A Route to Stabilize Uranium(II) and Uranium(I) Synthons in Multimetallic Complexes

Herein, we report the redox reactivity of a multimetallic uranium complex supported by triphenylsiloxide (−OSiPh₃) ligands, where we show that low valent synthons can be stabilized via an unprecedented mechanism involving intramolecular ligand migration. The two- and three-electron reduction of the oxo-bridged diuranium(IV) complex [{(Ph₃SiO)₃(DME)U}₂(μ-O)], 4 , yields the formal “U^II/U^IV”, 5 , and “U^I/U^IV”, 6 , complexes via ligand migration and formation of uranium-arene δ-bond interactions. Remarkably, complex 5 effects the two-electron reductive coupling of pyridine affording complex 7 , which demonstrates that the electron-transfer is accompanied by ligand migration, restoring the original ligand arrangement found in 4 . This work provides a new method for controlling the redox reactivity in molecular complexes of unstable, low-valent metal centers, and can lead to the further development of f-elements redox reactivity.     

Zinc(II) complexes with Schiff bases derived from ethylenediamine and salicylaldehyde: the synthesis and photoluminescent properties

The effect of the nature of organic ligands and complex formation on the photoluminescent characteristics (relative quantum yield, excited-state lifetime) and thermal stability of tetradentate Schiff bases (H₂L), derivatives of salicylaldehyde (H₂(SAL)¹, H₂(SAL)²), o-vanillin (H₂(MO)¹, H₂(MO)²) with ethylenediamine and o-phenylenediamine, and their zinc(II) complexes was studied. Zinc(II) complexes were synthesized by the reaction of H₂L with Zn(AcO)₂·2H₂O in MeOH at room temperature or under reflux. In the case of H₂L = H₂(SAL)², H₂(MO)¹, H₂(MO)², complexes of the composition ZnL·H₂O were isolated irrespective of the temperature. For H₂L = H₂(SAL)¹, the reaction results in Zn(SAL)¹·H₂O at room temperature and in anhydrous dimeric complex [Zn(SAL)¹]₂ under reflux. Density functional calculations of H₂L and ZnL confirmed that (1) luminescence of these compounds is due to the π-π* transition between orbitals of the organic ligand and (2) enhancement of conjugation of the chain and introduction of electron-donating substituents lead to a decrease of the energy gap and, there-fore, to a bathochromic shift of the emission maximum. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 9, pp. 1846–1855, September, 2008.     

Evidence for stepwise processes in the charge reversal of negative ions

Various processes during the charge reversal of the simple negative ions OH⁻, Cl^−·₂, CN⁻ and C₂H⁻ have been revealed by application of a voltage to the collision cell in the second field-free region of a VG Micromass ZAB-2F mass spectrometer. It is shown for all these ions that the two-electron stripping process required for charge reversal can take place not only in one step, but also in two steps. Moreover, for the Cl^−·₂ ions, it has been found that they can fragment to Cl⁻ ions prior to the two-electron stripping process. In the charge reversal of the OH⁻ and CN⁻ ions, some processes have been found which strongly indicate that even a one-step three-electron stripping is possible in addition to a stepwise process of two- and one-electron stripping. Many of the electron stripping processes are accompanied at some stage by fragmentation.     

Evaluation of two-center,two- and three-electron integrals involving correlation factors over Slater-type orbitals. II. Kinetic and potential energy integrals and examples of numerical results

This article is concerned with the construction of the general algorithm for evaluating two-center, two- and three-electron integrals occurring in matrix elements of one-electron operators in the basis of variational correlated functions. This problem has been solved here in prolate spherical coordinates, using the modified and extended form of the Neumann expansion of the interelectronic distance function r^k_ij derived in Part I of this series for k = ?1, 0, 1, 2. This work expands the method proposed by one of us in the preceding paper for integrals of the types mentioned above. The results of numerical calculations for different types of the two- and three-electron integrals are presented. The problem of convergence of the proposed procedures used is also discussed.     

Modified valence indices from the two-particle density matrix

The modified ionic and covalent valence indices are introduced, defined in the framework of the two-particle density matrix, with respect to the reference state of separated atoms or ions (SAL ). They include only quadratic contributions in changes of the molecular charge-and-bond order matrix elements, relative to the SAL . General properties of the modified valence indices are examined and illustrative qualitative results for model systems are presented. Numerical UHF SCF MO valence data for selected diatomic and triatomic molecules are reported and interpreted in terms of the valence saturation effect and the ionic vs. covalent valence competition. A three-orbital valence model of a symmetric transition state of the bond-forming–bond-breaking reaction supports the BEBO model postulate of preservation of the total “bond order.” The model predictions are compared with the UHF numerical values. © 1994 John Wiley & Sons, Inc.     

