Intercombination lines of Mg I-, Al I- and Si I-like ions in the beam foil spectra of Ti,Fe, Ni and Cu

In delayed spectra of foil-excited beams of Ti, Fe, Ni and Cu ions lines have been observed which are identified with intercombination transitions 3s ^{2 1} S ₀ — 3s 3p ³ P ₁ ⁰ , 3s ² 3p ² P ⁰ — 3s 3p ^{2 4} P and 3s ² 3p ^{2 3} P — 3s 3p ^{3 5} S ₂ ⁰ in magnesiumlike, aluminiumlike and siliconlike spectra, resp. Wavelengths and decay properties have been determined. The results are compared to recent theoretical predictions.     

Synthesis and coordination chemistry of tetrabutyldithioimidodiphosphinates

Butyl substituted imidodithiophosphinates R₂P(S)NP (S)R′₂ (R=ⁿBuⁱBu^sBuR′=ⁿBuⁱBu^sBu) have been synthesised via an HBr elimination reaction between R₂P(S)NH₂ and R′₂P(S)Br The compounds were characterised spectroscopically Crystallographic and spectroscopic studies reveal ⁿBu₂P(S)NHP(S)ⁿBu₂ and ^sBu₂P(S)NHP(S)ⁱBu₂ to be hydrogen bonded transoid dimers and ⁱBu₂P(S)NHP(S)ⁱBu₂ to be a transoid hydrogen bonded chain Reactions of the imidodithiophosphinates with ZnCl₂ or MCl₂COD gave the coordination complexes M[R₂P(S)NP (S)R′₂]₂ (R=ⁿBuⁱBu^sBuR′=ⁿBuⁱBu^sBuM=ZnPd: R=ⁿBuⁱBu^sBuPt).     

Electronic structure of free and doped actinides: N and Z dependences of energy levels and electronic structure parameters

Theoretical study of electronic structure of antinide ions and its dependence on N and Z are presented in this paper. The main 5f^N and excited 5f^Nn′l′^N′ configurations of actinides have been studied using Hartree-Fock-Pauli approximation. Results of calculations of radial integrals and the energy of X-ray lines for all 5f ions with electronic state AC⁺¹−AC⁺⁴ show approximate dependence on N and Z. A square of N and cubic of Z are ewalized for the primary electronic parameters of the actinides. Theoretical values of radial integrals for free actinides and for ions in a cluster AC⁺ⁿ:[L]_k are compared, too.     

Autoionization resonances in atomic Ga,In, and Pb

Autoionization resonances of the type (n?1)d→np, wheren pertains to the outermost shell of Ga, In and Pb, were studied with the use of electron spectrometry in combination with synchrotron radiation. The relative strengths of the exit channels for the various resonance states were measured. In the case of Ga and In, a complete partitioning of the total absorption cross section into thes ^{2 1} S,sp ¹ P, andsp ³ P components (exit channels) was achieved, and in the case of Pb the decay of the resonance states into the major exit channels 6s ² 6p ² P _1/2, 6s ² 6p ² P _3/2, 6s 6p ^{2 4} P _1/2, 6s 6p ^{2 2} D _3/2 and 6s 6p ^{2 2} P _1/2 was determined. In Ga, strong coupling was observed for those states of the 4p ² manifold that have the same symmetries as the final ionic states, e.g. 4p ^{2 3} P→4s 4p ³ P and 4p ^{2 1} S→4s ^{2 1} S. In In, there is a similar, but weaker correlation, which also includes two-electron excitation channels. Comparison between Ga and In shows that thesp ³ P channel is much stronger in In (52% vs 40% in Ga) while thesp ¹ P channel is correspondingly weaker (28% vs 37%), with thes ^{2 1} S channel remaining practically unchanged (20 vs 23%). In Pb, the 6s ² 6P ² P _1/2 channel displays interference patterns due to a strong, competing direct transition, whereas the other channels do not, indicating population predominantly via the resonance states.     

New levels and calculations in the Nd I spectrum

The energies of all the levels of Nd I 4f ⁴ 6s ^{2 5} F and of⁵ S ₂ as well as of 4f ⁴ 5d 6s ⁷ H ₂ have been determined by means of laser-induced fluorescence in a hollow cathode. Their interpretation was carried out with the use of hyperfine structure data and a new parametric calculation of (4f ⁴ 6s ² + 4f ⁴ 5d 6s). Furthermore, the energies andJ values of 5 new odd levels were found.     

