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The PAW method has been used to compute the iron L$_{2,3}$ edges of x-ray absorption spectra (XAS) and x-ray magnetic circular dichroism (XMCD) of the spin-crossover Fe(phen)$_{2}$(NCS)$_{2}$ molecule when adsorbed on Cu(001) surface and in the gas phase, for both the high spin (HS) and low spin (LS) states. It is found that the calculated XAS and XMCD with the static core hole or the Slater transition state half hole are in less good agreement with experiment than those using the so called initial state. This disagreement is due to the reduction of the iron spin magnetic moment caused by the static screening of the core hole by the photo-electron. The L$_{2,3}$ XAS formula is found to be directly related to the unoccupied $3d$ density of states (DOS), and hence the symmetry broken $e_g$ and the $t_{2g}$ iron DOS are used to explain the XAS and XMCD results. It is demonstrated that the dependence of the HS XMCD on the direction of incident x-ray circularly polarized light with respect to the magnetization direction can be used to determine the iron octahedron deformation, while the XMCD for various magnetization directions is directly related to the anisotropy of the orbital magnetic moment and the magneto-crystalline energy. It is also shown that the magnetic dipole moment $T_z$ is very large due to the strong distortion of the iron octahedron and is necessary for an accurate determination of the sum rule computed spin magnetic moment., Comment: 39 pages, 5 figures

Density functional theory (DFT) including van der Waals weak interaction in conjunction with the so called rotational invariant DFT+U, where $U$ is the Hubbard interaction of the iron site, is used to show that the fluorinated spin crossover Fe(phen$)_{2}$(NCS$)_{2}$ molecule whether in the gas phase or adsorbed on Cu(001) surface switches from the original low spin state to the high spin state. Using Bader electron density analysis, this inversion of the spin-crossover is explained in terms of electron doping of the Fe-octahedron cage which led to an increase of the Fe-N bond lengths. Consequently, the ligand-field splitting is drastically reduced, making the high-spin ground state more stable than the low-spin state. The calculated scanning tunneling microscopy (STM) images in the Tersoff-Hamann approximation show a clear distinction between the fluorinated and the unfluorinated molecule. This theoretical prediction is awaiting future STM experimental confirmation., Comment: 20 pages, 7 figures

We present a general method of constructing \textit{in-situ} pseodopotentials from first principles, all-electron, full-potential electronic structure calculations of a solid. The method is applied to bcc Na, at equilibrium volume. The essential steps of the method involve (i) calculating an all-electron Kohn-Sham eigenstate. (ii) Replacing the oscillating part of the wavefunction (inside the muffin-tin spheres) of this state, with a smooth function. (iii) Representing the smooth wavefunction in a Fourier series, and (iv) inverting the Kohn-Sham equation, to extract the pseudopotential that produces the state generated in steps (i)-(iii). It is shown that an \textit{in-situ} pseudopotential can reproduce an all-electron, full-potential eigenvalue up to the sixth significant digit. A comparison of the all-electron theory, \textit{in-situ} pseudopotential theory and the standard nonlocal pseudopotential theory demonstrates good agreement, e.g., in the energy dispersion of the 3$s$ band state of bcc Na., Comment: 13 pages, 3 figures

Electrically manipulating the quantum properties of nano-objects, such as atoms or molecules, is typically done using scanning tunnelling microscopes and lateral junctions. The resulting nanotransport path is well established in these model devices. Societal applications require transposing this knowledge to nano-objects embedded within vertical solid-state junctions, which can advantageously harness spintronics to address these quantum properties thanks to ferromagnetic electrodes and high-quality interfaces. The challenge here is to ascertain the device's effective, buried nanotransport path, and to electrically involve these nano-objects in this path by shrinking the device area from the macro- to the nano-scale while maintaining high structural/chemical quality across the heterostructure. We've developed a low-tech, resist- and solvent-free technological process that can craft nanopillar devices from entire in-situ grown heterostructures, and use it to study magnetotransport between two Fe and Co ferromagnetic electrodes across a functional magnetic CoPc molecular layer. We observe how spin-flip transport across CoPc molecular spin chains promotes a specific magnetoresistance effect, and alters the nanojunction's magnetism through spintronic anisotropy. In the process, we identify three magnetic units along the effective nanotransport path thanks to a macrospin model of magnetotransport. Our work elegantly connects the until now loosely associated concepts of spin-flip spectroscopy, magnetic exchange bias and magnetotransport due to molecular spin chains, within a solid-state device. We notably measure a 5.9meV energy threshold for magnetic decoupling between the Fe layer's buried atoms and those in contact with the CoPc layer forming the so-called 'spinterface'. This provides a first insight into the experimental energetics of this promising low-power information encoding unit.

