The relation between thermodynamically stable and electronic structure preparation is one of the fundamental questions in physics, geophysics and chemistry. Since the discovery of the novel structure, this has remained as one of the main questions regarding the very foundation of elemental metals. Needless to say this has also bearings on extreme conditions physics, where again the relation between structure and performance is of direct interest. Crystal structures have been mainly at ambient conditions, i.e. at room temperature and ambient pressure. Nevertheless it was realized early that there is also a fundamental relation between volume and structure, and that this dependence could be most fruitfully studied by means of high pressure experimental techniques. From a theoretical point of view this is an ideal type of experiment, since only the volume is changed, which is a very clean variation of the external conditions. Therefore, at least in principle, the theoretical approach remains the same irrespective of the high pressure loading of the experimental sample. Theoretical modeling is needed to explain the measured data on the pressure volume relationships in crystal structures. Among those physical properties manifested itself under high pressure, superconductivity has emerged as a prominent property affected by pressure. Several candidate structure of materials are explored by ab initio random structure searching (AIRSS). This has been carried out in combination with density functional theory (DFT). The remarkable solution of AIRSS is possible to expect a superconductivity under high pressure. This chapter provide a systematically review of the structural prediction and superconductivity in elemental metals, i.e. lithium, strontium, scandium, arsenic.
- ab initio random structure searching
- density functional theory
It is a long time since Kohn and Sham pave the way to the self-consistent equation, based on the exchange and correlation effects in 1965, leading the Kohn–Sham (KS) Equation . This has ignited the success of quantum physics and chemistry, specifically many-body problem, owing to the KS equation can be utilized for the ground state energy. Briefly stated, the KS equation formalism of density functional theory (DFT) described the motion of electron nuclei, which separated to be two part: the energy of electron
Regarding thermodynamic properties, the Gibbs free energy is considered for the static crystal energy of materials; however, the KS equation formalism of DFT carried out at a temperature of 0 K. The Gibbs free energy therefore reduced to the Enthalpy. This, appearing at first glance to be high potential for high-pressure physics, is actually demonstrated the importance of superconductivity. According to the aforementioned theoretical findings by the KS equation formalism of DFT, resulting the exchange and correlation effects
The extensive studies of electronic structure were initiated chiefly by the KS equation formalism of DFT. In principle, one should note the quasiparticle eigenvalues of occupied states is useful for achieving the electronic band structure, density of sates, phonon dispersion. It is also interesting to note the DFT used mainly strong sides for prediction the metallicity, leading to the prediction of superconducting transition temperature. For considered the superconductivity, the PBE formalism of GGA for exchange-correlation energy is suitable for interpret the metallicity. This implied that the reliable theoretical study has quite a predictive potential, moreover, the GGA-PBE for the exchange-correlation energy give an accurate description of dynamical stability of crystal structure. One of the well-known Bardeen-Cooper-Schrieffer (BCS) theory  were already discussed phonon mediated superconductivity, leading to the way to vast both experimental and theoretical studies on high-pressure research. At this stage, using the KS equation formalism of DFT with the GGA-PBE for the exchange-correlation energy were used to have unique features of phonon mediated superconductivity, showing towards the evidence of superconducting materials as well.