Multiconfigurational SCF approach for high-symmetry molecules and its applications to fullerene trianion

A symmetry-adapted multiconfiguration self-consistent field (MC SCF) approach aimed at calculations of high-symmetry molecules is proposed. The self-consistency procedure applicable to the molecular terms of any symmetry and multiplicity is developed. It holds the symmetry transformation properties of varied molecular orbitals, thus taking advantage of the relationships within the set of two-electron integrals through molecular invariants. For orbital optimization, a unified coupling operator is constructed on the basis of the pseudosecular method providing for efficient convergence to energy minimum. Based on the group-theory technique, computer codes have been developed for straightforward determination of the invariant expansions for two-electron integrals and configuration interaction (CI) matrix elements. Calculated in this way, the expansion coefficients are presented for the three-electron states that originate from joint t_1u and t_1g shells of an icosahedral fullerene C₆₀, the case important for the calculations of anion C₆₀³⁻ representing the charge state of the fullerene molecule in the superconducting ionic solids K₃C₆₀ or Rb₃C₆₀. The results of MC SCF calculations for lowest quasi-π-electronic states of C₆₀³⁻ are discussed. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 68: 293–304, 1998     

Two Paths to Oxidative C−H Amination Under Basic Conditions: A Theoretical Case Study Reveals Hidden Opportunities Provided by Electron Upconversion**

Traditionally, cross-dehydrogenative coupling (CDC) leads to C−N bond formation under basic and oxidative conditions and is proposed to proceed via a two-electron bond formation mediated by carbenium ions. However, the formation of such high-energy intermediates is only possible in the presence of strong oxidants, which may lead to undesired side reactions and poor functional group tolerance. In this work we explore if oxidation under basic conditions allows the formation of three-electron bonds (resulting in “upconverted” highly-reducing radical-anions). The benefit of this “upconversion” process is in the ability to use milder oxidants (e. g., O₂) and to avoid high-energy intermediates. Comparison of the two- and three-electron pathways using quantum mechanical calculations reveals that not only does the absence of a strong oxidant shut down two-electron pathways in favor of a three-electron path but, paradoxically, weaker oxidants react faster with the upconverted reductants by avoiding the inverted Marcus region for electron transfer.     

Electronic absorption and circular dichroism spectra of Δ-[Os(bipy)2(bipy−)]+, Δ-[Os(bipy)(bipy−)2]0 and Δ-[Os(bipy−)3]−

The electronic absorption and circular dichroism spectra of the complexes produced by the one-, two- and three-electron reduction of Δ-[Os(bipy)₃]²⁺ are reported for the first time. The spectra confirm that, as in the cases of the Fe^II and Ru^II analogues, the electrons are localised on the bipyridine ligand and the complexes are correctly formulated [Os(bipy)₂(bipy⁻)]⁺, [Os(bipy)(bipy⁻)₂]⁰ and [Os(bipy⁻)₃]⁻. The absorption spectra of the series of fully reduced complexes [M(bipy⁻)₃]⁻: M  Fe, Ru, Os are compared.     

A conjecture for some partial differential operators on L 2( R n)

OnX =L ²(R ⁿ), letQ = (Q ₁,Q ₂,…,Q _n) andP = (P ₁,P ₂, …,P _n) be the operators given by (Q _jf) (x) =x _jf(x),P _j = - i∂/∂x _j. For anyC ^∞ functionh:R ⁿ →R putH ₀ =h(P) andH =H ₀ + (1 +Q ²)^-δ, where δ > 1/2. By the method of scattering theory we prove thatH _ac, the absolutely continuous part ofH is unitarily equivalent toH ₀ when (a)n = 1 and (b) forn ≥ 2, whenh is in a large class of polynomials. It is conjectured that the results are true for any polynomialh. We use the techniques of Enss’ method and the idea of bound states for momentum.     

