Volume 103, Issue 7, 15 August 1995
Index of content:

Irreducible dipole components of three interacting H_{2} molecules and the triple Q _{1} transition near 12 466 cm^{−1}
View Description Hide DescriptionWe have previously obtained parameter‐free models of the overlap‐induced, irreducible, ternary dipole components of three interacting H_{2} molecules, which were successful in reproducing existing measurements of the ternary collision‐induced absorption in the H_{2} fundamental band [Phys. Rev. A 49, 4508 (1994)]. Here, we use these models to calculate the intensity of the triple Q _{1} transition, which has been recently observed in compressed hydrogen gas in absorption near 12 466 cm^{−1}. Simultaneous transitions in three interacting H_{2} molecules are thought to arise from irreducible, ternary dipole components. We calculate an intensity of the triple Q _{1} transition in reasonable agreement with the measurement, within a factor of two or three for the three temperatures for which measurements exist. This fact demonstrates once more that the so‐called antiparallel dipoles‐induced dipole model, which is based on Jansen’s one‐effective electron approximation, is capable of describing ternary spectroscopic interactions in semi‐quantitative detail. Other ternary, irreducible dipole components are shown to be less significant.

Calculations of the dynamic Debye–Scherrer diffraction patterns for small metal particles
View Description Hide DescriptionDynamic diffraction pattern profiles are calculated for randomly oriented aggregates of gold and silver in the size range from 147 to 5083 atoms and at incident electron energies of 40 kV and 100 kV. The Debye–Scherrer diffraction patterns were obtained by combining a series of multislice calculations performed on model particles over a range of orientations. Calculations are performed for both fcc and icosahedral structures. The results show that corrections to the kinematical theory (Debye equation) are more important than predicted by the two‐beam theory of Blackman. One calculation, a fcc 923‐atom silver aggregate at 100 kV, showed a distortion to the (111) Bragg peak causing it to to shift its center to a higher scattering angle. Scattering corrections to the icosahedral results are less important than for an equivalent sized fcc aggregate and preserve the general diffraction features seen in kinematic calculations.

Pairwise and nonpairwise additive forces in weakly bound complexes: High resolution infrared spectroscopy of Ar_{ n }DF (n=1,2,3)
View Description Hide DescriptionHigh resolution infrared spectra of the v _{DF}=1←0 stretch in Ar_{ n }DF (n=1–3) have been recorded using a slit‐jet infrared spectrometer.Analysis of the rotationally resolved spectra provides vibrationally averaged geometries and vibrational origins for a DF chromophore sequentially ‘‘solvated’’ by Ar atoms. Calculations using pairwise additive Ar–Ar and Ar–DF potentials predict lowest energy equilibrium structures consistent with the vibrationally averaged geometries inferred spectroscopically. Variational calculations by Ernesti and Hutson [A. Ernesti and J. M. Hutson, Faraday Discuss. Chem. Soc. (1994)] using pairwise additive potentials predict rotational constants which are in qualitative agreement with, but consistently larger than, the experimental values. The inclusion of nonpairwise additive (three‐body) terms improves the agreement, though still not to within the uncertainty of the pair potentials. The vibrational redshifts of 8.696, 11.677, and 14.461 cm^{−1} for n=1–3, respectively, reflect a nonlinear dependence of the redshift on the number of Ar atoms. Both the variational calculations of Ernesti and Hutson and diffusion quantum Monte Carlo calculations [M. Lewerenz, J. Chem. Phys. (in press)] using pairwise additive potentials systematically overpredict the magnitude of these redshifts, further signifying the need for corrective three‐body terms. Analysis of the Ar_{ n }DF (n=2,3) rovibrational line shapes reveals an upper limit to homogeneous broadening on the order of 2–3 MHz, consistent with vibrational predissociation lifetimes in excess of 50 ns.

The T _{1} resonance Raman spectra of 1,3,5‐hexatriene and its deuterated isotopomers: An ab initio re‐investigation
View Description Hide DescriptionWe report a quantum‐chemical study of the resonance Raman spectra of the lowest triplet state of 1,3,5‐hexatriene. Optimized structures in T _{1} and in the state (T _{ n }) in resonance with the excitation wavelength are obtained at the ab initio CASSCF level of theory. Vibrational force fields of the E‐, Z‐ and P‐rotamers in the lowest triplet state are evaluated and the displacement parameters that govern the activity of totally symmetric modes are derived. The vibrational structure of the RR spectra is modelled for d_{0}‐hexatriene and four deuterated isotopomers. Comparison of simulated and observed spectra shows that the activity of the E‐isomer of hexatriene accounts very satisfactorily for the observed bands. The contribution of the Z‐form is shown to be negligible in agreement with its population in T _{1}.

