Structural and bonding character of potassium-doped p-terphenyl superconductors

TL;DR

This study uses first-principles calculations to analyze the structural, electronic, and magnetic properties of potassium-doped p-terphenyl superconductors, revealing stable doping levels, ionic bonding, charge transfer effects, and complex band structures related to superconductivity.

Contribution

It provides detailed theoretical insights into the structural and electronic characteristics of K-doped p-terphenyl, clarifying the stability and bonding mechanisms underlying its superconductivity.

Findings

K doping concentration between 2 and 3 is most stable

Strong ionic bonding exists between K atoms and organic molecules

Charge transfer influences magnetic and metallic properties

Abstract

Recently, there is a series of reports by Wang et al. on the superconductivity in K-doped p-terphenyl (KxC18H14) with the transition temperatures range from 7 to 123 Kelvin. Identifying the structural and bonding character is the key to understand the superconducting phases and the related properties. Therefore we carried out an extensive study on the crystal structures with different doping levels and investigate the thermodynamic stability, structural, electronic, and magnetic properties by the first-principles calculations. Our calculated structures capture most features of the experimentally observed X-ray diffraction patterns. The K doping concentration is constrained to within the range of 2 and 3. The obtained formation energy indicates that the system at x = 2.5 is more stable. The strong ionic bonding interaction is found in between K atoms and organic molecules. The charge transfer accounts for the metallic feature of the doped materials. For a small amount of charge transferred, the tilting force between the two successive benzenes drives the system to stabilize at the antiferromagnetic ground state, while the system exhibits non-magnetic behavior with increasing charge transfer. The multiformity of band structures near the Fermi level indicates that the driving force for superconductivity is complicated.

Figures

Tables

Table 1. Table 1: The optimized crystal lattice constants a 𝑎 a , b 𝑏 b , c 𝑐 c , the angle β 𝛽 \beta between two axes and the volume V 𝑉 V of pristine C 18 H 14 comparing with the experimental values.

Method	$a$ (Å)	$b$ (Å)	$c$ (Å)	$\beta$ (∘)	$V$ (Å3)
Expt.111Ref. ref37, .	13.613	5.613	8.106	92	619
Expt.222Ref. ref38, .	13.621	5.613	8.116	92.01	621.1
Expt.333Ref. ref39, .	13.59	5.59	8.08	92.9	613.4
Expt.444Ref. ref40, .	13.58	5.58	8.02	92.10	607.3
Expt.555Ref. ref41, .	13.55	5.63	8.15	92.60	621.1
vdW-DF2	13.569	5.542	7.911	92.8	594.2
LDA	13.215	5.292	7.443	93.57	519.6
GGA	13.596	6.283	8.574	88.89	732.2

Table 2. Table 2: The optimized crystal lattice constants a 𝑎 a , b 𝑏 b , c 𝑐 c , the angle β 𝛽 \beta between two axes, the tilted angle δ 𝛿 \delta between two successive benzene rings with respect to each other and the volume V 𝑉 V for every doping level.

System	Space-group	$a$ (Å)	$b$ (Å)	$c$ (Å)	$\alpha$ (∘)	$\beta$ (∘)	$\gamma$ (∘)	$\delta$ (∘)	$V$ (Å3)
K1C18H14	$P{2}_1$	13.500	6.863	7.181	90	83.12	90	9.5-10.6	660.6
K1.5C18H14	$P1$	7.110	7.274	14.743	89.76	64.56	90.02	17.2-20.3	688.6
K2C18H14	$P{2}_1$	14.001	7.032	7.151	90	75.54	90	0.2-0.6	681.8
K2.5C18H14	$P1$	14.585	6.278	9.058	99.25	73.54	96.77	1.1-2.5	782.7
K3C18H14	$P{2}_1/c$	14.503	5.463	10.243	90	76.13	90	0	787.8

Equations

$$E_{\text{f}}=E_{\text{doped}}-E_{\text{pristine}}-x{\mu }_{\text{K}}^{\text{bulk}}-x[{\mu }_{\text{K}}-{\mu }_{\text{K}}^{\text{bulk}}]$$

Full text

I Introduction

Superconducting materials have been a hot research topic in physics and materials science due to their important application values in energy, information, quantum devices and other advanced technologies. Researchers have been devoted to the design and synthesis of new superconducting materials, the understanding of superconducting mechanism and the exploration of superconductors with higher transition temperature ($T_{c}$). In 2010, the superconductivity of $T_{c}\sim 18$ Kelvin was discovered in potassium (K) metal doped piceneref1 , which opens a new avenue in the quest for organic hydrocarbon superconductors. Subsequently, the superconductivity has also observed in alkali, alkaline-earth metals and rare-earth elements doped phenanthreneref2 ; ref3 ; ref4 ; ref5 , chryseneref5 , phenaceneref6 , coroneneref7 , phenaceneref6 and 1,2;8,9-dibenzopentaceneref8 , respectively. Especially, using density functional theory and Eliashberg’s theory of superconductivity, we have predicted K-doped benzene (K2C6H6) to be superconductive with the $T_{c}$ around 6.2 Kelvin, and proposed that all hydrocarbons should show $T_{c}$ in a similar temperature range of $5<T_{c}<7$ Kelvin under conventional conditionsref9 . The results greatly increase the understanding of the superconductivity of polycyclic aromatic hydrocarbons (PAHs).

