantly dominate. For the chiral structures, four different sinister-rectus chirality measures, ^SRCM: pure geometrical, labeled, mass, and charge, were calculated by our CHIMEA program. We found that the labeled and mass chirality measures calculated for the two types of chiral isomers did correlate with each other. For each chiral C₆₉X molecule, spectroscopic VCD, IR, Raman, and NMR characteristics are discussed and demonstrated for their possible use for future identification and distinction of the isomers.     

Theoretical studies of uracil–(H2O)n (n = 1–7) clusters by ab initio and ABEEMσπ/MM fluctuating charge model

Uracil–(H₂O)_n (n = 1–7) clusters were systemically investigated by ab initio methods and the newly constructed ABEEMσπ/MM fluctuating charge model. Water molecules have been gradually placed in an average plane containing uracil. The geometries of 38 uracil–water complexes were obtained using B3LYP/6-311++G** level optimizations, and the energies were determined at the MP2/6-311++G** level with BSSE corrections. The ABEEMσπ/MM potential model gives reasonable properties of these clusters when comparing with the present ab initio data. For interaction energies, the root mean square deviation is 0.96 kcal/mol, and the linear coefficient reaches 0.997. Furthermore, the ABEEMσπ charges changed when H₂O interacted with the uracil molecule, especially at the sites where the hydrogen bond form. These results show that the ABEEMσπ/MM model is fine giving the overall characteristic hydration properties of uracil–water systems in good agreement with the high-level ab initio calculations.     

Order–disorder phenomena in crystalline phases of compounds E(XMe3)4 where E = C,Si, Ge and X = Si,Sn

We discuss the dynamic solid‐state properties of crystalline phases E(XMe₃)₄ as seen by solid‐state NMR and powder X‐ray diffraction. In the first part we will qualitatively describe some of the NMR tools suitable for such investigations. In the second part we will give examples from the group of solid compounds E(XMe₃)₄ with E = C, Si, Ge and X = Si, Sn. Copyright © 2002 John Wiley & Sons, Ltd.     

Theoretical study of the structural,elastic, electronic and optical properties of XCaF3 (X = K and Rb)

The PLANE WAVE pseudo-potential method within density functional theory (DFT) has been used to investigate the structural, elastic, electronic and optical properties of XCaF₃ (X = K and Rb) insulating. The studied compounds show a weak resistance to shear deformation compared to the resistance to the unidirectional compression. KCaF₃ and RbCaF₃ are considered ductile. The elastic constants and related parameters were predicted. The stiffness is more important in KCaF₃, whereas, the lateral expansion is more important in RbCaF₃. KCaF₃ and RbCaF₃ have R- Г indirect band gap. The main peaks in the imaginary part of the dielectric function correspond to the transition from the occupied state F₋p to the unoccupied states Ca: s or K, Rb: p. At lower energies, KCaF₃ and RbCaF₃ show the same optical properties. Under pressure effect, the peaks of imaginary part of dielectric function were shifted toward high energy.     

Triel–hydride triel bond between ZX3 (Z = B and Al; X = H and Me) and THMe3 (T = Si,Ge and Sn)

Complexes between THMe₃ (T = Si, Ge and Sn) and ZX₃ (Z = B and Al; X = H and Me) have been characterized using MP2/aug‐cc‐pVTZ calculations. These complexes are chiefly stabilized by a triel–hydride triel bond with the T–H bond pointing to the π‐hole on the triel atom. The triel–hydride interaction is mainly attributed to the charge transfer from the T–H bond orbital to the empty p orbital of the triel atom. These complexes are very stable with a large interaction energy (>10 kcal mol^?1) excluding THMe₃···BMe₃ (T = Si and Ge), indicating that the sp²‐hydridized triel atom has a strong affinity for the T–H bond. The formation of THMe₃···BH₃ results in proton transfer, characterized by conversion of orbital interaction and large charge transfer (ca 0.5e). The large deformation is primarily responsible for the abnormally greater interaction energy in THMe₃···BH₃ (>30 kcal mol^?1) than in the AlH₃ analogue. Methyl substitution on the triel atom weakens the triel–hydride interaction and causes a larger interaction energy in THMe₃···AlMe₃ with respect to its BMe₃ counterpart. Most of these interactions possess characteristics of covalent bonds. Polarization makes a contribution to the stability of most complexes nearly equivalent to the electrostatic term.     

Stereochemical behavior of geminal and vicinal 77Se–13C spin–spin coupling constants studied at the SOPPA(CC2) level taking into account relativistic corrections

A systematic theoretical study of geminal and vicinal ⁷⁷Se–¹³C spin–spin coupling constants in the series of the open‐chain selenides and selenium‐containing heterocycles revealed that relativistic effects play an essential role in the selenium–carbon coupling mechanism, especially when the coupling pathway includes a triple bond, contributing to about 10–15% of their total values and noticeably improving the agreement of the calculated couplings with experiment. Both geminal and vicinal ⁷⁷Se–¹³C spin–spin coupling constants show marked stereochemical behavior as documented by their calculated dihedral angle dependence that could be used as a practical guide in stereochemical studies of organoselenium compounds. Copyright © 2014 John Wiley & Sons, Ltd.     

