Date: Fri, 1 Sep 89 18:54 CDT From: AGGWI@TTACS1.Bitnet Subject: new-paper message 2 To: s171vc09@VB.CC.CMU.EDU X-VMS-To: s171vc09@VB.CC.CMU.EDU Original_To: BITNET%"s171vc09@cmccvb" AB INITIO COMPUTATIONS OF ONE AND TWO HYDROGEN OR DEUTERIUM ATOMS IN THE PALLADIUM TETRAHEDRAL SITE Francis F.Muguet , Palmyre M-P Bassez-Muguet # S.P.Q.R laboratory P.O Box 4260 Texas Tech University, Lubbock, Texas 79409 # permanent adress : Laboratoire de chimie physique I.U.T de Strasbourg-Sud Universite Robert Schuman Illkirch Graffenstaden 67000 France. (Received ________ ABSTRACT We report ab initio cluster computations of deuterium atoms in a tetrahedral palladium site, performed at the UHF level with extended basis sets. An interstitial deuteron is found to be energetically favored over an interstitial deuterium atom. Computations with one interstitial deuterium atom or with one deuteron reveal an increase in electron density near the deuteron. Not only valence electrons but inner core electrons of the palladium atoms are present in the vicinity of the deuteron. A potential energy curve is calculated with two deuterium atoms approaching each other, with one deuterium fixed at the center of a tetrahedral site. In regard to the environment provided by molecular deuterium, our results show that the tetrahedral site does not favor a closer deuteron encounter. No metastable dimer geometry is found. The two deuterons repel each other despite the screening. These computations represent more than 250 CPU hours of a new generation biprocessor vector computer. ___ _____ Key words : cold fusion, ab initio computation, palladium/hydrogen system, palladium/deuterium system, palladium tetrahedral site. 1. INTRODUCTION Recently, M. Fleischmann, S. Pons and M. Hawkins (1) observed a relatively high energy release during an electrolysis of deuterated water using a palladium cathode. To explain the excess heat, these authors propose a nuclear fusion of deuterium inside the palladium lattice. The possibility of starting a nuclear reaction between deuterons Page 2 is conditioned by the Coulombic repulsion barrier, which is 211.671 hartrees at an internuclear distance of 250 fm or 0.0025 Å. In order to understand if this barrier can be overcome, we have made some calculations on deuterium atoms in a palladium tetrahedral site. The palladium/deuterium lattice is supposed to be in the beta-phase, where deuterium atoms, present under the form of deuterons, move without their respective electrons. Nevertheless it must be cautioned that metastable supersaturated alpha-phase might also exist even at high loading ratio (2). The cubic face centered palladium lattice possesses both octahedral and tetrahedral interstitial sites. In the case of octahedral occupancy, the stoechiometric formula of the saturated palladium hydride is PdH. In the case of tetrahedral occupancy, the formula is PdH2 (3). Fleischmann, Pons and Hawkins (1) hinted that presumably deuterons were located in the octahedral lattice positions, yet Pons (4) latter revealed that his electrodes were containing approximatly two or more deuterium atoms for each palladium atom. This latter loading factor of two is somewhat extraordinary, and the information must be received with caution, until further confirmation. At room temperature, in equilibrium, the loading factor of a palladium hydride is 0.67. However it is now clear that the loading factor must be above 0.8 for cold fusion to occur. Interestingly, L. Fuller (5),who reports a microexplosion in a palladium cathode, hints that he has reached a loading factor of 1.2. For a nuclear reaction to occur, a high degree of confinement is necessary. From simple geometrical considerations, tetrahedral sites should offer a higher confinement than octahedral sites. Not suprisingly, very recently Wilets and coworkers (6) have concluded within the degenerate electron gas computational framework that adequate confinement at tetrahedral sites requires a softer potential, and thus tetrahedral sites seem more favorable that octahedral sites. Several hypotheses have been proposed for the explanation of this cold fusion. For instance, two deuterons may sit as a pair in the same interstitial site, at a very short distance from one another, thus allowing a tunnelling reaction. According to Jones et al.