Ferro- and Antiferromagnetic Interactions in Oxalato-Centered Inverse Hexanuclear and Chain Copper(II) Complexes with Pyrazole Derivatives

Two novel copper(II) complexes of formulas {[Cu(4-Hmpz)₄][Cu(4-Hmpz)₂(µ₃-ox-κ²O¹,O²:κO^2′:κO^1′)(ClO₄)₂]}_n (1) and {[Cu(3,4,5-Htmpz)₄]₂[Cu(3,4,5-Htmpz)₂(µ₃-ox-κ²O¹,O²:κO^2′:κO^1′)(H₂O)(ClO₄)]₂[Cu₂(3,4,5-Htmpz)₄(µ-ox-κ²O¹,O²:κ²O^2′,O^1′)]}(ClO₄)₄·6H₂O (2) have been obtained by using 4-methyl-1H-pyrazole (4-Hmpz) and 3,4,5-trimethyl-1H-pyrazole (3,4,5-Htmpz) as terminal ligands and oxalate (ox) as the polyatomic inverse coordination center. The crystal structure of 1 consists of perchlorate counteranions and cationic copper(II) chains with alternating bis(pyrazole)(µ₃-κ²O¹,O²:κO^2′:κO^1′-oxalato)copper(II) and tetrakis(pyrazole)copper(II) fragments. The crystal structure of 2 is made up of perchlorate counteranions and cationic centrosymmetric hexanuclear complexes where an inner tetrakis(pyrazole)(µ-κ²O¹,O²:κ²O^2′,O^1′-oxalato)dicopper(II) entity and two outer mononuclear tetrakis(pyrazole)copper(II) units are linked through two mononuclear aquabis(pyrazole)(µ₃-κ²O¹,O²:κO^2′:κO^1′-oxalato)copper(II) units. The magnetic properties of 1 and 2 were investigated in the temperature range 2.0–300 K. Very weak intrachain antiferromagnetic interactions between the copper(II) ions through the µ₃-ox-κ²O¹,O²:κO^2′:κO^1′ center occur in 1 [J = −0.42(1) cm⁻¹, the spin Hamiltonian being defined as H = −J∑S_1,i · S_2,i+1], whereas very weak intramolecular ferromagnetic [J = +0.28(2) cm⁻¹] and strong antiferromagnetic [J’ = −348(2) cm⁻¹] couplings coexist in 2 which are mediated by the µ₃-ox-κ²O¹,O²:κO^2′:κO^1′ and µ-ox-κ²O¹,O²:κ²O^2′,O^1′ centers, respectively. The variation in the nature and magnitude of the magnetic coupling for this pair of oxalato-centered inverse copper(II) complexes is discussed in the light of their different structural features, and a comparison with related oxalato-centered inverse copper(II)-pyrazole systems from the literature is carried out.     

Hyperfine structure and isotope shift of some even parity levels in the YbI spectrum

Using laser induced fluorescence spectroscopy the hyperfine structure of the even parity levels 4f ¹⁴6s6d ³ D ₁, 4f ¹⁴ 6s8s ³ S ₁ and 4f ¹³ 5d6s6p (7/2, 5/2)J=1,2,3 as well as of the odd parity level 4f ¹⁴ 6s6p ³ P ₂ in neutral ytterbium has been investigated. The isotope shift of the transitions 4f ¹⁴6s6p ³ P ₀ → 4f ¹⁴ 6s6p ³ D ₁ and 4f ¹⁴ 6s6p ³ P ₂ → 4f ¹⁴ 6s8s ³ S ₁, 4f ¹³ 5d6s6p (7/2, 5/2)J=1,2,3 could be measured with high accuracy. The results for the 4f ¹⁴ 6s6p ³ D ₁ level show a considerable influence of second order effects of the hyperfine interaction. The isotope shifts of the 4f ¹⁴ 6s8s ³ S ₁ and 4f ¹³ 5d6s6p (7/2, 5/2)J=1 levels indicate a possible configuration mixing for these levels.     

