We explore the unknown structure of phosphorus in phase IV (P-IV phase) based on first-principles calculations using the metadynamics simulation method. Starting from the simple cubic structure, we find a new modulated structure of the monoclinic lattice. The modulation is crucial to the stability of the structure. Through refining the structure further by changing the modulation period, we find the structure whose x-ray powder diffraction pattern is in best agreement with the experimental pattern. We expect that the modulation period of the structure in the P-IV phase is very close to that found in this study and probably incommensurate. DOI: 10.1103/PhysRevLett.96.095502 PACS numbers: 61.50.Ah, 62.50.+p, 64.70.Kb Recent progress in high-pressure physics has enhanced our recognition of a wide variety of crystal structures. Development of high-pressure techniques has also enabled the identification of structures that are stabilized only in a narrow pressure range. Interesting structures were found unexpectedly through high-pressure experiments. For instance, modulated structures are often found in the highpressure phases of elements. Lattice modulations have been found in group Vb elements, including As, Sb, and Bi Scarcity of experimental ultrahigh-pressure data restricts high-pressure studies. Thus, researchers often encounter difficulties in the identification of a crystal structure on the basis of experimental data alone. A theoretical approach provides additional information on the same problem. First-principles theory for determining crystal structures is believed to be sufficiently accurate. However, the limitations of computational resources sometimes impede full structure searches.We will focus on the case of phase IV of the phosphorus (P-IV) phase. Observation of the P-IV phase was first reported by Akahama et al. [8] in 1999. In the sequence of pressure-induced transformations, the simple cubic (sc) phase (P-III) appears at 10 GPa at low temperature. Akahama et al. [8] reported the appearance of a simple hexagonal (sh) phase, i.e., the P-V phase, which stabilizes above 137 GPa, and an intermediate phase, i.e., the P-IV phase, between sc and sh on the basis of x-ray diffraction data. At even higher pressures, the bcc structure (P-VI) has been theoretically predicted [9] and later identified in an experiment at 262 GPa [10]. The structure of phase IV, however, has not been identified experimentally. Ordinary Rietveld analysis based on a knowledge of the monoclinic symmetry alone has not been successful, presumably owing to the complexity of the lattice. Thus, we must guess the crystal structure or a pseudocrystal.Several structures have been tested as candidate structures for P-IV. Ahuja considered a structure of space group Imma [11]. Ehlers and Christensen studied relative stability of the Ba-IV structure against sc and sh in the pressure range from 100 to 200 GPa [12]. The Ba-IV structure is a kind of modulated structure. Despite these extensive studies, the structure of P-IV remains unidentifi...

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We have explored the stable phases of solid hydrogen by calculating band-theoretical energies in the local density approximation, for the system of oriented molecules at Mbar pressures and at zero temperature. It is shown that the hexagonal-close-packed lattice persists up to -300 GPa with a structure of space group Pca2\, which has wide band gaps. The subsequent phase is still molecular with a rutile structure with c/a-0.9 which must be conducting. The molecular phase terminates at -600 GPa, where the atomic phase with a planar structure appears. PACS numbers: 62.50.+p, 64.70.Kb, 7l.30.+h Remarkable studies are in progress for clarifying the properties of solid hydrogen at Mbar pressures, with a strong interest shown in the insulator-to-metal (IM) transition [1,2]. In 1988 Hemley and Mao [3] observed a discontinuous shift to lower frequency for the vibron (intramolecular vibration) at -150 GPa (1.5 Mbar). Hemley, Mao, and Shu (HMS) [4] studied the low-frequency rotational and lattice-phonon spectra, concluding that the hexagonal-close-packed (hep) lattice persists above 150 GPa. The new phase is molecular, and likely to be orientationally ordered at low temperature according to Silvera and co-workers [2,5] and others [3]. The nature of the new phase has been controversial. Mao and Hemley [6] proposed that metallization occurs in molecular phases; an IM transition may occur at Mbar pressures through a closing of the gap between the valence and conduction bands [7]. Subsequently Mao, Hemley, and Hanfland (MHH) [8] measured the optical reflectance and predicted the IM transition to occur at 149 GPa by utilizing a Drude model. However, Eggert et al. [9] later provided optical data inconsistent with the Drude model, making MHH's prediction inconclusive. The metallization of hydrogen remains an open question.Theoretically, Barbee, Garcia, Cohen, and Martins (BGCM) [10] studied hep molecular hydrogen oriented along the c axis, by calculating band-theoretical energies in the local density approximation (LDA). BGCM's mhep phase is more stable than the Pa3 structure which was studied in the LDA earlier by Min, Jansen, and Freeman [1!]. The Pa3 structure is known to occur for solid nitrogen (a-N2) in the face-centered-cubic (fee) lattice ( Fig. 1) with molecular axes along body diagonals of the cubic unit cell. BGCM's result was consistent with HMS regarding the persistence of the hep lattice. The m-hep phase must be metallic above 150 GPa according to Chacham and Louie's quasiparticle calculation of band gaps [12]. Very recently, Kaxiras, Broughton, and Hemley (KBH) [13] reported that new hep structures exist with lower energies and with much wider band gaps than the m-hep phase, in the LDA. Unfortunately their search for the lowest-energy structure (LES) was confined to structures of two molecules in a unit cell. More recently Ashcroft [14] suggested a layered structure of four mole-cules in a unit cell as the LES, by a certain reasoning. The LES of the hep lattice remains unsettled.Knowledge of the LES is fundamental fo...

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