(7), in order to achieve a fusion rate of about 10**-34/s, deuterons must be confined within 0.3 Å. This confinement might be achieved dynamically, where the inter-deuterons distance could be oscillating aroung the 0.5 Å value. Szalewicz and coworkers (8) found in the case of an hydrogen molecule, that vibrationnaly excited states should augment the fusion rate by several order of magnitude. Another hypothesis is that two deuterons form a metastable pair, the internuclear distance of which is reduced, because somehow the effective mass of the binding electron(s) is(are) greatly enhanced. It is somewhat the analog of the muon catalyzed fusion. According to Jones and coworkers (7) the electron mass should increase up to 1 MeV, Page 3 which looks improbable. Furthermore as stressed by Legget and Baym (9), the quasiparticle possesses an extended delocalization since it is a physico-mathematical entity created by the interaction of the electron with the lattice. On sub-angstrom scales only the bare electron mass may count. Another hypothesis is that the deuterium nuclei are so much screened by surrounding electrons, that the Coulombic repulsion barrier is lowered when they form a metastable pair. According to Jones and coworkers (7) the introduction of an extra electron should not increase the fusion rate sufficiently. Another perpective is to look not for metastable pairs but for collision processes between two deuterons. According to Jones and coworkers (7), in order to achieve a fusion rate of about 10**-23/s, the deuteron current must have an energy in the order of about 380 eV, and it is not clear which mechanism can create such an energy. Hagelstein (10-13) has proposed that such an energy could be achieved by optical phonons generated by the electrical current flow inside the electrode. On another hand, Walling and Simons (14), have proposed that the Coulomb potential is scaled by metallic screening. Consequently, we propose to calculate, if the occupancy of a tetrahedral site by one deuteron is possible, what the form of the potential well is and what are the vibrationnal states in this well. We propose also to calculate if a pair of deuterons can occupy a tetrahedral site, and the potential energy curve between two deuterons, one in the tetrahedral site, and the other entering the site. This is of interest in order to assess crudely, within the framework of the sudden approximation, the collision process. In this paper, we report the first part of our calculations, which consists of computing the potential energy curve of two interacting deuterons, with one located in a tetrahedral site and the other approaching the site. This computation is made within a quasistatic approximation. We may notice that the palladium hydride is in a non-equilibrium state, and under the influence of an anisotropic electric field near the electrode interface. Surface effects and local lattice dislocations, defects or impurities may play a significant role. Thus it would be premature for us to propose any definite conclusion before considering these last features. 2. COMPUTATIONAL METHODS There is a large variety of approaches in solid state computations (15). A widely used method is the muffin-tin Linear Augmented Plane Wave. Such type of computation (16) has been reported at the same workshop to study the double occupancy in an octahedral site. According to this computation (16), it is worth remarking that, when the dimer dissociates, the two produced hydrogen atoms transit respectively into nearby tetrahedral sites. When the Page 4 emphasis of the computation is on structural prediction and ground state energy, an ab initio Hartree-Fock cluster treatment seems more appropriate. The homegeneous electron gas model is not particularly suited for structural computations. Since the system may be somewhat unusual, we fell also compelled not to use any semi-empirical pseudopotentials. The use of HF crystal orbital methods (15) presents a number of difficulties. First, the palladium atom contains 46 electrons, and a good atomic basis set makes the computation extremely costly. We could have used a soft-core potential to describe the core electrons, but correctly as we shall see later, we did not choose this simplification. Consequently, we kept the number of palladium atoms to a minimun in order to stay within the limitations of the computer hardware. Second,our interest is the study of the ground state energy of the system, when two hydrogen or deuterium atoms approach eachother. The situation is somewhat equivalent to the study of a point impurity, and it is known (15) that periodic boundary conditions create special problems. A first remedy is the supercell approach (15) but it is prohibitively expensive. Other methods are embedding techniques such as that proposed by Koster abd Slater (15). So far the computations were fairly crude but full SCF programs are currently under development by Pisani and coworkers (15). For these reasons, we have chosen to use standard well-proven molecular quantum calculations, and we have considered a tetrahedral site with only 4 palladium