Rotational structure and dissociation of the Rydberg states of CO investigated by ion‐dip spectroscopy
View Description Hide DescriptionIn a series of spectroscopic work of the Rydberg states of CO, we present the rotational analysis of the v=0 and 1 levels of the singlet ns, np, nd and nf‐Rydberg states (n=4–7). The spectra were measured by ion‐dip spectroscopy with triple resonance excitation via the 3sσ:B ^{1}Σ^{+} or the 3pσ:C ^{1}Σ^{+} state. All the spectra were rotationally well resolved and the term value, quantum defect and the rotational constant were obtained for each state. Through the analysis of the rotational structure, the coupling between the Rydberg electron and the ion core has been investigated. For the np‐Rydberg states, a switching from Hund’s case (b) to (d) was clearly observed with the increase of n. A significant perturbation was observed in the 6pπ ^{1}Π and 7pπ ^{1}Π states and it is suggested that these states are perturbed by the state with the same symmetry. For the nf‐Rydberg states, the observed electronic energy was well analyzed by the long range force model and the precise ionization potential was obtained. The Rydberg↔valence and inter‐Rydberg states interactions were also investigated. For the ns‐Rydberg states, the interaction matrix element with the repulsive state was estimated from the measurement of linewidth of the rotational levels. The potential curve of the repulsive state to which ns‐Rydberg states predissociate was also determined. Selective predissociation was found for the e‐symmetry levels both in the v=0 and 1 levels of the nf‐Rydberg state. A strong interaction between the v=0 levels of the 6d‐ and 7s‐Rydberg states was observed.

A resonance enhanced multiphoton ionization study of the CS_{2} molecule: The 4p Rydberg states
View Description Hide DescriptionThe resonance enhanced multiphoton ionization (REMPI) spectrum of jet‐cooled CS_{2} has been recorded in the one‐photon wavelength range 460–500 nm, corresponding to the three photonexcitation energy range 60 000–65 000 cm^{−1}. A previous assignment of one photon forbidden transitions in this region to 3dRydberg states is shown to be incorrect and reassigned to the 4pπ ^{1,3}Δ_{ u } states. In fact all the observed states in this region can be assigned to 4pRydberg states; the 4pσ ^{1,3}Π_{ u } states at 62 768 and 62 083 cm^{−1}, respectively, and the 4pπ ^{1,3}Δ_{ u } states at 64 214 and 63 698 cm^{−1}, respectively. Another band at 64 374 cm^{−1} may be due to a three photon excitation to the 4pπ ^{1}Σ^{+} _{ u }Rydberg state. Our resolution is sufficient to resolve band shapes enabling symmetry assignments when coupled with their polarization behavior. The fact that the origin bands are not degraded and that Δν=0 sequence bands are strongly excited whereas Δν≠0 transitions are either absent or very weak implies that the upper states have a linear geometry similar to that of the ground state. A comparison of singlet–triplet splittings suggests the 4pπ Δ_{ u } states have stronger Hund’s case (c) character than the 4pσ Π_{ u } state. While CS^{+} _{2} was generally the predominant ion formed, resonance ionization through the ^{1}Δ_{ u }←X ^{1}Σ^{+} _{ g } origin band led to an unusual predominance of S^{+} and CS^{+} ions. This is explained by multiphoton fragmentation of CS^{+} _{2} via an accidental one‐photon resonance from the X ^{2}Π_{1/2} (v=0) ionic ground state.

Optical emission studies of laser desorbed C_{60}
View Description Hide DescriptionThe optical emission spectra of laser desorbed C_{60} have been investigated as a function of laser fluence for desorption with a XeCl excimer laser (pulse length 20 ns). The observed spectra show close similarities to black‐body radiation and can be fitted with the Planck black body formula (modified for small particles) thus giving information on the temperature of the desorbed species. The temperatures obtained (2300–3000 K) are in good qualitative agreement with previous, indirect temperature estimates. Spatially and temporally resolved measurements provide additional insight into the desorption mechanisms. An estimate of cooling rates indicates that thermionic electron emission and C_{2} fragmentation dominate for temperatures above about 3000 K but below this value the dominant cooling mechanism is black‐body radiation.