Precision energies and hyperfine structures of the 5s5p 3 P 0,1,2 0 and 5s6s 3 S 1 levels in In II

Absolute frequencies of hyperfine components of the 230.6 nm (5s ^{2 1} S ₀?5s5p ³ P ₁ ⁰ ), 193.6 nm (5s5p ³ P ₀ ⁰ ?5s6s ³ S ₁), 197.7 nm (5s5p ³ P ₁ ⁰ ?5s6s ³ S ₁) and 207.9 nm (5s5p ³ P ₂ ⁰ ?5s6s ³ S ₁) transitions in In II emitted from a hollow-cathode source have been measured using a high-resolution, scanning échelle monochromator. The measured frequencies of these four transitions have been used to determine the energies and hyperfine interaction constants of the 5s5p ³ P ₀ ⁰ ,³ P ₁ ⁰ ,³ P ₂ ⁰ and 5s6s ³ S ₁ levels in In II. The hyperfine interaction constants for the dominant isotope¹¹⁵In are found to be: 5s5p ³ P ₁ ⁰ A=0.2322(2) cm^?1,B=?0.0159(9) cm^?1 5s5p ³ P ₂ ⁰ A=0.1699(4) cm^?1,B= 0.021 (6) cm^?1 5s6s ³ S ₁ A=0.4022(4) cm^?1,B= 0.002 (2) cm^?1. The absolute frequency of the very narrow, strongly forbidden In II 236.5 nm (5s ^{2 1} S ₀?5s5p ³ P ₀ ⁰ ) transition, which has been proposed as a candidate for a new optical frequency standard, is found to be 42275.986(7) cm^?1.     

Geometric and electronic structure of ground and excited states of groupVA diatomics. A theoretical LCGTO-MP-LSD study

LCGTO-MP-LSD calculation was performed for the ground and several low-lying excited states of homo- (N₂, P₂, As₂, and Sb₂) and hetero-nuclear (PN, AsN, AsP, AsSb, SbN, and SbP) groupVA diatomics. For all the systems the ground state is found to be¹Σ⁺. For N₂ and P₂, the¹Σ _g ⁺ ground state is followed by the³Σ _u ⁺ ,³Π _g ,³Δ _u ,¹Π _g , and¹Δ _u low-lying exited states while for As₂ the order is found to be³Σ _u ⁺ ,³Δ _u ,³Π _g ,¹Δ _u ,¹Π _g . Finally for Sb₂ the relative stability of excited states is³Σ _u ⁺ ,³Δ _u ,¹Δ _u ,³Π _g ,¹Π _g . For the hetero-nuclear diatomics the¹Σ⁺ ground state is, in the case of PN, AsN, AsP, SbN, and SbP, followed by the³Σ⁺,³Δ,³Π,¹Π and¹Δ low-lying excited states while for the AsSb diatomic an inversion of stability of the two last singlets occurs. The calculated spectroscopic parameters (Re, ωe, andDe) are in good agreement with all the available experimental results while, theTe values are overestimated by about 0.5 eV. Mulliken population analysis shows that both homo- and hetero-nuclear groupVA diatomics are essentially triple bonded systems.     

Solubility product and related thermodynamic quantities of silver and barium chromates in formamide

The values of ΔG⁰, ΔH⁰, and ΔS⁰ for the dissolution process, M₂(CrO₄)_x + solvent — 2 M^x+ (solvated) + xCrO₄^2? (solvated), where M is Ag or Ba, and x is 1 or 2, have been determined in formamide from solubility studies. The negative value of ΔS⁰ indicates that there is more order in the dissolved state than in the undissolved state.     

Kinetics and mechanism of the oxidation of acrylic acid and methyl methacrylate

The kinetics of the initiated oxidation of acrylic acid and methyl methacrylate in the liquid phase were studied volumetrically by measuring oxygen uptake during the reaction. Both processes proceed via the chain mechanism with quadratic-law chain termination. The oxidation rate is described by the equation w = k ₂/(2k ₆)^1/2[monomer]w _i ^1/2 , where w _i is the initiation rate and k ₂ and k ₆ are the rate constants of chain propagation and termination. The parameter k ₂/(2k ₆)^1/2 is 7.58 × 10^?4 (l mol^?1 s^?1)^1/2 for acrylic acid oxidation and 2.09 × 10^?3 (l mol^?1 s^?1)^1/2 for the oxidation of methyl methacrylate (T = 333 K). For the oxidation of acrylic acid, k ₂ = 2.84 l mol^?1 s^?1 (T = 333 K) and the activation energy is E ₂ = 54.5 kJ/mol; for methyl methacrylate oxidation, k ₂ = 2.96 l mol^?1 s^?1 (T = 333 K) and E ₂ = 54.4 kJ/mol. The enthalpies of the reactions of RO ₂ ^? with acrylic acid and methyl methacrylate were calculated, and their activation energies were determined by the intersecting parabolas method. The contribution from the polar interaction to the activation energy was determined by comparing experimental and calculated E ₂ values: ΔE _μ = 5.7 kJ/mol for the reaction of RO ₂ ^? with acrylic acid and ΔE _μ = 0.9 kJ/mol for the reaction of RO ₂ ^? with methyl methacrylate. Experiments on the spontaneous oxidation of acrylic acid provided an estimate of the rate of chain initiation via the reaction of oxygen with the monomer: w _i,0 = (3.51 ± 0.85) × 10^?11 mol l^?1 s^?1 (T = 333 K).     