So far the highest $T_{c}$ reached is 33.1 Kelvin in PAH superconductors, which was obtained in K-doped 1,2;8,9-dibenzopentaceneref8 . However, previous theoretical studies showed that PAH superconductors usually exhibit the antiferromagnetic (AFM) ground stateref10 ; ref11 ; ref12 ; ref13 and exist the strong electronic correlation effectsref13 ; ref14 ; ref15 ; ref16 ; ref17 ; ref18 , indicating the superconducting mechanism is complicated in aromatic hydrocarbons. Our theoretical predictions have argued that electronic correlationsref9 or pressureref19 could enhance high $T_{c}$ in aromatic hydrocarbons. Hence, organic based compounds are candidates of high temperature or room temperature superconductors, since the interaction of electrons with much higher excitation energy than the phonon energy can result in a substantially higher $T_{c}$ in these low dimensional materialsref20 ; ref21 . Thus, the higher $T_{c}$ can be expected in this kind of aromatic hydrocarbons.

Recently, p-terphenyl (C18H14), a hydrocarbon compound containing three benzene rings connected by C-C bonding, draws a lot of attention. Different from the feature of sharing armchair edge in PAHs such as phenanthrene, chrysene, picene, coronene and 1,2;8,9-dibenzopentacene, benzene rings are connected by the single C-C bond in the p-terphenyl molecule. Namely, p-terphenyl is a non-polycyclic aromatic hydrocarbon. With regard to the study of superconductivity of this system, Wang et al. claimed the superconductivity of 7.2 Kelvin in the synthesized KxC18H14ref22 . Later, Wang et al. claimed to observe a higher $T_{c}$ of 43 Kelvinref23 and even 123 Kelvinref24 in the K-doped p-terphenyl. They also ruled out the possibilities of the formation of K-doped C60 and graphite as suggested previously ref25 . By using high resolution photoemission spectroscopy on potassium surface-doped p-terphenyl crystals, Li et al. presented the spectroscopic evidence for pairing gaps at the surfaces of these materials, with the gaps persisting to 60 K or aboveref26 . Furthermore, Liu et al. observed the superconductivity like transition at about 125 Kelvin in their fabricated potassium doped p-terphenyl with the help of magnetization measurementsref27 . These subsequent works greatly promote the study to superconductivity of the material. However, the doping level and superconducting phases with different $T_{c}$ have not been determined yet, not to mention the desired pairing mechanism. So identifying the structures and chemical bonds is crucial to the understanding of the superconducting phases as well as superconductivity, which is the focus of the current study.

p-Terphenyl has twisting degrees of freedom around the long molecular axis, which will result in complicated situations when K atoms are doped into p-terphenyl crystal. It has been well known that crystalized p-terphenyl exhibits two phases with the variation of temperature of $P2_{1}/c$ symmetry at room temperature and $P\bar{1}$ symmetry below 193 Kelvinref28 ; ref29 . In addition, the pressure also drives a transition from $C_{2}$ to $D_{2h}$ symmetry around 1.3 GParef30 . In this work, we will investigate the K doping effects on structural, electronic, and magnetic properties in p-terphenyl at ambient pressure by the first-principles calculations. The obtained structures will be compared with experiments. The details for the structural and bonding features will be provided. These results are helpful for the determination of the doping level and thermaldynamically stable phases as well as the understanding of the charge transfer process and mechanism in these newly discovered superconductors.

II Method

To study the structural and electronic properties of KxC18H14, we employed the Vienna ab initio simulation package (VASP) ref31 ; ref32 based on the projector augmented wave method. For the plane-wave basis-set expansion, an energy cutoff of 600 eV was adopted. The Monkhorst-Pack k-point grids are generated according to the specified k-point separation of 0.02 Å*-1* and the convergence thresholds are set as $10^{-6}$ eV in energy and $10^{-3}$ eV/Å in force. The generalized gradient form (GGA) of the exchange-correlation functional (Perdew-Burke-Ernzerh of 96, PBE) was adoptedref33 . And considering the non-local interaction, we has added the correction of van der Waals (vdW) in version of vdW-DF2 in this calculationref34 . The necessity of vdW-DF2 functional has been confirmed by our previous studiesref35 ; ref36 .