atoms in fixed positions in the metal experimental geometry at 25°C with an inter-palladium distance of 2.750 Å. Other solid state researchers have used molecular quantum methods,in similar cases. For example Beckman and Koutecky (17) have performed detailled HF-CI computations with lithium hydrides. Our choice is further reinforced because it is possible to proceed with computations in the presence of an electric field, and also because we are interested in future studies of electronic correlation and localized vibration of the hydrogen and deuterium atoms. However this procedure has its strength and limitations. The most obvious limitation is that it cannot reproduce the delocalized plane waves of the free electron gas. Anyhow if there is any local metallic screening of the Coulombic interaction between the two protons or deuterons, it should cause a collapse of the plane wave into a localized region nearby the two positive nuclei in order to provide a sufficient electron density. Consequently, in our case, it is not a severe limitation. In fact one of the problem associated with plane wave methods is precisely the description of the electronic density in the vicinity of nuclei. The description of the conduction band or the free electrons of the "Fermi sea" would not be accurate in our computations, but as stressed above we are mainly interested in localized electrons. We fail to see how highly mobile Page 5 and fast conduction electrons can offer a substantial screening, except may be at very high current density, which does not correspond to the reported experimental conditions (1,2). All the computations are performed at the unrestricted Hartree-Fock level, using the GAMESS (18) set of programs. Two types of basis sets MINI and MIDI (19) are used for the palladium atom. The MINI basis set comprises 15 primitive s gaussians contracted into 5 atomic orbitals (AOs), 12 primitive s gaussians contracted into 3 AOs, 6 primitive d gaussians contracted into 2 AOs. The MIDI basis set is similar except for the outer s and d AOs which are relaxed into 2 AOs respectively. The MIDI basis set allows more flexibility and has been used in the majority of the computations. Three types of bases are used for the deuterium atom. One set comprises the Dunning-Huzinaga (20) DH basis set which includes 4 s gaussians ,the inner three being contracted into one AO, supplemented by 2 p AOs of respective exponents 1.4 and 0.25. A second basis set is further supplemented by 3 s AOs of respective exponents 0.072 0.028 and 0.011, following approximatively an even tempered expansion. A third basis set similar to the latter is further supplemented by a d AO of exponent 0.40. The inner s AO is completly uncontracted, when two deuterium atoms are at close approach. In the SCF DIIS (21) iteration scheme, the convergence parameter for the convergence in density is set to 5 10**-8. The integral cutoff is set down to 10**-12 to improve accuracy. The UHF natural orbitals (NO) are computed for each run. A Mulliken (22) and Lowdin (23) population analysis is also carried out. The Mulliken population scheme splits equally the overlap population between the atoms. The Lowdin population analysis gives a much more realistic picture of the population when in the presence of a light atom like deuterium. Finally a rough estimation of the basis set superposition error (24), is computed with the counterpoise scheme (25). The counterpoise scheme by no means gives an exact appreciation, some controversies still remain about its accuracy, but it is the method most often implemented for estimating the BSSE. All these extremely costly computations represent more than 250 hours of CPU time, and were performed on an ARDENT computer with 2 vector processors and 1.2 Gbyte of disk work area. The GAMESS (18) program was implemented with some minor modifications on the ARDENT by the authors. 3. RESULTS AND DISCUSSION The pure tetrahedral palladium cluster is first calculated then one instertitial deuterium atom is added, with various total charges [Table I]. The basis set superposition error (BSSE) is estimated to be of the order of 0.07 Hartree, after substracting the energy of Pd4 from the energy of Pd4 counterpoise : Page 6 BSSE = -19684.633 + 19684.570 = - 0.063 hartrees Therefore, the relatively small magnitude of the BSSE should not invalidate our later results. The calculation of the stabilization energies takes the BSSE into account. The stabilization energy of the Pd4D cluster with a null charge is equal to : -19685.188 + 19685.069 + 0.063 = -0.056 hartrees. For a Pd4D cluster with a positive charge, the stabilization energy is equal to : -19684.981 + 19684.570 + 0.063 = -0.348 hartrees The occupation