Theoretical investigation of the rates of electron transfer processes Q−I + QII → QI + Q−II and Q−I + Q−II → QI + Q2−II in photosynthesis

A theoretical investigation on the rates of electron-transfer processes Q⁻_I + Q_II → Q⁻_I + Q⁻_II and Q⁻_I + Q⁻_II → Q_I + Q²⁻_II was carried out by using the Marcus theory of long-range electron transfer in solution. The molecular reorganizational parameter λ, the free-energy change ΔG⁰ for the overall reaction, and the electronic matrix element H_DA for these two processes were calculated from the INDO-optimized geometries of molecules Q_I, Q_II, and histidine. Q_I and Q_II are plastoquinones (PQ) which are hydrogen-bonded to a histidine each, and the two histidines may or may not be coordinated to a Fe²⁺ ion. The plastoquinone representing Q_I is additionally flanked by two peptide fragments. Each of the species (Pep)₂Q_I · His and His · Q_II has been considered to be immersed in a dielectric continuum that represents the surrounding molecules and protein folds. INDO calculations confirm the standard reduction potential for the first process (calculated 0.127 V; observed 0.13 V) and predict a midpoint potential of 0.174 V for the second process at 300 K at pH 7 (experimental value remains uncertain but is known to be close to 0.13 V). The plastoquinone fragment carries almost all the net charge (about 95.7%) in [PQ · His]⁻ and the net charge in [PQH · His]⁻. The electron is transferred effectively from the plastoquinone part of [(Pep)₂Q_I · His]⁻ to the plastoquinone moiety of Q_II · His in the first step and to the plastoquinone fragment of HisH⁺ · Q⁻_II in the second step. Therefore, we made use of the formula for the rate of through-space electron transfer from Q_I to Q_II (and to Q⁻_II). The plastoquinones are, of course, electronically coupled to histidines, and the transfer is, in reality, through the molecular bridge consisting of histidines and also Fe²⁺. The through-bridge effect is inherent in our calculation of ΔG⁰, H_DA, and the reorganization parameter λ. We investigated the correlation between half-times for the transfer and (D⁻¹_op− D⁻¹_s), where D_op and D_s are, respectively, optical and static dielectric constants of the condensed phase in the vicinity of the plastoquinones. We found that with reasonable values of D_op (2.6) and D_s (8.5) the experimental rates are adequately explained in terms of transfers from the plastoquinone moiety of Q_I to that of Q_II. The t_1/2 values calculated for the two processes are 247 and 472 μs in the absence of Fe²⁺ and 134 and 181 μs in the presence of Fe²⁺. These are in good agreement with the observed values which are ≈ 100 and ≈ 200 μs when Fe²⁺ is present in the matrix and which are known to be almost twice as large when the Fe²⁺ is evicted from the matrix. The present work also shows that the Marcus-Hush theory of long-range electron transfers can be successfully applied to the investigation of processes occurring in a semirigid condensed phase like the thylakoid membrane region. © 1997 John Wiley & Sons, Inc.     

The Valence Orbitals of the Alkaline-Earth Atoms

Quantum chemical calculations of the alkaline-earth oxides, imides and dihydrides of the alkaline-earth atoms (Ae=Be, Mg, Ca, Sr, Ba) and the calcium cluster Ca₆H₉[N(SiMe₃)₂]₃(pmdta)₃ (pmdta=N,N,N′,N′′,N′′-pentamethyldiethylenetriamine) have been carried out by using density functional theory. Analysis of the electronic structures by charge and energy partitioning methods suggests that the valence orbitals of the lighter atoms Be and Mg are the (n)s and (n)p orbitals. In contrast, the valence orbitals of the heavier atoms Ca, Sr and Ba comprise the (n)s and (n−1)d orbitals. The alkaline-earth metals Be and Mg build covalent bonds like typical main-group elements, whereas Ca, Sr and Ba covalently bind like transition metals. The results not only shed new light on the covalent bonds of the heavier alkaline-earth metals, but are also very important for understanding and designing experimental studies.     

Syntheses and Crystal Structures of BaAgTbS3, BaCuGdTe3, BaCuTbTe3, BaAgTbTe3, and CsAgUTe3