Theoretical study of LiK and LiK+ in adiabatic representation

The potential energy curves have been calculated for the electronic states of the molecule LiK within the range 3 to 300 a.u., of the internuclear distance R. Using an ab initio method, through a semiempirical spin-orbit pseudo-potential for the Li (1s ²) and K (1s ²2s ²2p ⁶3s ²3p ⁶) cores and core valence correlation correction added to the electrostatic Hamiltonian with Gaussian basis sets for both atoms. The core valence effects including core-polarization and core-valence correlation are taken into account by using an l-dependent core-polarization potential. The molecular orbitals have been derived from self-consistent field (SCF) calculation. The spectroscopic constants, dipole moments and vibrational levels of the lowest electronic states of the LiK molecule dissociating into K (4s, 4p, 5s, 3d, and 5p) + Li (2s, 2p, 3s, and 3p) in ^{1, 3}Σ, ^{1, 3}Π, and ^{1, 3}Δ symmetries. Adiabatic results are also reported for ²Σ, ²Π, and ²Δ electronic states of the molecular ion LiK⁺ dissociating into Li (2s, 2p, 3s, and 3p) + K⁺ and Li⁺ + K (4s, 4p, 5s, 3d, and 5p). The comparison of the present results with those available in the literature shows a very good agreement in spectroscopic constants of some lowest states of the LiK and LiK⁺ molecules, especially with the available theoretical works. The existence of numerous avoided crossing between electronic states of ²Σ and ²Π symmetries is related to the charge transfer process between the two ionic systems Li⁺K and LiK⁺.     

Penning ionization and photoionization electron spectrometry of hydrogen fluoride

An electron spectrometric study has been performed on HF using metastable helium and neon atoms as well as helium and neon resonance photons. High-resolution electron spectra were obtained for a pure He(2³ S) beam, a mixed He(2¹ S, 2³ S) beam, a mixed Ne(3s,³ P ₂,³ P ₀) beam, and for HeI and NeI VUV light. From the comparison of vibrational populations of HF⁺ (X ²£ _i ,v′) and HF⁺ (A ²Σ⁺,v′) produced by He(2³ S) metastables and HeI resonance photons, we conclude that there is only a slight perturbation of the HF (X ¹Σ⁺) potential in He(2³ S) Penning ionization; no perturbation is found for HF⁺ (X ²Π _i ,v′) formation from Ne(³ P _2,0) metastable ionization of HF. For He(2¹ S)+HF theX- andA-ionic state vibrational peak shapes are substantially broader than in the He(2³ S)+HF case pointing to an additional, charge exchanged interaction (He⁺+HF^?) in the entrance channel of the former system. The vibrational population found for NeI _α photoionization of HF for formation of HF⁺ (X ²Π _i ,v′) is found to differ considerably from that for NeI _β photoionization and from the Franck-Condon factors for unperturbed HF(X ¹Σ⁺) and HF⁺ (X ²Π _i ) potentials suggesting the presence of an autoionizing superexcited state of HF in the energy vicinity of the NeI _α resonance photons. The HF⁺ (X)²Π_3/2:²Π_1/2 fine-structure branching ratios vary significantly with the ionizing agent in a similar way as previously found in HCl and HBr.     