To study the impact of oxygen vacancies on spin-polarized transport, we have computed the electronic and transport properties of single (F centers) and paired (M centers) oxygen vacancies using density functional theory. These point defects can generate barrier heights as low as 0.4V for FeCo electrodes irrespective of the defect's spatial position within the barrier, and of the orientation of the M center. These defects promote a strong decrease in the conductance of the spin up channel in the magnetic tunnel junctions (MTJ)'s parallel (P) magnetic state that mainly accounts for an order-of-magnitude drop in TMR, from about 10000$\%$ in the ideal case toward values more in line with experiment. When placed in the middle layer of the MgO barrier, the F center introduces additional P $\uparrow$ transmission away from the $\Gamma$ point. This scattering lowers TMR to 145$\%$. In contrast, the M center merely broadens this transmission around $\Gamma$, thereby boosting TMR to 315$\%$. Rotating a M center so as to partly point along the transmission direction sharpens transmission around $\Gamma$, further increasing TMR to 1423$\%$. When these defects are placed at the MTJ interface, the transmission and ensuing TMR, which reaches $\approx$ 4000$\%$, suggest that such junctions behave as would an ideal MTJ, only with a much lower barrier height. Our results thus theoretically reconcile the concurrent observations of high TMR and low barrier heights, such as post-deposition oxidation of metallic Mg, which can generate oxygen vacancies at the lower MTJ interface, and annealing which can promote M centers over F centers., Comment: 31 pages, 11 figures

To mitigate climate change, our global society is harnessing direct (solar irradiation) and indirect (wind/water flow) sources of renewable electrical power generation. Emerging direct sources include current-producing thermal gradients in thermoelectric materials, while quantum physics-driven processes to convert quantum information into energy have been demonstrated at very low temperatures. The magnetic state of matter, assembled by ordering the electron's quantum spin property, represents a sizeable source of built-in energy. We propose to create a direct source of electrical power at room temperature (RT) by utilizing magnetic energy to harvest thermal fluctuations on paramagnetic (PM) centers. Our spin engine rectifies current fluctuations across the PM centers' spin states according to the electron spin by utilizing so-called 'spinterfaces' with high spin polarization. As a rare experimental event, we demonstrate how this path can generate 0.1nW at room temperature across a 20 micron-wide spintronic device called the magnetic tunnel junction, assembled using commonplace Co, C and MgO materials. The presence of this path in our experiment, which also generates very high spintronic performance, is confirmed by analytical and ab-initio calculations. Device downscaling, and the ability for other materials systems than the spinterface to select a transport spin channel at RT widens opportunities for routine device reproduction. The challenging control over PM centers within the tunnel barrier's nanotransport path may be addressed using oxide- and organic-based nanojunctions. At present densities in MRAM products, this spin engine could lead to 'always-on' areal power densities well beyond that generated by solar irradiation on earth. Further developing this concept can fundamentally alter our energy-driven society's global economic, social and geopolitical constructs.

The organic spinterface describes the spin-polarized properties that develop, due to charge transfer, at the interface between a ferromagnetic metal (FM) and the molecules of an organic semiconductor. Yet, if the latter is also magnetic (e.g. molecular spin chains), the interfacial magnetic coupling can generate complexity within magnetotransport experiments. Also, assembling this interface may degrade the properties of its constituents (e.g. spin crossover or non-sublimable molecules). To circumvent these issues, one can separate the molecular and FM films using a less reactive nonmagnetic metal (NM). Spin-resolved photoemission spectroscopy measurements on the prototypical system Co(001)//Cu/Mnphthalocyanine (MnPc) reveal that the Cu/MnPc spinterface atop ferromagnetic Co is highly spin-polarized at room temperature, up to Cu spacer thicknesses of at least 10 monolayers. Ab-initio theory describes a spin polarization of the topmost Cu layer after molecular hybridization that can be accompanied by magnetic hardening effects. This spinterface's unexpected robustness paves the way for 1) integrating electronically fragile molecules within organic spinterfaces, and 2) manipulating molecular spin chains using the well-documented spin transfer torque properties of the FM/NM bilayer., Comment: 16 pages. Submitted