Five new quaternary chalcogenides of the 1113 family, namely BaAgTbS₃, BaCuGdTe₃, BaCuTbTe₃, BaAgTbTe₃, and CsAgUTe₃, were synthesized by the reactions of the elements at 1173–1273 K. For CsAgUTe₃ CsCl flux was used. Their crystal structures were determined by single‐crystal X‐ray diffraction studies. The sulfide BaAgTbS₃ crystallizes in the BaAgErS₃ structure type in the monoclinic space group C³,_2h‐C2/m, whereas the tellurides BaCuGdTe₃, BaCuTbTe₃, BaAgTbTe₃, and CsAgUTe₃ crystallize in the KCuZrS₃ structure type in the orthorhombic space group D¹_,2⁷_,h‐Cmcm. The BaAgTbS₃ structure consists of edge‐sharing [TbS₆^9–] octahedra and [AgS₅^9–] trigonal pyramids. The connectivity of these polyhedra creates channels that are occupied by Ba atoms. The telluride structure features ²_∞[MLnTe₃^2–] layers for BaCuGdTe₃, BaCuTbTe₃, BaAgTbTe₃, and ²_∞[AgUTe₃^1–] layers for CsAgUTe₃. These layers comprise [MTe₄] tetrahedra and [LnTe₆] or [UTe₆] octahedra. Ba or Cs atoms separate these layers. As there are no short Q ··· Q (Q = S or Te) interactions these compounds achieve charge balance as Ba²⁺M⁺Ln³⁺(Q^2–)₃ (Q = S and Te) and Cs⁺Ag⁺U⁴⁺(Te^2–)₃.     

Evaluation of Hylleraas-CI atomic integrals by integration over the coordinates of one electron. I. Three-electron integrals

A method to evaluate the nonrelativistic electron-repulsion, nuclear attraction and kinetic energy three-electron integrals over Slater orbitals appearing in Hylleraas-CI (Hy-CI) electron structure calculations on atoms is shown. It consists on the direct integration over the interelectronic coordinate r _ij and the sucessive integration over the coordinates of one of the electrons. All the integrals are expressed as linear combinations of basic two-electron integrals. These last are solved in terms of auxiliary two-electron integrals which are easy to compute and have high accuracy. The use of auxiliary three-electron ones is avoided, with great saving of storage memory. Therefore this method can be used for Hy-CI calculations on atoms with number of electrons N ≥ 5. It has been possible to calculate the kinetic energy also in terms of basic two-electron integrals by using the Hamiltonian in Hylleraas coordinates, for this purpose some mathematical aspects like derivatives of the spherical harmonics with respect to the polar angles and recursion relations are treated and some new relations are given.     

Four‐Center Oxidation State Combinations and Near‐Infrared Absorption in [Ru(pap)(Q)2]n (Q=3,5‐Di‐tert‐butyl‐N‐aryl‐1,2‐benzoquinonemonoimine,pap=2‐Phenylazopyridine)

The complex series [Ru(pap)(Q)₂]ⁿ ([ 1 ]ⁿ–[ 4 ]ⁿ; n=+2, +1, 0, ?1, ?2) contains four redox non‐innocent entities: one ruthenium ion, 2‐phenylazopyridine (pap), and two o‐iminoquinone moieties, Q=3,5‐di‐tert‐butyl‐N‐aryl‐1,2‐benzoquinonemonoimine (aryl=C₆H₅ ( 1⁺ ); m‐(Cl)₂C₆H₃ ( 2⁺ ); m‐(OCH₃)₂C₆H₃ ( 3⁺ ); m‐(tBu)₂C₆H₃ ( 4 ⁺)). A crystal structure determination of the representative compound, [ 1 ]ClO₄, established the crystallization of the ctt‐isomeric form, that is, cis and trans with respect to the mutual orientations of O and N donors of two Q ligands, and the coordinating azo N atom trans to the O donor of Q. The sensitive C? O (average: 1.299(3) Å), C? N (average: 1.346(4) Å) and intra‐ring C? C (meta; average: 1.373(4) Å) bond lengths of the coordinated iminoquinone moieties in corroboration with the N?N length (1.292(3) Å) of pap in 1 ⁺ establish [Ru^III(pap⁰)(Q^.?)₂]⁺ as the most appropriate electronic structural form. The coupling of three spins from one low‐spin ruthenium(III) (t_2g⁵) and two Q^.? radicals in 1 ⁺– 4 ⁺ gives a ground state with one unpaired electron on Q^.?, as evident from g=1.995 radical‐type EPR signals for 1 ⁺– 4 ⁺. Accordingly, the DFT‐calculated Mulliken spin densities of 1 ⁺ (1.152 for two Q, Ru: ?0.179, pap: 0.031) confirm Q‐based spin. Complex ions 1 ⁺– 4 ⁺ exhibit two near‐IR absorption bands at about λ=2000 and 920 nm in addition to intense multiple transitions covering the visible to UV regions; compounds [ 1 ]ClO₄–[ 4 ]ClO₄ undergo one oxidation and three separate reduction processes within ±2.0 V versus SCE. The crystal structure of the neutral (one‐electron reduced) state ( 2 ) was determined to show metal‐based reduction and an EPR signal at g=1.996. The electronic transitions of the complexes 1 ⁿ– 4 ⁿ (n=+2, +1, 0, ?1, ?2) in the UV, visible, and NIR regions, as determined by using spectroelectrochemistry, have been analyzed by TD‐DFT calculations and reveal significant low‐energy absorbance (λ_max>1000 nm) for cations, anions, and neutral forms. The experimental studies in combination with DFT calculations suggest the dominant valence configurations of 1 ⁿ– 4 ⁿ in the accessible redox states to be [Ru^III(pap⁰)(Q^.?)(Q⁰)]²⁺ ( 1 ²⁺– 4 ²⁺)→[Ru^III(pap⁰)(Q^.?)₂]⁺ ( 1 ⁺– 4 ⁺)→[Ru^II(pap⁰)(Q^.?)₂] ( 1 – 4 )→[Ru^II(pap^.?)(Q^.?)₂]^? ( 1 ^?– 4 ^?)→[Ru^III(pap^.?)(Q^2?)₂]^2? ( 1 ^2?– 4 ^2?).     