On the line intensity ratios of prominent Si II,Si III,and Si IV multiplets

Line intensities of singly, doubly and triply ionized silicon (Si II, Si III, and Si IV, respectively) belonging to the prominent higher multiplets, are of interest in laboratory and astrophysical plasma diagnostics. We measured these line intensities in the emission spectra of pulsed helium discharge. The Si II line intensity ratios in the 3s3p²²D–3s²4p²P^o, 3s²3d²D–3s²4f²F^o, and 3s²4p²P^o–3s²4d²D transitions, the Si III line intensity ratios in the 3s3d³D–3s4p³P^o, 3s4p³P^o–3s4d³D, 3s4p³P^o–3s5s³S, 3s4s³S–3s4p³P^o, and 3s4f³F^o–3s5g³G transitions, and the Si IV line intensity ratios in the 4p²P^o–4d²D and 4p²P^o–5s²S transitions were obtained in a helium plasma at an electron temperature of about 17,000 ± 2000 K. Line shapes were recorded using a spectrograph and an ICCD camera as a highly-sensitive detection system. The silicon atoms were evaporated from a Pyrex discharge tube designed for the purpose. They represent impurities in the optically thin helium plasma at the silicon ionic wavelengths investigated. The line intensity ratios obtained were compared with those available in the literature, and with values calculated on the basis of available transition probabilities. The experimental data corresponded well with line intensity ratios calculated using the transition probabilities obtained from a Multi Configuration Hartree–Fock approximation for Si III and Si IV spectra. We recommend corrections of some Si II transition probabilities.     

Population and deactivation of lowest lying barium levels by collisions with He,Ar, Xe and Ba ground state atoms

Excitation transfer between the barium low lying excited states 6s6p ³ P ₁ ⁰ , 6s5d ¹ D ₂ and 6s5d ³ D _J by collisions with He,Ar,Xe and Ba has been investigated. The population densities in all levels involved were probed by absorption or by fluorescence usingcw lasers. The depopulation cross sections of the Ba³ P ₁ ⁰ state by collisions with noble gases were found to be σ_He(³ P ₁ ⁰ )=5.5·10^?16 cm², σ_Ar(³ P ₁ ⁰ )=4.6·10^?16 cm², and σ_Xe(³ P ₁ ⁰ )=1.7·10^?16 cm². For Ar, the collisional depopulation of the³ P ₁ ⁰ level is exclusively due to the transition to the¹ D ₂ state. Under the assumption that the³ D _J metastable states are populated collisionally by¹ D ₂ →³ D _J transfer only, we have deduced the upper limit for the corresponding cross section σ ₁₃ ^Ar =1.5·10^?18 cm². From the Ba¹ D ₂ and Ba³ D _J steady-state diffusion distributions, collisional relaxation rates of the¹ D ₂ and³ D _J levels were evaluated. The collisional relaxation rates by Ar and Ba yielded total cross sections for the depopulation of metastable levels: σ_Ar(¹ D ₂)=1.5·10^?17 cm², σ_Ba(¹ D ₂)?1·10^?13 cm², σ_Ar(³ D _J)=7·10^?21 cm², and σ_Ba(³ D _J)=1·10^?15 cm². Furthermore, it was found that the main contribution of the collisional depopulation of the¹ D ₂ state by Ar is related to back transfer to the³ P _J ⁰ state, whereas the deactivation of the³ D _J metastable state is due to back transfer to the¹ D ₂ state. Taking into account other cross sections reported in literature we can conclude that collisional deactivation of both metastable levels by Ba ground state atoms can be attributed to their mutual collisional mixing.     

Heat capacity, enthalpy and entropy of bismuth niobate and bismuth tantalate

The heat capacity and the heat content of bismuth niobate BiNbO₄ and bismuth tantalate BiTaO₄ were measured by the relaxation method and Calvet-type heat flux calorimetry. The temperature dependencies of the heat capacities in the form C_pm=128.628+0.03340 T−1991055/T²+136273131/T³ (J K^-1 mol^-1) and 133.594+0.02539 T−2734386/T²+235597393/T³ (J K^-1 mol^-1) were derived for BiNbO₄ and BiTaO₄, respectively, by the least-squares method from the experimental data. Furthermore, the standard molar entropies at 298.15 K S_m(BiNbO₄)=147.86 J K^-1 mol^-1 and S_m(BiTaO₄)=149.11 J K^-1 mol^-1 were assessed from the low temperature heat capacity measurements. To complete a set of thermodynamic data of these mixed oxides an attempt was made to estimate the values of the heat of formation from the constituent binary oxides.     