The quantum mechanical tunnelling process conserves the quantum properties of the particle considered. As applied to solid-state tunnelling (SST), this physical law was verified, within the field of spintronics, regarding the electron spin in early experiments across Ge tunnel barriers, and in the 90s across Al2O3 barriers. The conservation of the quantum parameter of orbital occupancy, as grouped into electronic symmetries, was observed in the '00s across MgO barriers, followed by SrTiO3 (STO). Barrier defects, such as oxygen vacancies, partly conserve this electronic symmetry. In the solid-state, an additional subtlety is the sign of the charge carrier: are holes or electrons involved in transport? We demonstrate that SST across MgO magnetic tunnel junctions (MTJs) with a large resistance-area (RA) product involves holes by examining how shifting the MTJ's Fermi level alters the ensuing barrier heights defined by the barrier's oxygen vacancies. In the process, we consolidate the description of tunnel barrier heights induced by specific oxygen-vacancy induced localized states. Our work opens prospects to understand the concurrent observation of high TMR and spin transfer torque across MgO-based nanopillars., Comment: 8 pages including 2 figures

We report a combined experimental and theoretical study of the Kondo effect in a series of binuclear metal-organic complexes of the form [(Me(hfacac)_2)_2(bpym)]^0, with Me = Nickel (II), Manganese(II), Zinc (II); hfacac = hexafluoroacetylacetonate, and bpym = bipyrimidine, adsorbed on Cu(100) surface. While Kondo-features did not appear in the scanning tunneling spectroscopy spectra of non-magnetic Zn_2, a zero bias resonance was resolved in magnetic Mn_2 and Ni_2 complexes. The case of Ni_2 is particularly interesting as the experiments indicate two adsorption geometries with very different properties. For Ni_2-complexes we have employed density functional theory to further elucidate the situation. Our simulations show that one geometry with relatively large Kondo temperatures T_K ~ 10K can be attributed to distorted Ni_2 complexes, which are chemically bound to the surface via the bipyrimidine unit. The second geometry, we assign to molecular fragmentation: we suggest that the original binuclear molecule decomposes into two pieces, including Ni(hexafluoroacetylacetonate)_2, when brought into contact with the Cu-substrate. For both geometries our calculations support a picture of the (S=1)-type Kondo effect emerging due to open 3d shells of the individual Ni^{2+} ions., Comment: 11 pages, 10 figures, Supplementary Information is attached as a separate PDF file, submitted to Phys. Rev. B

A possible mechanism for the resistive switching observed experimentally in Fe/MgO/V/Fe junctions is presented. Ab initio total energy calculations within the local density approximation and pseudopotential theory shows that by moving the oxygen ions across the MgO/V interface one obtains a metastable state. It is argued that this state can be reached by applying an electric field across the interface. In addition, the ground state and the metastable state show different electric conductances. The latter results are discussed in terms of the changes of the density of states at the Fermi level and the charge transfer at the interface due to the oxygen ion motion.

The design of large-scale electronic circuits that are entirely spintronics-driven requires a current source that is highly spin-polarised at and beyond room temperature, cheap to build, efficient at the nanoscale and straightforward to integrate with semiconductors. Yet despite research within several subfields spanning nearly two decades, this key building block is still lacking. We experimentally and theoretically show how the interface between Co and phthalocyanine molecules constitutes a promising candidate. Spin-polarised direct and inverse photoemission experiments reveal a high degree of spin polarisation at room temperature at this interface. We measured a magnetic moment on the molecules's nitrogen pi orbitals, which substantiates an ab-initio theoretical description of highly spin-polarised charge conduction across the interface due to differing spinterface formation mechanims in each spin channel. We propose, through this example, a recipe to engineer simple organic-inorganic interfaces with remarkable spintronic properties that can endure well above room temperature.

The interface structure of Fe/MgO(100) magnetic tunnel junctions predicted by density functional theory (DFT) depends significantly on the choice of exchange and correlation functional. Bader analysis reveals that structures obtained by relaxing the cell with the local spin-density approximation (LSDA) display a different charge transfer than those relaxed with the generalized gradient approximation (GGA). As a consequence, the electronic transport is found to be extremely sensitive to the interface structure. In particular, the conductance for the LSDA-relaxed geometry is about one order of magnitude smaller than that of the GGA-relaxed one. The high sensitivity of the electronic current to the details of the interface might explain the discrepancy between the experimental and calculated values of magnetoresistance., Comment: Submitted to PRL, 5 figures