Temperature dependencies of the reactions of CO^{−} _{3}(H_{2}O)_{0,1} and O^{−} _{3} with NO and NO_{2}
View Description Hide DescriptionWe have measuredtemperature dependencies of the rate constants for CO^{−} _{3} and O^{−} _{3} reacting with NO and NO_{2}. In addition, the temperature dependence of the CO^{−} _{3}(H_{2}O) reaction with NO was determined, and a 196 K rate constant was measured for the reaction of CO^{−} _{3}(H_{2}O) with NO_{2}. The reactions with NO all proceed by O^{−} transfer to produce NO^{−} _{2}. The temperature dependencies of the rate constants for the reactions of CO^{−} _{3} and O^{−} _{3} with NO are represented as 1.5×10^{−7}*T ^{−1.64} and 4.4×10^{−7}*T ^{−2.15} cm^{3} s^{−1}, respectively, and agree very well with previous measurements. The rate constant for the reaction of CO^{−} _{3}(H_{2}O) with NO is 4.1×10^{−5}*T ^{−2.72} cm^{3} s^{−1}. Previous measurements of the rate constants for CO^{−} _{3}, CO^{−} _{3}(H_{2}O), and O^{−} _{3} reacting with NO_{2} appear to be in error; our measuredrate constants for the first two reactions are represented as 2.6×10^{−5}*T ^{−2.38} and 9.1×10^{−9}*T ^{−0.79} cm^{3} s^{−1}, respectively. The rate constant for the reaction CO^{−} _{3}(H_{2}O) with NO_{2} is 7.9×10^{−11} cm^{3} s^{−1} at 196 K. The reactions of CO^{−} _{3} and CO^{−} _{3}(H_{2}O) with NO_{2} proceed by O^{−} transfer, producing NO^{−} _{3}. While the reaction of O^{−} _{3} with NO_{2} proceeds mainly by charge transfer at room temperature, about half the reactivity at 200 K is due to charge transfer with the remainder arising from O^{−} transfer. Atmospheric implications of the present results are discussed.

Photodissociation of ICN in liquid chloroform: Molecular dynamics of ground and excited state recombination, cage escape, and hydrogen abstraction reaction
View Description Hide DescriptionThe photodissociation of ICN in liquid chloroform on different electronic states of the Ã band is studied using molecular dynamics simulations. By taking into account nonadiabatic transitions to the ICN ground state and by using a simple statistical model for the reaction between the CN radical and a chloroform molecule, the competition between recombination, cage escape and hydrogen abstraction reaction with the solvent is examined. Good agreement with the cage escape results of a recent experiment by Raftery et al. [J. Chem. Phys. 101, 8572 (1994)] is found. Simulations which did not include the nonadiabatic transitions to the ground state overestimated the probability for cage escape by about a factor of two. Very fast translational relaxation of the CN fragment and very low probability for achieving a transition state configuration for the abstraction reaction are calculated. This supports the suggestion that the abstraction reaction proceeds thermally and is controlled by a structural (entropic) barrier.

Entrainment, phase resetting, and quenching of chemical oscillations
View Description Hide DescriptionWe examine the effect of periodic and discrete perturbations on the phase of an oscillatory chemical reaction system near a Hopf bifurcation. Discrete perturbations reset the phase of the oscillation and periodic perturbations entrain the frequency of the oscillation for perturbation frequencies in a small range about each rational multiple of the natural frequency. These phase responses may be determined from time series of a single essential species. The new phase resulting from discrete perturbations and the relative phase between the oscillation and the forcing of an entrained oscillation are described by the same response function, which is a simple sinusoid. We show that for single species perturbations, the amplitude and phase offset of this response function equal the magnitude and the argument, respectively, of the corresponding component of the adjoint eigenvector of the Jacobi matrix (that corresponds to a pure imaginary eigenvalue). These phase response methods are simpler than quenching studies for determining the adjoint eigenvectors, and in addition yield the local isochrons of the periodic orbit.