There is alternative way to use the KS equation formalism of DFT with the GGA-PBE. It is well known to
High pressure physics is important for structural phase transitions in materials [8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18]. Regarding a crystal structure of materials under high pressure, it can enhance electronic properties of materials [19, 20, 21]. Nowadays, superconductivity is one of the most charming in physical properties. Many materials were predicted to be a superconducting transition temperature (
As mentioned above, a structural prediction is a key factor for achieving a
A curious aspect of a
According to the aforementioned superconductor findings, the characteristic of electronic structure is often attributed to the
Regarding superconductivity in the metals [12, 14, 17, 41], a lattice dynamic is a key factor for consideration a stable structure. In practice, we can achieve the superconducting structure through electron–phonon coupling (EPC) [12, 14, 17, 41]. For example, recent work on LaH10 has shown that the quantum effect is important for the stabilization and destabilization . In fact, both thermodynamically and dynamically structures have to consistent. Generally, the solution of dynamically structure is a harmonic phonon but the case of LaH10 shown that it displayed an anharmonic phonon. This because the EPC exhibited the destabilized structure. Hence, it is worth to note that Sr. is possible to be an anharmonic phonon in the Sr-III structure (the
In considered in the present work, we performed the first-principles calculations, based on the density functional theory, to examine the thermodynamic stability as a function of pressure. The static crystal energy of materials was considered at a temperature of 0 K. The calculation details of stable structure were determined by neglecting the entropy contributions. This is because the calculations were carried out at 0 K, indicating that the ground-state energy can confirm phase stability. Here, the KS equation formalism of DFT with the GGA-PBE for the exchange-correlation energy were used for Li, Sr., Sc, and As. For further details of the energy cutoff for plane waves and the Monkhorst–Pack k-point mesh as well as the DFT software have been described extensively in Refs. [10, 12, 13, 14]. Our works used the AIRSS technique, based on the density functional theory, to predict the novel structure. Following the AIRSS method, we calculated the enthalpies of the phases at any pressure using the simple linear approximation . For each relaxed structure, the structures were simulated to be a non-symmetry and randomly placed in atomic position. During the calculations of the structures, it started to relax from bias until it reaches unbias. The shape is generating by shaking within a reasonable pressure range. It led to higher-symmetry space groups obtained in a search. The AIRSS technique is the approach in the local minima by giving the lowest enthalpy. We have studied the phonon mediated superconductivity by using isotropic Eliashberg theory, as implemented in the quantum espresso (QE) [54, 55]. Following the result of isotropic Eliashberg theory, the Allen-Dynes modify McMillan Equation  was used to estimated the superconducting transition temperature.
3. Result and discussion
According to the aforementioned in the introduction, high pressure physics is useful in achieving a novel structure and superconductivity [12, 13, 14, 17, 33, 57, 58, 59]. Li is one of the challenging to find a novel structure [43, 60, 61, 62, 63]. Since it is interesting that there is complex structures were discovered in alkali metal, i.e. sodium (Na) , potassium (K) [65, 66, 67, 68], and rubidium (Rb) [69, 70]. Therefore, Li might be expected to possible to be a complex structure at high pressure. For the transitions sequence of Li, we found that the Im-3 m structure transformed into the Fm-3 m structure at pressure 8 GPa. Next, the Fm-3 m structure transformed into the R-3 m structure at pressure 39 GPa. With increasing pressure, the R-3 m structure transformed into the I-43d structure at pressure 44 GPa, then it transformed into C2mb at pressure 73 GPa. On further compression, the C2mb structure transformed into the C2cb structure at 80 GPa. Finally, it transformed into Cmca 120 GPa. It is interesting that there is no found the incommensurate host-guest structure at any pressure among such sequence [43, 60, 61, 62, 63, 71].
Li was observed by optical spectroscopic through diamond anvil cells (DAC) . The solution of the experimental study revealed that there is unknown phase above 50 GPa. Moreover, the characteristic of the high frequency band, i.e. Li-Li vibration, can interpret to be an incommensurate host-guest structure. The commensurate host-guest structure is defined by the different the number of the guest atoms in channels in along the c axis of the host structure, referring to the commensurate value cH/cG, also known as
As mentioned above, the unknown structure can be identified by a random search techniques. The random search technique is the high performance for the prediction of the materials. For elemental Li, the
The existence of the incommensurate host-guest structure can be considered from the ELF calculation. As a possible cause of this, one might think of there is the s-p