A detailed theoretical study on the electronic structure and magnetic properties of half-metallic ferromagnet CrO$_2$ was carried out by means of relativistic full-potential linear muffin-tin orbital method within the generalized gradient approximation (GGA) to the exchange correlation potential. Our calculation favours the [001] magnetization axis to be the easy axis of magnetization when compared to the [100] axis which is in agreement with the experiments. The calculated spin and orbital magnetic moments of Cr agrees well with the experimental and other theoretical works. The Cr L$_{2,3}$ x-ray absorption and x-ray magnetic circular dichroism (XMCD) spectra were calculated for both the quantization axis and compared with the experiment. In addition the oxygen K edge and XMCD spectra were also calculated which compares well with the experiments. The XMCD sum rules were used to compute the spin and orbital magnetic moments and results agree quite well with the direct calculation.

The calculated quasiparticle band structure of bulk hexagonal boron nitride using the all-electron GW approximation shows that this compound is an indirect-band-gap semiconductor. The solution of the Bethe-Salpeter equation for the electron-hole two-particle Green function has been used to compute its optical spectra and the results are found in excellent agreement with available experimental data. A detailed analysis is made for the excitonic structures within the band gap and found that the excitons belong to the Frenkel class and are tightly confined within the layers. The calculated exciton binding energy is much larger than that obtained by Watanabe {\it et al} using a Wannier model to interpret their experimental results and assuming that h-BN is a direct-band-gap semiconductor., Comment: 4 pages, 3 figures

The quasiparticle decays due to electron-electron interaction in silicon are studied by means of first-principles all-electron GW approximation. The spectral function as well as the dominant relaxation mechanisms giving rise to the finite life time of quasiparticles are analyzed. It is then shown that these life times and quasiparticle energies can be used to compute the complex dielectric function including many-body effects without resorting to empirical broadening to mimic the decay of excited states. This method is applied for the computation of the electron energy loss spectrum of silicon. The location and line shape of the plasmon peak are discussed in detail., Comment: 4 pages, 3 figures, submitted to PRL

A pressure-induced simultaneous metal-insulator transition (MIT) and structural-phase transformation in lithium hydride with about 1% volume collapse has been predicted by means of the local density approximation (LDA) in conjunction with an all-electron GW approximation method. The LDA wrongly predicts that the MIT occurs before the structural phase transition. As a byproduct, it is shown that only the use of the generalized-gradient approximation together with the zero-point vibration produces an equilibrium lattice parameter, bulk modulus, and an equation of state that are in excellent agreement with experimental results., Comment: 7 pages, 4 figures, submitted to Europhysics Letters

A new implementation of the GW approximation (GWA) based on the all-electron Projector-Augmented-Wave method (PAW) is presented, where the screened Coulomb interaction is computed within the Random Phase Approximation (RPA) instead of the plasmon-pole model. Two different ways of computing the self-energy are reported. The method is used successfully to determine the quasiparticle energies of six semiconducting or insulating materials: Si, SiC, AlAs, InAs, NaH and KH. To illustrate the novelty of the method the real and imaginary part of the frequency-dependent self-energy together with the spectral function of silicon are computed. Finally, the GWA results are compared with other calculations, highlighting that all-electron GWA results can differ markedly from those based on pseudopotential approaches., Comment: 11pages,3figures, submitted to PRB

First principles calculations of the magnetic properties and the magneto-optical Kerr effect (MOKE) of iron thin films epitaxially grown on the [001] surface of paramagnetic metals: copper, silver, gold, palladium, and platinum are presented. The role of hybridization with the substrate is investigated and it is shown how the relaxation effects influence the complex Kerr angle. The results are obtained by means of the relativistic full-potential linear muffin-tin method, and the film is modeled using a slab geometry within a supercell technique., Comment: 4 pages, 3 colour figures

The so-called local density approximation plus the multi-orbital mean-field Hubbard model (LDA+U) has been implemented within the all-electron projector augmented-wave method (PAW), and then used to compute the insulating antiferromagnetic ground state of NiO and its optical properties. The electronic and optical properties have been investigated as a function of the Coulomb repulsion parameter U. We find that the value obtained from constrained LDA (U=8 eV) is not the best possible choice, whereas an intermediate value (U=5 eV) reproduces the experimental magnetic moment and optical properties satisfactorily. At intermediate U, the nature of the band gap is a mixture of charge transfer and Mott-Hubbard type, and becomes almost purely of the charge-transfer type at higher values of U. This is due to the enhancement of the oxygen 2p states near the top of the valence states with increasing U value., Comment: 23 pages, 6 figures, submitted to Phys. Rev. B