A wave packet propagation study of inelastic and reactive F+D_{2} scattering
View Description Hide DescriptionWe compute the rotationally resolved differential cross sections for F(^{2} P _{3/2})+D_{2}(v=0,j) inelastic scattering as well as opacity functions for D_{2} rotational excitation and the reaction F+D_{2}→D+DF. Two values of the collision energy (89.7 and 187 meV) and two initial D_{2} rotational states (j=0 and j=1) are probed. Four calculation techniques have been compared: the quasiclassical trajectory approach and the Wigner method on the ground state (1^{2} A′) surface,wave packet propagation (with the D_{2} vibrational degree of freedom treated quantum mechanically) on the 1^{2} A′ surface, and wave packet propagation on the two coupled surfaces 1^{2} A′ and 2^{2} A′. The effect of the nonadiabatic spin–orbit coupling on the nonreactive F+D_{2}scattering is almost negligible, whereas the reaction cross sections in the two‐surface wave packet propagation treatment are considerably smaller than those in the calculations taking into account the ground state surface only.

Predissociation dynamics of the O_{2} B ^{3}Σ^{−} _{ u } state: Vibrational state dependence of the product fine‐structure distribution
View Description Hide DescriptionThe predissociation of the O_{2} B ^{3}Σ^{−} _{ u } state (υ=0–11) is investigated using fast beam photofragment translational spectroscopy. The energy resolution of the experiment, 7–10 meV, is sufficient to yield the correlated fine structure distribution P(j _{1},j _{2}) for the two O(^{3} P _{ j }) fragments. These spin–orbit branching ratios depend markedly on the vibrational quantum number, providing detailed insight into a relatively unexplored facet of molecular dissociationdynamics. No less than four repulsive states are expected to mediate the predissociation of the B ^{3}Σ^{−} _{ u } state, primarily via spin–orbit coupling, and the couplings among these states at long range (R∼5–7 Å) determine the final spin–orbit distributions P(j _{1},j _{2}). We have attempted to model these distributions in both the adiabatic and diabatic limits, with neither limit proving very successful. A more phenomenological approach to fitting our data suggests that products with j _{1}=j _{2}=2 result from single transitions between adiabatic potentials at long range, whereas the populations in the other product states are determined by multiple transitions among the repulsive states.

Photophysics and dynamics of the lowest excited singlet state in long substituted polyenes with implications to the very long‐chain limit
View Description Hide DescriptionIn this paper we explore the intramolecular relaxation processes within two long carotenoids, namely decapreno‐β‐carotene (M15) and dodecapreno‐β‐carotene (M19) with 15 and 19 conjugated double bonds (N), respectively. Amplified 200 fs pulses at 590 nm were used to excite the optically allowed S _{0}→S _{2} (1 ^{1} A _{ g }→1 ^{1} B _{ u }) transition of the two carotenoids. The excited state dynamics were probed by continuum light between 400–890 nm in solvents with different polarizabilities. The transient absorption spectra consist of a bleaching region, due to loss of ground state absorption, and of an excited state absorption region at longer wavelengths, due to the S _{1}→S _{ n } transition. The S _{ n } state was assigned to an n ^{1} B _{ u } state. The overall wavelength dependence of the measured kinetics could be well described by introducing three decay time constants. One reflects the S _{1} lifetime (τ_{1}) and was determined to 1.1 and 0.5 ps for M15 and M19, respectively. A second lifetime, between 5 and 15 ps, was attributed to vibrational cooling in the ground state. A third decay time was in the subpicosecond range, and was ascribed to the vibrational redistribution and relaxation of the S _{1}potential surface after being populated by the subpicosecond S _{2}–S _{1}internal conversion. No significant change of the decay constants was observed for M15 embedded in a 77 K matrix. This shows that the relaxation rates are only influenced by intramolecular processes.
The S _{2} lifetime was shorter than the pulse duration and was estimated to be in the order of 100 fs. The S _{0}→S _{2} transition of M15 in the liquid phase exhibits a 0.39 anisotropy at short times, while the S _{1}→S _{ n } transition has an initial value of only 0.31. This corresponds to an angle of 23° between the transition dipoles. The measured S _{1} rate constants were analyzed, together with decay constants of shorter carotenes, in terms of the energy gap law. When going from the shortest (N=5) to the longest (N=19) polyene, τ_{1} decreases about 6000 times, i.e., from 3 ns to 0.5 ps. By using an empirical form of the energy gap law the 0–0 transition of S _{1}(2 ^{1} A _{ g })→S _{0} was estimated to be located at 11 300 and 10 200±1 000 cm^{−1} for M15 and M19, respectively. By fitting the excitation energies of all carotenes in the series (3≤N≤19) with a truncated two or three term expansion of a power series in 1/N the long‐chain limit values were extrapolated to be 11 000 and 3 500 cm^{−1} for the 1 ^{1} B _{ u } and 2 ^{1} A _{ g } state, respectively. The implication of these limit values on the electronic structure of polyacetylene are discussed.