Structural phase transitions in alkaline earth metal under high pressure is interested among the periodic table. Nowadays, there are several works reported a transition sequences [33, 37, 40, 47, 58]. It is interesting to consider that a transition sequences of Ca and Sr. are similar. Ca shown that it exhibited stable structure at high temperature and low pressure through compression [58, 73]. The experimental observations  and the theoretical study [58, 73] reported that the simple cubic (sc) structure is stable at room temperature. At this point, the solution of theoretical study revealed that the sc structure is stable by performing a molecular dynamics (MD) calculation . This is because the MD calculation can include a temperature via
In 2009, Ca was reported a novel structure at high pressure that it is the
It is interesting to note that structural phase transitions in Sr. [33, 34, 35, 36, 37, 47]. The remarkable studies revealed that there are discrepancy between the experimental observations [34, 35, 36] and the theoretical studies [33, 37, 47]. The experimental observations were reported that the Fm-3 m structure transformed into the Im-3 m structure, then it transformed into the
In 2012, Sr. was predicted that there is a candidate structure . The relative enthalpy of Sr. was reported that the Cmcm structure is thermodynamically favored over the Fm-3 m structure, the Im-3 m structure, and the
However, the discrepancy between the experimental observations and the theoretical studies were not solved yet. In 2015, the discrepancies in transition sequence between the experimental and theoretical works was explained by Tsuppayakorn-aek et al. . Regarding transition sequence in Sr., it was investigated by the hybrid exchange-correlation functional, i.e. screened exchange local density approximation (sX-LDA) [78, 79, 80]. The stable structure of the
The remarkable result of the Ref.  shown that the
Regarding the superconductor in the
Structural prediction at high pressure is suitable for identifying unknown structure. Scandium (Sc) is one of d-transition metal, showing that there is an unknown structure (Sc-III) at high pressure . The transition sequences is found that the hcp structure transformed into the host-guest structure [83, 84]. The host-guest structure is thermodynamically stable up to 70 GPa . It is interesting to note that what is the unknown structure beyond the host-guest structure above 70 GPa. In 2018, Tsuppayakorn-aek et al.  was identified the unknown structure by
Regarding superconductor of the P41212 structure, it was found to be the metallicity by considering density of state (DOS), leading to investigate the
Tsuppayakorn-aek et al.  was revealed in that the
Sc is one of the group-IIIB element was shown that structural phase transformation displayed the complex to simple transition. Also, it promoted the superconducting temperature transition to be 8.36 K at 110 GPa, which it is in good agreement with the experimental observation.
The group-V element is one of central interest in superconductor. It is interesting to note that arsenic (As), antimony (Sb), and bismuth (Bi) share the remarkable similarity of structural and property [87, 88]. Structural of the group-V element was reported that As-III, Sb-IV, and Bi-III are the incommensurate host-guest structure [89, 90, 91, 92]. Also, it is worth to note that the Im-3 m structure is thermodynamically stable favored over the incommensurate structure [87, 88].
Tsuppayakorn-aek et al.  was explored the high-pressure phase in As. This because it is interesting to find the high-pressure phase, leading to go beyond the Im-3 m structure. The structural prediction was investigated up to 300 GPa. The predicted structure was shown that the body-centered tetragonal (bct) structure with space group I41/acd to be the stable structure at high pressure. The I41/acd structure is energetically and dynamically stable. Also, it is thermodynamically favored over the host-guest structure. The I41/acd structure displayed that it compete with the Im-3 m structure. Moreover, The I41/acd structure and the Im-3 m structure are very closed in enthalpy from 100 to 300 GPa. Also, the I41/acd structure is sub-spacegroup of the the Im-3 m structure. It is possible that the I41/acd structure is coexistence phase with the Im-3 m structure.
Here, the I41/acd structure was discovered to be the metallicity, indicating that it is superconducting phase. As already mentioned, the I41/acd structure and the Im-3 m structure are wonderfully closed in enthalpy. It is interesting to investigate the superconducting phase of both of them. An important and a fundamental of the spectral function led to consider superconductor. In fact, the spectral function is associated with the electron–phonon coupling (EPC). The I41/acd structure was regarded in superconductor, it was found that the estimated
The remarkable results of the
Now, it is worth to note that the I41/acd structure hold the metallic state at 300 GPa. Tsuppayakorn-aek et al.  suggested that the I41/acd structure is not favored superconductor above 300 GPa, indicating that it is likely to transform into a normal metallic state (Figure 9). As a possible cause of this, one might think of phase transformation . Moreover, the EPC of the I41/acd structure is very poor characterized by compression. At this point, it is possible that a novel phase might occur above 300 GPa.
This project is funded by National Research Council of Thailand (NRCT): (NRCT5-RSA63001-04). This research is partially funded by Chulalongkorn University; Grant for Research. P.T. acknowledge support from the Second Century Fund (C2F), Chulalongkorn University.
Conflict of interest
The authors declare no conflict of interest.