Distinguishing the Strength of Electronic Coupling for Mo2‐Containing Mixed‐Valence Compounds within the Class III Regime

Two, symmetrical, mixed‐valence (MV), complex cations—{[Mo₂(DAniF)₃]₂(μ‐oxamidate)}⁺ ( 1 ⁺) and {Mo₂(DAniF)₃]₂(μ‐dithiooxamidate)}⁺ ( 2 ⁺; DAniF=N,N′‐di(p‐anisyl)formamidinate)—are significantly differentiated in terms of electronic coupling between the two [Mo₂] units. For 1 ⁺ the intervalence (IV) charge‐transfer band in the near‐IR spectrum is truncated in half on the low‐energy side as predicted for MV compounds at the Class II–III limit (2H_ab/λ=1; for which H_ab=electronic coupling matrix element and λ=reorganization energy). In contrast, the very strongly coupled analogue 2 ⁺, as indicated by 2H_ab/λ=3.5 (> >1), exhibits a higher energy and more symmetrical IV band. As rare examples, this pair of MV species shows distinct optical behaviors for MV systems crossing the Class III region. Optical analysis and DFT calculations are carried out to elucidate the transformation from vibronic to electronic vertical transition.     

The Laplacian of the electronic density at the valence-shell charge concentration (VSCC): A comparative study of effective core potential and full-electron calculations in Mo compounds. II

The effective core potential (ECP), using a basis set of different qualities, and ab initio full-electron (FE) calculations were carried out for MoS⁻²₄, MoO⁻²₄, and MoOCl₄ molecules. The topology of − ▿²p(r_cp) (the negative Laplacian of the charge density at its critical points) in the atomic valence shell was studied. Results clearly indicate that semicore (ECP2) approaches are able to reproduce, in a qualitative way, the topology of the Laplacian distribution with respect to those obtained by the FE method. Modifications of basis sets, such as introduction of polarization functions on the ligands, affect the electronic charge distribution (number of critical points in MoOCl₄) for FE as well as for ECP2 approaches. The ECP2 scheme predicts correctly the order of − ▿²p_x(r_cp) (X = O, S, Cl, Mo) in the valence shell; nevertheless, it fails in the relative magnitudes of − ▿²p_Mo(r_cp) between Mo compounds in respect to FE calculations. A scaling factor consistently improves the values of − ▿²p(r_cp) and p(r_cp), which are larger than those obtained with FE, particularly the − ▿²p(r_c) values. © 1996 John Wiley & Sons, Inc.     

Kinetics and mechanism of the chromium(III)–picolinato chelate ring opening in some chromium(III)–oxalato–picolinato complexes in acidic aqueous solutions

Two Cr^III–picolinato complexes were obtained and characterized in solution. The [Cr(C₂O₄)(pyac)₂]^– and [Cr(C₂O₄)₂(pyac)]^2– ions (pyac = picolinic acid anion) in acidic solutions undergo a reversible one-end Cr^III–picolinato chelate ring opening via Cr^III—N bond breaking. The reaction rate was determined spectrophotometrically in the 0.1–1.0 M HClO₄ range at I = 1.0 M. The observed pseudo-first order rate constant depends on [H⁺] according to the equation: k _obs = a + b[H⁺] + c/[H⁺]. A reaction mechanism, which assumes participation of the protonated and unprotonated forms of the reactants, has been proposed. The kinetic parameters a, b, c have been defined as a = k ₁, b = k ₂ Q ₁, c = k _–1/Q ₂, where k ₁, k _–1,k ₂ are rate constants for the forward and reverse processes and Q ₁, Q ₂ are the protolytic equilibrium constants in the term of the proposed mechanism. The activation parameters have been determined and discussed.     