Temperature dependence vapour pressure measurements of Mg(tmhd)2(tmeda) [(tmhd = 2,2,6,6-tetramethyl-3,5-heptanedione, tmeda = N,N,N′,N′-tetramethylethylenediamine]

The reaction between the magnesium β-diketonate complex Mg(tmhd)₂(H₂O)₂ and 1 equiv. of N,N,N′,N′-tetramethylethylenediamine (tmeda = Me₂NCH₂CH₂NMe₂) in hexane at room temperature yielded Mg(tmhd)₂(tmeda). The standard enthalpy of sublimation (83.2 ± 2.3 kJ mol⁻¹) and entropy of sublimation (263 ± 6.3 J mol⁻¹ K⁻¹) of Mg(tmhd)₂(tmeda) were obtained from the temperature dependence vapour pressure, determined by adopting a horizontal dual arm single furnace thermogravimetric analyser as a transpiration apparatus. From the observed melting point depression DTA, the standard enthalpy of fusion (58.3 ± 5.2 kJ mol⁻¹) was evaluated, using the ideal eutectic behaviour of Mg(tmhd)₂(tmeda) as a solvent with bis(2,4-pentanedionato)magnesium(II), Mg(acac)₂ as a non-volatile solute.     

Darstellung,Charakterisierung und Struktur funktionalisierter Fluorphosphaalkene des Typs R3E–P=C(F)NEt2 (R/E = Me/Si,Me/Ge,CF3/Ge,Me/Sn)

Preparation, Characterization, and Structure of Functionalized Fluorophosphaalkenes of the Type R₃E–P=C(F)NEt₂ (R/E = Me/Si, Me/Ge, CF₃/Ge, Me/Sn) P‐functionalized 1‐diethylamino‐1‐fluoro‐2‐phosphaalkenes of the type R₃E–P=C(F)NEt₂ [R/E = Me/Si ( 2 ), Me/Ge ( 3 ), CF₃/Ge ( 4 ), Me/Sn ( 5 )] are prepared by reaction of HP=C(F)NEt₂ ( 1 , E/Z = 18/82) with R₃EX (X = I, Cl) in the presence of triethylamine as base, exclusively as Z‐Isomers. 2–5 are thermolabile, so that only the more stable representatives 2 and 4 can be isolated in pure form and fully characterized. 3 and 5 decompose already at temperatures above –10 °C, but are clearly identified by ¹⁹F and ³¹P NMR‐measurements. The Z configuration is established on the basis of typical NMR data, an X‐ray diffraction analysis of 4 and ab initio calculations for E and Z configurations of the model compound Me₃Si–P=C(F)NMe₂. The relatively stable derivative 2 is used as an educt for reactions with pivaloyl‐, adamantoyl‐, and benzoylchloride, respectively, which by cleavage of the Si–P bond yield the push/pull phosphaalkenes RC(O)–P=C(F)NEt₂ [R = tBu ( 6 ), Ad ( 7 ), Ph ( 8 )], in which π‐delocalization with the P=C double bond occurs both with the lone pair on nitrogen and with the carbonyl group.     

The distribution pattern of squares on the stability of F4F6-(BN)n (n = 10–22) polyhedrons

To gain an insight into the structures and stability of F₄F₆-(BN)_n polyhedrons with alternation of B and N atoms, a density functional theory study was performed on all isomers of F₄F₆-(BN)_n polyhedrons with n between 10 and 22. The calculation results demonstrate that the lowest energy isomers do not contain B₄₄ bonds (the bonds shared by two squares) and the energies of those isomers containing B₄₄ bonds increase with the number of B₄₄ bonds linearly, indicating that the energetically favored structures of F₄F₆-(BN)_n polyhedrons satisfy the isolated square rule and square adjacency penalty rule. The structural analysis reveals that the stability is determined by the pyramidalization of B and N atoms at the square–square fusion. The binding energy is fitted to the numbers of edges and a model is proposed for predicting the relative stability of these B–N polyhedral molecules.     

Structural and electronic properties of stable Aun (n = 2–13) clusters: A density functional study

All-electron scalar relativistic calculations have been performed to investigate the electronic structures of neutral gold clusters (Au_n, n = 2–13) in the gas phase using density functional theory with the generalized gradient approximation. Full geometry optimizations of topologically different clusters and clusters belonging to different symmetry groups have been carried out. Binding energies, ionization potentials, electron affinities, and chemical hardness values are calculated and they are found to be comparable with the available experimental and theoretical results. The most stable structure of each of the cluster has a two-dimensional planar configuration. A three dimensional distorted Y shaped structure (4b) for Au₄, a tri-capped triangle (6b), a chair (6f), and a see-saw structure (6j) for Au₆, an eclipsed sandwich structure (7g) for Au₇, a condensed trigonal bipyramid (9e) and a boat shaped structure (9f) for Au₉, a staggered sandwich (11c) and an eclipsed sandwich structure (11d) for Au₁₁, a ladderane structure (12d) for Au₁₂, and a staggered (13d) and a distorted sandwich structure (13e) for Au₁₃ are characterized for the first time in this work.     