We have performed a theoretical study of the magnetic circular dichroism in the x-ray absorption spectra (XMCD) of the equiatomic CoPt and FePt ordered alloys as a function of the spin quantization axis. We found that the magnetization axis is along the [001] direction and the magneto-crystalline anisotropy energy (MCA) for the FePt compound is twice as large as that of the CoPt compound in agreement with experiment. The band structure and the total density of states confirm that all electronic states contribute to the MCA, and not just the states at the vicinity of the Fermi level. The orbital magnetic moments decrease with respect to the angle between the [001] axis and the spin quantization axis, and are much larger for the CoPt compound. We show that the orbital moment anisotropy is reflected in the XMCD signal., Comment: 19 pages, 11 figure submitted in Physical Review B

The most popular electronic structure method, the linear muffin-tin orbital method (LMTO), in its full-potential (FP) and relativistic forms has been extended to calculate the spectroscopic properties of materials form first principles, i.e, optical spectra, x-ray magnetic circular dichroism (XMCD) and magneto-optical kerr effect (MOKE). The paper describes an overview of the FP-LMTO basis set and the calculation of the momentum matrix elements. Some applications concerning the computation of optical properties of semiconductors and XMCD spectra of transition metal alloys are reviewed., Comment: 21 pages, 6 figures, Workshop on the TB-LMTO method, Monastery of Mont St. Odile, October 4-5, 1998

We have implemented the so called GW approximation (GWA) based on an all-electron full-potential Projector Augmented Wave (PAW) method. For the screening of the Coulomb interaction W we tested three different plasmon-pole dielectric function models, and showed that the accuracy of the quasiparticle energies is not sensitive to the the details of these models. We have then applied this new method to compute the quasiparticle band structure of some small, medium and large-band-gap semiconductors: Si, GaAs, AlAs, InP, SiMg$_2$, C and (insulator) LiCl. A special attention was devoted to the convergence of the self-energy with respect to both the {\bf k}-points in the Brillouin zone and to the number of reciprocal space $\bf G$-vectors. The most important result is that although the all-electron GWA improves considerably the quasiparticle band structure of semiconductors, it does not always provide the correct energy band gaps as originally claimed by GWA pseudopotential type of calculations. We argue that the decoupling between the valence and core electrons is a problem, and is some what hidden in a pseudopotential type of approach., Comment: 49 pages, 5 figures

We used our previously implemented GW approximation (GWA) based on the all-electron full-potential projector augmented wave (PAW) method to study the optical properties of small, medium and large-band-gap semiconductors: Si, GaAs, AlAs, InP, Mg$_2$Si, C, and LiCl. The aim being to study the size of both local-field (LF) and the quasi-particle (QP) corrections to the calculated dielectric function obtained using the local density approximation (LDA). We found that while the QP corrections tend to align the calculated structures in the optical spectra with their experimental counterparts, the LF effects don't change these peak positions but systematically reduce the intensities of the so called $E_1$ and $E_2$ structures in all the optical spectra. The reduction of the intensity of the $E_1$ peak worsen the agreement with experiment while that of $E_2$ improves it. We then show that the local-field correction improves considerably the calculated static dielectric constants of all studied semiconductors. Because the static dielectric constant is a ground state property, the remaining discrepancy with experiment should be attributed to the the LDA itself. On the other hand, as expected, the calculation of the static dielectric constant using the GW quasiparticle energies and including the LF effects is underestimated for all the semiconductors. The excitonic effects should then correct for this discrepancy with experiment., Comment: 24 pages, 12 figures

The X-ray magnetic circular dichroism (XMCD) has been measured at the Co K edge in Co-hcp and R-Co compounds (R=La, Tb, Dy). The structure of the experimental XMCD spectra in the near-edge region has been observed to be highly sensitive to the magnetic environment of the absorbing site. Calculations of the XMCD have been carried out at the Co K edge in Co metal, LaCo$_5$ and TbCo$_5$ within the multiple-scattering framework including the spin-orbit coupling. In the three systems, the XMCD spectra in the near-edge region are well reproduced. The possibility to separate and quantitatively estimate the local effects from those due to the neighboring atoms in the XMCD cross section makes possible a more physical understanding of the spectra. The present results emphasize the major role played by the $d$ states of the Tb ions in the XMCD spectrum at the Co K edge in the TbCo$_5$ compound., Comment: 34 pages, revtex, 10 eps figures included with epsf, after referee review