DFT study of nitroxide radicals: explicit modeling of solvent effects on the structural and electronic characteristics of 4‐amino‐2,2,6,6‐tetramethyl‐piperidine‐N‐oxyl

An explicit DFT modeling of water surroundings on the electron paramagnetic resonance properties of 4‐amino‐2,2,6,6‐tetramethyl‐piperidine‐N‐oxyl (TA) has been performed. A stepwise hydration of TA is accompanied with certain changes in geometrical parameters (bond lengths and angles) and redistribution of partial electric charges in TA. An aqueous cluster of 45 water molecules can be considered as an appropriate model for a complete aqueous shell around TA, although most of the structural and electronic characteristics of TA already converge at about 10 water molecules. Water surroundings induce an increase in electron spin density on the nitrogen atom of the nitroxide fragment due to stabilization of the polar resonance structure > N^+?? O^? at the expense of less polar structure > N? O^?. The water‐induced rise of the isotropic splitting constant a_iso, calculated from the contact term of the hyperfine interaction, comprises Δa_iso(ρ_N2) = 2.2–2.5 G, which is typical of experimental value for TA. There are two contributions to the solvent effect on the a_iso(ρ_N2) value: the redistribution of spin density in the nitroxide fragment (polarity effect) and water‐induced distortions of TA geometry. Microscopic variations in a hydrogen‐bonded water network cause noticeable fluctuations of the splitting constant a_iso(ρ_N2). Calculations of the atomic spin density (σ_N2) allowed us to compute the splitting constant from the relationship a_iso(σ_N2) = Qσ_N2, where Q = 36.2 G. A practical advantage of using this relationship is that it gives ‘smoothed’ values of the splitting constant, which are sensitive to the environment polarity but remain tolerant to microscopic fluctuations of the hydrogen‐bonded water network around a spin‐label molecule. Copyright © 2010 John Wiley & Sons, Ltd.     

Complete to second-orderab initio level calculations of electronicg-tensors

The electronicg-tensors for NO₂, CO⁺ and H²O⁺ are calculated at the restricted open-shell Hartree-Fock (ROHF) level using the Rayleigh-Schrödinger perturbation approach. All known first- and second-order contributions have been evaluated, including the relativistic mass correction, one- and two-electron spin Zeeman gauge correction terms, and one- and two-electron second-order terms. Substantial code development has been necessary, including an integral routine for computing the two-electron spin-Zeeman gauge correction term.Calculations have been done using triple zeta and quadruple zeta basis sets with additional polarization and semi-diffuse functions. Effective gauge invariance is obtained by placing the gauge origin at the molecule's electronic charge centroid. Excited state energies in the sum-over-states expansion are expressed using determinantal energies, thus avoiding the non-uniqueness of ROHF eigenvalues.Our results successfully reproduce trends in gas phaseg-shifts (g=g–g _e). However, discrepancies between our calculatedg-shifts and experimental ones, sometimes on the order of 50%, point to the need for a correlated treatment.     

Extension and parameterisation of lattice potential energy equations for salts containing complex anions and cations: 1. The Pnam and Pna21 phases of ammonium sulphate

We report results of an extended term-by-term calculation of the total lattice potential energy of the two phases, Pnam and Pna2₁, of ammonium sulphate, parameterised as U_pot (NH₄)₂)SO₄| =

A_ijQ(H)ⁱQ(O)^j, where Q(H) and Q(O) are fractional changes on the hydrogen and oxygen atoms of the cation and anion respectively. At the transition temperature, the potential energies of the two phases are equated to give an equation of the form:

Ω_pqQ(H)^pQ(O)^q = 0, representing the intersection of the potential energy surfaces and the relationship between the charges on anion and cation.While this equation does not uniquely define either Q(O) or Q(H), the parameters Ω_pq are such that substitution of a reasonable value of Q(H) from our study on the ammonium halides for example) generates a chemically reasonable value for Q(O) (which accords well with the value obtained in our SO^2?₄ studies). A value: U_pot[(NH₄)₂SO₄] = 1766 ± 3 kJ mol^?1 is assigned.