We have performed density functional theory (DFT) calculations of iron−porphyrin (FeP) and its complexes with O2, CO, NO, and imidazole (Im). Our fully optimized structures agree well with the available experimental data for synthetic heme models. Comparison with crystallographic data for proteins highlights interesting features of carbon monoxymyoglobin. The diatomic molecule induces a 0.3−0.4 Å displacement of the Fe atom out of the porphyrin nitrogen (Np) plane and a doming of the overall porphyrin ring. The energy of the iron−diatomic bond increases in the order Fe−O2 (9 kcal/mol) < Fe−CO (26 kcal/mol) < Fe−NO (35 kcal/mol). The ground state of FeP(O2) is an open shell singlet. The bent Fe−O2 bond can be formally described as FeIII−O2 -, and it is characterized by the anti-ferromagnetic coupling between one of the d electrons of Fe and one of the π* electrons of O2. FeP(CO) is a closed shell singlet, with a linear Fe−C−O bond. The complex with NO has a doublet ground state and a Fe−NO geometry intermediate between that of FeP(CO) and FeP(O2). The bending of the Fe−(diatomic) angle requires a rather low energy for these three complexes, resulting in large-amplitude oscillations of the ligand even at room temperature. The addition of an imidazole ligand to FeP moves the Fe atom out of the porphyrin plane toward the imidazole and decreases significantly the energy differences among the spin states. Moreover, our calculations underline the potential role of the imidazole ligand in controlling the electronic structure of FeP by changing the out-of-planarity of the Fe atom. The presence of the imidazole increases the strength of the Fe−O2 and Fe−CO bonds (15 and 35 kcal/mol, respectively), but does not affect the energy of the Fe−NO bond, while the resulting FeP(Im)(NO) complex exhibits a longer and weaker Fe−Im bond.

The stability of different phases of the three-dimensional nonrelativistic electron gas is analyzed using stochastic methods. With decreasing density, we observe a continuous transition from the paramagnetic to the ferromagnetic fluid, with an intermediate stability range (20 6 5 # r s # 40 6 5) for the partially spin-polarized liquid. The freezing transition into a ferromagnetic Wigner crystal occurs at r s 65 6 10. We discuss the relative stability of different magnetic structures in the solid phase. [ S0031-9007(99) PACS numbers: 71.10. Ca, 05.30.Fk, 75.10.Lp Ever since the pioneering work of Wigner and Seitz [1] on the cohesive energy of metals, the calculation of the ground state energy of the interacting electron gas became the object of considerable theoretical interest [2]. Indeed, the electron gas provides the simplest model in which nontrivial magnetic structures and electron localization can be realized by varying a single parameter, namely, the average electron density r.In the present paper we investigate the relative stability of various broken symmetry phases of the nonrelativistic three-dimensional electron gas, both fluid and solid, using stochastic methods. We find that the paramagnetic to ferromagnetic (full spin polarization) transition is not first order, but a continuous one, involving partial spin polarization states (weak ferromagnetism) [3]. Moreover we find that the transition to a Wigner crystal occurs at a significantly larger density than the value commonly accepted [3,4] and that near the quantum freezing transition the fcc and bcc crystal phases are nearly degenerate.The jellium model consists of N electrons enclosed in a box of volume V (periodically repeated in space) in the presence of a neutralizing background of positive charge. Two parameters characterize its zero temperature phase diagram, namely, the particle density r N͞V and the spin polarization z jN " 2 N # j͞N, where N "͑#͒ is the number of spin-up(down) electrons (N N " 1 N # ). The system is governed by the Hamiltonian (Hartree a.u.)where r i and p i are the position and linear momentum of particle i, and L is a constant representing the effect of the background. Since we are interested in the macroscopic properties of this model system, the thermodynamic limit (N, V !`, keeping r constant) is to be performed in the end by finite size extrapolation. [4,5] and semianalytic methods [6]. Not surprisingly, the least known regime is the strongly correlated one, for which an early quantum Monte Carlo calculation [4] is still the most authoritative study.To delve into the strong coupling regime we employ the variational (VMC) and diffusion (DMC) quantum Monte Carlo methods. The starting point is provided by a variational wave function of the Jastrow type:where det "͑#͒ ͓w͔ is a spin-up(down) Slater determinant of one-electron orbitals w that are either plane waves (fluid phases) or localized functions (crystal phases). In the equation above, R ͑r 1 , . . . , r N ͒ and S ͑s 1 , . . . , s N ͒ represent the full set of po...