Electrochemical growth of superparamagnetic cobalt clusters
View Description Hide DescriptionThe magnetization of stabilized cobaltcolloids in tetrahydrofuran has been studied by a superconducting quantum interference device(SQUID) and magnetic balance measurements in dependence of applied magnetic field and temperature. The colloids are generated by a newly developed electrochemical method which allows one to generate clusters containing about 1000 atoms with a narrow size distribution. The final size distribution of the clusters is examined by high resolution transmission electron microscopy and small angle x‐ray scattering. The magnetization curves have been determined with special emphasis on changes at the freezing point of the solution. The curves of the liquid phase can be reasonably described by the Langevin function and the magnetic moments of isolated cobalt clusters that have been recently measured by Stern–Gerlach experiments. Deviations that appear at the freezing point can be understood in terms of magnetic anisotropy effects. It is shown that the cluster sizes and the susceptibilities of the dispersions are related. Therefore the growth of the clusters during the electrolysis can be directly observed by measuring the susceptibility in dependence of the charge transport in the cell.

Vibrational relaxation of CO (v=1) by inelastic collisions with ^{3}He and ^{4}He
View Description Hide DescriptionCalculations of the vibrational relaxation rate constants of the CO–^{3}He and CO–^{4}He systems are extended to lower temperatures than in any previous calculation and a comparison made with new experimental results in the temperature range 35–295 K for CO–^{3}He and previously published results in the range 35–2300 K for CO–^{4}He. Both the coupled states (CS) and infinite‐order sudden (IOS) approximations are used, with the self‐consistent‐field configuration interaction CO–He interaction potential of Diercksen and co‐workers. The CS approximation is found to give a similar level of agreement with experiment for the two isotopic species, while the performance of the IOS approximation is system dependent. The discrepancy between experimental and theoretical IOS rate constants is quite different for collisions involving ^{3}He and ^{4}He, so that it is not profitable to compare IOS results directly with experiment for these two systems at temperatures below 300 K. The differences between the measured and the CS calculated rate constants for both the CO–^{4}He and CO–^{3}He systems are thought to be due predominantly to inaccuracies in the interaction potential. Relaxation rate constants for CO target molecules in collision with HD, D_{2} and H_{2} are compared with results involving ^{3}He, ^{4}He, and ‘‘^{2}He,’’ revealing some systematic trends depending only on mass. However, for all hydrogen species there are marked upturns in the rate constants at low temperatures relative to those for helium atoms, while the rate constants for HD are greater than those for ^{3}He throughout the temperature range. Calculations at small initial kinetic energies for the CO–He systems reveal an unexpected increase in relaxation cross section with reduction in kinetic energy. This implies that at very low temperatures the CO–He rate constants will show an upturn with decreasing temperature. The fact that this effect is smaller than that for the CO‐hydrogen systems and occurs at lower temperatures is consistent with the shallower CO–He attractive well compared with that for CO–H_{2}.

H_{2}O photodissociation dynamics based on potential energy surfaces from density functional calculations
View Description Hide DescriptionWe investigate the usefulness of density functional theory(DFT) for calculating excited statepotential energy surfaces. In the DFT calculations, the generalized gradient approximation (GGA) is used. As a test case, the photodissociation of H_{2}O through the first excited Ã ^{1} B _{1} state was considered. Two‐dimensional potential energy surfaces were obtained for both the X̃ ^{1} A _{1}ground state and the first excited state. Wave packet calculations employing these surfaces were used to obtain both the absorptionspectrum and partial photodissociation cross sections, which are resolved with respect to the final vibrational state of the OH fragment. Comparisons are made with a previously calculated high level ab initiopotential energy surface, with dynamics calculations using that surface, and with experiment. The vertical excitation energy for the (X̃ ^{1} A _{1}→Ã ^{1} B _{1}) transition calculated using DFT is in good agreement with the previous ab initio calculations. The absorptionspectrum and the partial cross sections obtained with the DFT treatment are in good agreement with experiment.