Isotope shift and hyperfine structure measurements in titanium I

High accuracy measurements of hyperfine structure due to⁴⁷Ti and⁴⁹Ti in the 3d ² 4s ² a ³ F ₂?3d ² 4s4p z ⁵ D ₁ absorption line at σ=18482.772 cm^?1 have been performed by use of a Doppler-free experiment, where a beam of titanium atoms is crossed by a CW single mode tunable dye laser. They have allowed for the determination of isotope shifts between⁴⁶Ti,⁴⁷Ti,⁴⁸Ti,⁴⁹Ti and⁵⁰Ti. By use of accurate values of mean square nuclear charge radii for the even isotopes, it has been possible to separate mass shifts from field shifts and to determine accurate values for the mean square nuclear charge radii of⁴⁷Ti and⁴⁹Ti. The field shift presents a marked odd-even staggering.     

Penning ionization and photoionization electron spectrometry of hydrogen bromide

An electron spectrometric study has been performed on HBr using metastable helium and neon atoms as well as helium resonance photons. High resolution electron spectra were obtained for a mixed He(2¹ S, 2³ S) beam, a pure He(2³ S) beam, a mixed Ne(3s ³ P ₂,³ P ₀) beam, and for HeI VUV light. From the comparison of vibrational populations of HBr⁺ (X, v′) and HBr⁺ (A, v′), formed by either He^* and Ne^* Penning ionization (PI) or HeI photoionization, we conclude that HBr⁺ (X) formation by PI exhibits only little perturbation of HBr potentials, whereas HBr⁺ (A) formation by PI exhibits substantial bond stretching of HBr due to metastable atom attack preferably from the H end. For He(2¹ S) + HBr theX- andA-state vibrational peak shapes are substantially broader than for the He(2³ S) + HBr case pointing to an additional, charge exchanged interaction (He⁺ + HBr^?) in the entrance channel of the former system which is also responsible for a broad feature found at lower electron energies in the He(2¹ S, 2³ S) induced PI electron spectra. For the first time, we have detected the low energy electrons in both the He(2¹ S) + HBr and He(2³ S) + HBr spectra, associated with the major mechanism for the formation of Br⁺ ions: energy transfer to repulsive HBr** Rydberg states, dissociating to H(1s) and autoionizing Br** atoms. The HBr⁺ (X)² II _3/2:² II _1/2 fine structure branching ratios vary significantly with the ionizing agent in a similar way as for the isoelectronic, atomic target case krypton.     

Syntheses and crystal structures of mono- and bi-metallic zinc compounds of symmetrically- and asymmetrically-substituted bis(amino)cyclodiphosph(V)azanes

The dioxocyclodiphosph(V)azane cis-[(^tBuHN)OP(μ-N^tBu)₂PO(NH^tBu)] reacted with two equivalents of diethylzinc to form the centrosymmetric dimer {[(OPN^tBu)₂(N^tBu)₂ZnEt](ZnEt · THF)}₂ (1) while under identical conditions, the sulfur and selenium analogues afforded only the monoethylzinc compounds {[(^tBuHN)EP(μ-N^tBu)₂PE(N^tBu)](ZnEt · THF)}ES(2), Se (3). To further probe the apparent ligand effects on coordination number and coordination site, cis-[(PhHN)SP(μ-N^tBu)₂PS(NH^tBu)] (5) was synthesized from cis-[ClP(μ-N^tBu)₂P(NH^tBu)] (4) and both were characterized by single-crystal X-ray diffraction. Two equivalents of 5 reacted with diethylzinc to produce the homoleptic, trispirocyclic complex {[(^tBuHN)SP(μ-N^tBu)₂PS(NPh)]₂Zn} (6). A second asymmetrically-substituted cyclodiphosph(V)azane, namely [(^tBuNH)SP(μ-N^tBu)₂PNp-tol(NH^tBu)] (7), was also synthesized and structurally characterized. In contrast to 5, only one equivalent of this ligand reacted with excess diethylzinc, via its N,N^′, rather than its N,S side, to afford {[(^tBuHN)SP(μ-N^tBu)₂PNp-tolyl(N^tBu)](ZnEt)} (8).     

Application of the modified van der waals equation for unsaturated vapour and liquid states

The Law-Lielmezs (L-L) modification of the Van der Waals equation of state: P = RT/(V-b)-a(T)/V² where: a(T) = a(T_c)·a(T_c·a(T¹) and: a(T¹) = 1 + pT^1q has been extended to include unsaturated states in terms of a correcting function C_f(such that the α(T¹) term becomes: a(T¹) = 1 + _pC_fT^1q The proposed extension has been compared with the results obtained by the use of the original Van der Waals equation of state.