Theoretical study of electronic spectra of linear carbon clusters HC2nS (n = 1–5)

In this work we report the structures and stabilities of linear carbon clusters HC_2nS (n = 1–5) in their ground states using the B3LYP density functional. The rotational constants at the optimized geometries give excellent agreement with the experimental and previous theoretical values. The vertical excitation energies of the 2²Π ← X²Π transitions at the CASPT2 level are 3.16, 2.66, 2.05, 1.78, and 1.55 eV, respectively, in good agreement with the corresponding observed values of 3.01, 2.48, 2.10, 1.84, and 1.65 eV. Also, the exponential-decay curves for these vertical excitation energies obtained from experiments and theoretical calculations are illuminated.     

Rearrangement and decomposition of (CH3)3M (M = Si, Ge, Sn) ions: A DFT study

Pathways for the rearrangement and decomposition of the (CH₃)₃M⁺ (M = Si, Ge, Sn) ions are traced by the detection of stationary points on the potential energy surfaces of these ions by the B3LYP/aug-cc-pVDZ method. All three systems have stationary points similar in geometry, but very different in energy, especially on going from M = Si, Ge on the one hand to M = Sn on the other. In addition to previously found isomers of (CH₃)₃Si⁺ which have their analogs in the two other systems, “side-on” complexes with ethane and propane were revealed for all cations studied. Predicted changes in transition state and dissociation energies on going from M = Si to M = Sn allowed us to rationalize the trends for the relative decomposition product yields observed in mass-spectrometry studies of these cations.     

Theoretical design of singlet localized σ-diradicals: C(MH2)3C (M = Si, Ge, Sn, Pb)

Some localized singlet 1,3-σ-diradicals, C(MH₂)₃C, (M = Si, Ge, Sn, Pb) were theoretically designed by the orbital phase theory and density functional theory calculations. The bicyclic carbon-centered singlet diradicals were more stable than the lowest triplets. Except for M = C, σ-bonded isomers were not located for 1,3-σ-diradicals. 1,4-σ-diradicals, C(M₂H₄)₃C, also had singlet ground states, but they were less stable than σ-bonded isomers.     

Theoretical study of the interaction of a proton with the O, F and Cl atoms of enflurane (CHFCl–CF2–O–CHF2)

Ab initio MP2 and density functional B3LYP calculations were performed to investigate the interaction of a proton with the O, F and Cl atoms of enflurane (CHFCl–CF₂–O–CHF₂) in the gas phase. The study included the optimized structures, proton affinities, interactions energies and thermodynamic properties of protonated enflurane. The proton affinities (PAs) of the O and Cl atoms are 154.5 and 139.8 kcal mol⁻¹, respectively, whereas PAs of five of the fluorine atoms are between 143.6 and 165.5 kcal mol⁻¹ (MP2 results). In contrast to protonation at the O and Cl atoms, protonation at each of the F atoms of enflurane reveals a striking result, it leads to a cleavage of the C–F bond and formation of an ion–dipole complex between the enfluranyl cation and neutral hydrogen fluoride. The [(enfluranyl)⁺FH] complexes are weakly bound, the SAPT-calculated interaction energy varies between −12.5 and −11.7 kcal mol⁻¹. The long range attraction in these complexes is dominated by the electrostatic term (70%), whereas the induction and dispersion components contribute by about 15% each. Protonation at the chlorine atom of enflurane does not lead to a cleavage of the C–Cl bond. For the O-protonated enflurane the results from the natural bond orbital analysis (NBO) are discussed in details.     

H2O,H2, HF,F2 and F2O nuclear magnetic shielding constants and indirect nuclear spin–spin coupling constants (SSCCs) in the BHandH/pcJ‐n and BHandH/XZP Kohn–Sham limits

Good performance of segmented contracted basis sets XZP, where X = D, T, Q and 5, for obtaining H₂O, H₂, HF, F₂ and F₂O nuclear isotropic shielding constants in the BHandH Kohn–Sham basis set limit was shown. The results of two‐ and three‐parameter complete basis set limit extrapolation schemes were compared with experimental results, earlier literature data and benchmark ab initio results. Similar convergence patterns of shieldings obtained from calculations using general purpose XZP basis sets and from polarization‐consistent basis sets pcS‐n and pcJ‐n, where n = 0, 1, 2, 3 and 4, designed to accurately predict magnetic properties were observed. On the contrary, the SSCCs were more sensitive to the XZP basis set size and generally less accurate than those estimated using pcJ‐n basis set family. The BHandH density functional markedly outperforms B3LYP method in predicting heavy atom shieldings and SSCCs values in the studied systems. Copyright © 2009 John Wiley & Sons, Ltd.