of a tetrahedral interstitial site by a complete deuterium atom yields only a marginal stabilization energy. The occupation by a deuteron is more favored. A geometric optimization of the Pd4D system is performed and ,not suprisingly, an equilibrium geometry is found. The equilibrium geometry comprises a deuterium atom located at the center of mass of the system. The energies at the equilibrium geometry with various basis sets and with various charges are listed in table I. We note a significant increase in the Mulliken and Lowdin charges [Table 2] on the deuterium atom by comparison with the hydrogen molecule environment. There is more electron density in the vicinity of the deuteron. An inspection of the coefficients of the NOs reveals that inner core palladium AOs are involved in some NOs which have significant contributions from the deuterium AOs. In other words, palladium inner electrons are present in the vicinity of the deuterium atoms, and thus should participate in the screening. This invalidates the use of soft-core pseudopotentials. Another type of calculation is performed considering a fixed deuterium atom located at the center of mass of the tetrahedral site, and a second incoming deuterium positioned at various distances of the interstitial deuterium. The inter-deuterium distance is varied from 1.35 Å to 0.15 Å. Quite naturally, the incoming deuteron passes through the center of a triangular side. The symmetry group is C3v. Single-point UHF computations are effected at selected distances. Three series of computations are made with the total charges -1,0,+2. [ Table III]. The corresponding curves ( fig 1,2,3) are fitted ,for the eye, with an exponential function, with the MERV program (26). For comparison, similar computations are performed for the D2 and the D2+ molecule [ Table 4]. The curves ( fig 4,5) are also fitted for the eye with an exponential function. We can notice in fig 1 a small bump around 0.6 Å, and also in figure 3 a small bump around 0.7 Å. These bumps correspond to the entrance of the incoming deuteron inside the tetrahedral cluster. The barrier is very low, which is unfortunate, since this barrier would prevent the incoming deuteron, once inside the cluster, from escaping outside the tetrahedral site. Presumably a similar bump would have appeared in fig 2., if the energy were computed around 0.65 Å. In regard to the various molecular systems studied so Page 7 far, we compare the variations of energy when the deuterium internuclear distance varies respectively from 0.60 Å to 0.35 Å and from 0.35 Å to 0.15 Å [Table V]. Not suprisingly the positive deuterium molecular ion provides the worst environment for a close deuteron encounter, but the palladium clusters are still no more favorable than molecular deuterium. It is clear that in comparison with the deuterium molecule no dramatic barrier lowering effect and no major screening effect appears. The Coulomb barrier is not significantly reduced within a tetrahedral site according to a quasistatic equilibrium framework. The unscreened Coulombic nuclear repulsion energy is computed at various distances to give an idea of the order of magnitude of the energies involved. [ Table VI ]. Two geometry optimization runs are tried for the deuterium dimer [Table VII ] starting from two different geometries. The positions of the two deuteriums atoms are completely free to vary within the rigid palladium structure. The starting geometry, of the first optimization run, comprises one deuterium atom located at the center of mass and another deuterium atom located at a distance of 0.6 Å. The symmetry group is C3v. As the optimization progresses, the incoming deuterium atom is repelled. The starting geometry of the second geometry optimization run comprises two deuterium atoms placed in a symmetric position in regard to the center of mass at a respective distance of 0.31 Å. The symmetry group is C3v. The energy computed, at the starting geometry, is too high, furthermore the gradient is out of range. It was thus deemed not appropriate to pursue such an unpromising, yet costly, optimization. We can conclude that, inside a tetrahedral site, there is no metastable equilibrium geometry of a deuterium dimer which exhibits a smaller internuclear distance than in molecular deuterium. This conclusion is strictly correct only under the assumption that the quasistatic approximation used in all the computations, is roughly valid. Our conclusions are preliminary but eliminate conjectures found in the literature which hint that fusion could result from a straightforward electron screening, at least in a tetrahedral site. Since we have included neither vibrations, (possibly vibronic effects), nor an electric