An implementation of the multiple-scattering approach to x-ray magnetic circular dichroism (XMCD) in K-edge x-ray absorption spectroscopy is presented. The convergence problems due to the cluster size and the relativistic corrections are solved using an expansion of the Dirac Green function for complex energies up to the second order in 1/$c$. The Fermi energy is dealt with via a complex plane integration. Numerical methods used to obtain the semi-relativistic Green function in the whole complex plane are explained. We present a calculation of the magnetic circular dichroism at the K-edge of bcc-iron including the core hole effect. A good agreement is found at high energy. The physical origins of the XMCD spectrum near the edge and far from the edge are analyzed. The influence of the core hole, the possibility of a multiple-scattering expansion and the relation of XMCD with the spin-polarized density of states are discussed. A simple interpretation of XMCD at the K-edge is presented in terms of a rigid-band model., Comment: 38 RevTex pages and 18 figs in a compressed and uufiled tar file; Phys. Rev. B (in press)

We have calculated the band-$f$ hybridizations for Ce$_x$La$_{1-x}$M$_3$ compounds ($x=1$ and $x\rightarrow 0$; M=Pb, In, Sn, Pd) within the local density approximation and fed this into a non-crossing approximation for the Anderson impurity model applied to both dilute and concentrated limits. Our calculations produce crystalline electric field splittings and Kondo temperatures with trends in good agreement with experiment and demonstrate the need for detailed electronic structure information on hybridization to describe the diverse behaviors of these Ce compounds., Comment: 13 pages(RevTeX), 3 Postscript figures

The macroscopic dielectric function in the random-phase-approximation without local field effect has been implemented using the local density approximation with an all electron, full-potential linear muffin-tin orbital basis-set. This method is used to investigate the optical properties of the semiconductors Si, Ge, and GaAs under hydrostatic pressure. The pressure dependence of the effective dielectric function is compared to the experimental data of Go\~ni and coworkers, and an excellent agreement is found when the so called ``scissors-operator'' shift (SOS) is used to account for the correct band gap at $\Gamma$. The effect of the $3d$ semi-core states in the interband transitions hardly changes the static dielectric function, $\epsilon_\infty$; however, their contribution to the intensity of absorption for higher photon energies is substantial. The spin-orbit coupling has a significant effect on $\epsilon_\infty$ of Ge and GaAs, but not of Si. The $E_1$ peak in the dynamical dielectric function is strongly underestimated for Si, but only slightly for Ge and GaAs, suggesting that excitonic effects might be important only for Si., Comment: 29 RevTex pages and 12 figs; in press in Physical Review B

A parameter-free, mean-field, multi-orbital Hubbard model with nonspherical Coulomb and exchange interactions, implemented around all-electron local-density approximation (LDA) calculations, correctly predicts the band-gap energy, the absence of dimerization, and the antiferromagnetic ground state of halogen-bridged linear-chain Ni compounds. This approach also reproduces the insulating ground state and dimerization in PtX linear-chain compounds in agreement with experiment and previous calculations. Three "ps" figures are included at the end of the RevTex file and compressed using uufiles., Comment: 11 RevTex pages and three ps figures. Paper accepted by PRB Rapid Comm

This is a reply to J. T. Gammel's Comment (9404047) on Tuning of the CDW in MX Chains. We show that while the harmonic elastic energy can fit a small region around zero dimerization, it is insufficient to treat the large amplitude CDW of the MX systems which was the main physics of our Letter (Phys. Rev. Lett. {\bf 71}, 1415 (1993)). We also stress that \underline{anharmonic} elastic potentials are {\it essential} to explain the charge-density-wave systematics of an entire class of MX material., Comment: RevTex + 2 uuencoded postscript figures

Local-density-approximation calculations are used to show that the metal-metal distance along the chains controls the charge-density wave (CDW) in halogen-bridged transition-metal linear-chain (MX) compounds. The strength of the CDW can be understood in terms of a two band Su-Schrieffer-Heeger model if a hard-core ion-ion repulsion potential is also added. We predict a second-order phase transition from an insulating to a semi-metallic ground state and explain trends in dimerization, bond-length ratios, band gaps, and Raman breathing modes in terms of the metal-metal distance. Three "ps" figures are included at the end of the file., Comment: 13 pages