6D quantum calculation of energy levels for HF stretching excited (HF)_{2}
View Description Hide DescriptionConverged full‐dimensional (6D) quantum mechanical calculation of energy levels of intramolecular stretching excited (HF)_{2}(ν_{1}ν_{2}) is presented for (ν_{1}ν_{2})=(01), (10), (02), (20), and (11). The bound state calculation for the excited HF dimer employs the SQSBDE potential energy surface of Quack and Suhm and is for total angular momentumJ=0. This calculation provides the first rigorous theoretical result of energy levels for HF stretching excited HF dimer in full dimensions. The calculated fundamental transition frequencies are ν_{1}=3940.6 cm^{−1} and ν_{2}=3896.4 cm^{−1}. These values are somewhat larger than the corresponding experimental measurement of 3930.9 cm^{−1} for ν_{1} and 3868.3 cm^{−1} for ν_{2}. The overtone frequencies are calculated to be 2ν_{1}=7713.5 cm^{−1}, 2ν_{2}=7642.5 cm^{−1}, and ν_{1}+ν_{2}=7841.8 cm^{−1}. The theoreticaltunneling splittings of the fundamentals ν_{2} and ν_{1} are, respectively, a factor of 5.3 and 3.7 smaller than the ground state splitting, compared to a factor of 3 from the experimental measurement. The splittings of the overtone states 2ν_{2}, 2ν_{1}, and ν_{1}+ν_{2} are smaller than that of the ground state by factors of 9.6, 48, and 1.8, respectively. Some of the calculated energy levels of excited (HF)_{2} are spectroscopically characterized and assigned.

Local density functional studies of electronic structure of Be_{135}
View Description Hide DescriptionResults of extensive studies of metallic beryllium modeled with 135 atoms are reported using a first‐principles total energy molecular cluster approach based on the local density approximation. Binding energy, ionization potential,charge density, Mulliken populations, density of states and atomic forces are calculated. The results show that the ground state of Be_{135} is of a^{″} symmetry. The binding energy is 77.5 kcal/mol which is very close to the binding energy of bulk Be (75.3 kcal/mol). Comparison with earlier results from Hartree‐Fock calculations shows significant differences in the calculated binding energy, ionization potential, and Mulliken populations.

Quantum Monte Carlo studies of anisotropy and rotational states in He_{ N }Cl_{2}
View Description Hide DescriptionWe investigate ground and rotationally excited states of He_{ N }Cl_{2} (N=1,6,20) using variational (VMC) and diffusionMonte Carlo (DMC). The structure of these clusters is dominated by the He–Cl_{2} interaction, which has a well depth of about 30 K and a minimum in the perpendicular orientation. Results using the full, anisotropic potential are compared with those using an isotropic approximation. The effect of anisotropy is notable for the N=6 cluster in which the perpendicular well enhances the formation of a ring of six He atoms around the Cl–Cl bond axis. Because of the stability of this ring, the He_{6}Cl_{2} structure is not significantly affected by rotational excitation to the L=2 state. However, such an excitation does cause both the He and Cl_{2} densities to delocalize slightly in the He_{20}Cl_{2} cluster. For all of these cluster sizes, the Cl_{2} density is distributed on and about the cluster center. This behavior is similar to SF_{6} in He_{ N }, N<112, although the Cl_{2} is not as localized as the more strongly bound SF_{6}.

Calculating atomic properties using variational Monte Carlo
View Description Hide DescriptionUsing variational Monte Carlo and the explicitly‐correlated wave function forms optimized by Schmidt and Moskowitz, we compute a number of properties for the atoms He–Ne. The expectation value of the Hamiltonian using these wave functions contains between 70.0% and 99.8% of the correlation energy for the neutral atoms (17 parameters), 60.8% and 99.1% for selected cations (9 parameters), and 73.9% and 89.4% for selected anions (17 parameters). For those properties which sample the valence region, our results are in good agreement with previous calculations (where available). Because of a defect in the wave function form, a substantial error is found in those properties which two electrons that are in close proximity.