field,it would be premature to conclude that a deuteron fusion cannot occur in a tetrahedral site. The present computations are currently being continued by studying the vibration of the deuteron inside the tetrahedral cluster, and by considering the influence of an electric field. ACKNOWLEDGMENTS The availability of the ARDENT computer in our laboratory, was made possible by a Grant from the Advance Research Program of the state of Texas. The authors also acknowledge the Welch foundation and the NSF for their Page 8 support. We would like also to express our thanks to Dr.G.Wilse Robinson for his interest in our work, and to Cherryl Starkey for her assistance. We thank also Dr. Loren Fuller and Dr. S.-H. Hei for fruitful discussions during the workshop. Page 9 __________ REFERENCES 1. M. Fleischmann,S. Pons and M. Hawkins, Electrochemically induced nuclear fusion of deuterium. J. Electroanal. Chem. 261,301-308(1989) 2. T.B Flanagan and F.A Lewis, Trans. Farad. Soc. 55,1409-1420(1959) 3. A.C Switendick Electronic structure of transition metal hydrides. in __________ _____ ________ Transition metal hydrides edited by R. Bau, Adv. Chem. Ser vol. 167. ACS(1978) pp. 264-282 4. R. Pol Fusion Breakthrough? Science 1661-1662(31 March 1989) 5. L. Fuller (poster at the Workshop on Cold Fusion Phenomena, Santa Fe, NM, May 23-25 1989) 6. L. Wilets, M. Alberg, J.J Rehr and J. Mustre de Leon, Upper limit to fusion rates of isotopics hydrogen molecules at high electron density interstitial Pd sites. APS meeting April 1989. Abstract. 7. J. Rafelski, M. Gajda, D. Harley, S.E Jones, Theoretical limits on cold fusion in condensed matter. Preprint. 8. K. Szalewicz, J.D Morgan III, and H.J Monkhorst Fusion rates for hydrogen isotopic molecules of relevance for cold fusion, APS meeting April 1989. Abstract. 9. A.J Legget and G. Baym, Can "solid-state" effects enhance the cold fusion rate ?, Preprint. 10.P.L Hagelstein, A simple model for coherent DD fusion in the presence of a lattice, Preprint. 11.P.L Hagelstein, Phonon interactions in coherent fusion, Preprint 12.P.L Hagelstein, Rates for neutron and tritium production in coherent DD fusion, Preprint 13.P.L Hagelstein, Dephasing in coherent DD fusion and the long chain model, Preprint. 14.C.Walling and J.Simons, Two innocent chemists look at cold fusion, J. Phys. Chem. 93(12),4693-4696(1989). 15.C.Pisani, R. Dovesi R. and C. Roetti, ____________ __ ______ _________ __ ___________ _______ Hartree-Fock ab initio treatment of crystalline systems , Springer-Verlarg (1988) and references herein. 16.S.H Wei, A. Zunger, Predicted instability of octahedrally-centered diatomic hydrogen in Palladium (Workshop on Cold Fusion Phenomena, Santa Fe, NM, May 23-25 1989). 17.H.O Beckman and J. Koutecky, Surface Sci. 120;127-149(1982). Page 10 18.M.W Schmidt, S.T Elbert, M. Dupuis, D. Spangler and J.J Wendoloski. General Atomic and Molecular Electronic Structure System GAMESS 19. S.Huzinaga, J. Andzlem, M. Klobukowski, E. Radzio-Andzelm, Y. Sakai and ________ _____ ____ ___ _________ ____________ H.Tatewaki, Gaussian basis sets for molecular calculations , Elsevier (1984). ______ ___________ _________ 20. T.H Dunning and P.J Hay, Modern theoretical chemistry Plenum (1976) 21. T.P Hamilton and P. Pulay, J. Chem. Phys. 84(10) 5728-5734 (1986) 22. R.S Mulliken, J. Chem. Phys. 23(10),1833-1840 (1955) 23. P.O Lowdin, Phys. Rev. 97(6).1474-1520 (1955) 24. Z.Latajka and S.Scheiner, Chem. Phys. Lett. 140(4)338-343 (1987) 25. S.F Boys and F. Bernadi. Mol. Phys. 19(4),553-566 (1970) 26. J.M Gregory and C.B Fedler, ASAE 1986 Summer Meeting paper 86-5032 Page 11 Table I. Energy of the palladium tetrahedral cluster Pd4, and energy of the insertion complex Pd4D ---------------------------------------------------------------------- Structure Basis set Charge Energy# ---------------------------------------------------------------------- Pd4 Pd:MIDI 0 -19684.570 Pd4 Counterpoise Pd:MIDI Ghost:DH 3s 2p 0 -19684.633 ---------------------------------------------------------------------- Pd4 + D far apart Pd:MIDI D:DH 0 -19685.069$ ---------------------------------------------------------------------- Pd4D equilibrium Pd:MINI D:DH 2p 0 -19684.129 Pd4D Pd:MIDI D:DH 3s 2p 0 -19685.188 Pd4D Pd:MIDI D:DH 3s 2p +1 -19684.981 ---------------------------------------------------------------------- # atomic units ( 1 hartree = 27.21162 eV ) $ computed by adding together : the energy of a Pd4 cluster with the energy of an isolated D ( -19684.570 - 0.499 = -19685.069 ) Page 12 Table II. Population analysis on the deuterium atom. ---------------------------------------------------------------------- Total Mulliken Lowdin Structure Basis set charge charge charge ---------------------------------------------------------------------- D2 D:DH 0 0 Pd4D Pd:MIDI D:DH 3s 2p +1 -0.298 -0.711 Pd4D Pd:MIDI D:DH 3s 2p 0 -1.742 -0.901 ---------------------------------------------------------------------- Page 13 Table III. Potential energies of the (Pd4D,D) system for various cluster charges, and at different deuterium internuclear distances. ---------------------------------------------------------------------- Structure Basis set Charge Distance$ Energy# ---------------------------------------------------------------------- Pd4D + D Pd:MIDI D:DH 3s 2p +2 1.35 -19685.1131 " " 1.10 -19685.1124 " " 0.95 -19685.1018 " " 0.70 -19685.0557 " " 0.60 -19685.0155 " " 0.35 -19684.6651 " " 0.15 -19682.9615 ---------------------------------------------------------------------- Pd4D + D Pd:MINI D:DH 2p 0 1.35 -19684.7732 " " 1.10 -19684.7686 " " 0.85 -19684.7477 " D:DH* " 0.60 -19684.6901 " D:DH* " 0.35 -19684.3707 " D:DH* " 0.15 -19882.6863 ----------------------------------------------------------------------- Pd4D + D Pd:MIDI D:DH 3s2p1d -1 1.10 -19685.8333 " " 0.90 -19685.8207 " " 0.70 -19685.7871 " D:DH* " 0.60 -19685.6525 " D:DH* " 0.35 -19685.3451 " D:DH* " 0.15 -19683.6698 ----------------------------------------------------------------------- * uncontracted atomic basis set. # atomic units : hartree $ angstrom Page 14 Table IV. Potential energies of D2 for various charges, and at different internuclear distances. ------------------------------------------------------------------------ charge distance | SCF energy | CISD energy | Nuclear Repulsion ------------------------------------------------------------------------ D2 0 0.742 -1.1314 -1.1688 0.713 0.60 -1.1144 -1.1506 0.882 0.35 -0.8289 -0.8646 1.512 0.15 +0.8443 0.8076 3.528 ------------------------------------------------------------------------ D2 +1 1.0523 -0.60103 0.503 0.742 -0.56898 0.713 0.60 -0.5071 0.882 0.35 -0.1196 1.512 0.15 +1.6546 3.528 ------------------------------------------------------------------------ The basis sets are uncontracted DH distances are in angstroms. energies are in hartrees ( = 27.21162 eV) Page 15 Table V. Energy increments in D2 and in (Pd4D,D) systems when the deuterium internuclear distance varies from 0.60 to 0.35 Å and from 0.35 to 0.15 Å. ----------------------------------------------------------------------- Structure Charge Increments# ----------------------------------------------------------------------- | 0.60-0.35 Å | 0.35-0.15 Å | ----------------------------------------------------------------------- D2 +1 0.3875 1.7742 ----------------------------------------------------------------------- D2 0 0.2855 1.6732 ----------------------------------------------------------------------- Pd4D + D -1 0.3074 1.6753 ----------------------------------------------------------------------- Pd4D + D 0 0.3194 1.6844 ----------------------------------------------------------------------- Pd4D + D +2 0.3504 1.7036 ----------------------------------------------------------------------- # atomic units (hartree) Page 16 Table VI. Coulombic nuclear repulsion energies between two deuterons. Distances(angstrom) Energy(hartree) ------------------------------------------------------------------------ 0.0010 529.177 0.0025 211.671 0.0050 105.835 0.01 52.918 0.15 3.528 0.3 1.764 ------------------------------------------------------------------------ Page 17 Table VII. Energies computed during geometry optimization searches. Structure Basis set Charge Energy# Distance$ ----------------------------------------------------------------------- Pd4D +D Pd:MIDI D:DH 3s 2p 1d -1 -19685.6525 0.600 -19685.6992 0.748 -19685.7184 0.857 -19685.7320 0.995 -19685.7421 1.154 -19685.7500 1.311 -19685.7565 1.470 ------------------------------------------------------------------------ Pd4D2 Pd: MIDI D:DH 3s 2p 1d -1 -19685.2389* 0.620 ------------------------------------------------------------------------ * gradient out-of-range # hartree. $ angstrom. Page 18 _______ ________ FIGURES CAPTIONS FIGURE 1. Potential energy of the ( Pd4D,D ) system with total charge -1, as a function of the deuterium internuclear distance. FIGURE 2. Potential energy of the ( Pd4D,D ) system with total charge 0, as a function of the deuterium internuclear distance. FIGURE 3. Potential energy of the ( Pd4D,D ) system with total charge +2, as a function of the deuterium internuclear distance. FIGURE 4. Potential energy of the ( D,D ) system with total charge 0, as a function of the deuterium internuclear distance. ( continuous line : SCF energy , dashed line : CISD energy ) FIGURE 5. Potential energy of the ( D,D ) system with total charge +1, as a function of the deuterium internuclear distance.