III Results

III.1 Determining functional

Starting from the pristine C18H14, we firstly optimized the crystal lattice parameters of solid C18H14 with the $P2_{1}/c$ symmetry to test the feasibility of vdW-DF2 functional. The obtained crystal lattice parameters from vdW-DF2 functional are $a=13.569$ Å, $b=5.542$ Å, $c=7.911$ Å and the angle $\beta=92.8^{\circ}$, respectively. Seen from the crystal lattice parameters listed in Table I, the vdW-DF2 functional products the lattice constants are in good agreement with experimental ones, though the small distinguish exists among those reported experimental observationsref37 ; ref38 ; ref39 ; ref40 ; ref41 . The error is respectively controlled within 2.5% for the lattice constant and 4% for the volume. But GGA and local density approximation (LDA)ref42 functional respectively extremely overestimates and underestimates the lattice constants (unit volume). The result indicates that the non local interaction should not be ignored in this aromatic hydrocarbon. As shown in Fig. 1, the calculated XRD spectrum of solid C18H14 shown in Fig. 1 fits the experiment done by Wang et al.ref22 . Additionally, the average value of carbon-carbon bond lengths within the rings is about 1.40 Å and those between rings are about 1.49 Å, which are also consistent with experimental valuesref29 .

III.2 Structure of KxC18H14

Within the framework of the vdW-DF2 functional, we simulated K-doped p-terphenyl, and firstly considered three possible concentrations of $x=$ 1, 2 and 3 in KxC18H14. The total energy calculation indicates that the doping results in the phase transition of crystal structure. Both K1C18H14 and K2C18H14 are stabilized at $P2_{1}$ symmetry instead of $P2_{1}/c$. But K3C18H14 can exist in form of $P2_{1}/c$ symmetry. The crystal lattice parameters at three doping levels are summarized in Table II. We find that the variation of crystal lattice parameters is complicated after doping. The intercalation of K atoms leads to the obvious expansion in $b$ direction and the big contraction in $c$ direction in K1C18H14 and K2C18H14. K3C18H14 is abnormal since it expands in $a$ and $c$ directions while contracts in the $b$ direction. However, the doping makes the system volume increase. Figure 2 clearly shows the characteristics of KxC18H14 viewed from different directions. For K1C18H14, as shown in Fig. 2(a), the herringbone structure is formed and K atom is between two organic molecular layers when viewing along the $a$ direction, similar to K-doped piceneref1 and phenanthreneref2 . There is a tilted angle $\delta$ between two successive benzene rings with respect to each other, and it reaches the extent of $9.5^{\circ}-10.6^{\circ}$. And viewing from the $c$ direction, K atom is localized on the C-C bond connected benzene ring-1 with ring-2, and closer to ring-1. Scanning the fine bonding feature, we have found that the C-C bonds linked two benzene rings (hereafter call them as bridge bonds) are shortened to 1.46 Å from 1.49 Å while the C-C bonds near the bridge bond within the rings become long when one K atom is doped for every organic molecule. The variations of C-C bonds indicate that the charge is local near K atom instead of uniform distribution when transferring to $\pi$ orbital from K atom.

For K2C18H14, the herringbone structure is still existent as shown in Fig. 2(b). However, three benzene rings in organic molecule are almost coplanar. The tilted angle $\delta$ is only $0.2^{\circ}-0.6^{\circ}$. Along the $b$ direction, two K atoms are between two organic molecular layers, and viewing from the $c$ direction, K atom respectively lies on the bridge bond. In K2C18H14, the bridge bonds further shorten to 1.44 Å and the C-C bonds near the bridge bond within the rings become longer. The distinguish of C-C bond lengths within the same ring becomes big which implies a stronger molecular distortion in K2C18H14. Doping three K atoms into solid p-terphenyl, K3C18H14, the system keeps the $P2_{1}/c$ symmetry, but great changes have taken place in the structure as shown in Fig. 2(c). All organic molecules rotate and form a visible two-dimensional layered structure. Along the $b$ direction, three K atoms are all between two organic molecular layers, but viewing from the $a$ direction, K atoms and p-terphenyl molecules are coplanar. Viewing from the $b$ direction, the K atom is respectively on the center of benzene ring. The varying tendency of C-C bond lengths in K3C18H14 is similar to K1C18H14 and K2C18H14. The bridge bonds further shorten to 1.43 Å.

To identify the observed superconducting phase in experiment, we have analyzed the XRD result. Compared the experimental XRD between C18H14 and KxC18H14 with 7.2 Kelvin superconductivity, the abnormal peaks around $2\theta=10.4^{\circ}$ and $2\theta=33.2^{\circ}$ imply the formation of new phase and a possible phase transition after doping. Additionally, the wide XRD peaks indicate that the crystallinity of the sample is not very good so that mixture phase can exist. Our calculated XRD of K1C18H14, K2C18H14 and K3C18H14 are presented in Fig. 1. Unfortunately, we find that none of three structures is completely consistent with the experiment in XRD spectrum. Although the XRD of K2C18H14 or K3C18H14 is closer to the experimental result, the XRD peak around $2\theta=10.4^{\circ}$ has not observed in these two pure phases. Thus we further investigated the possibility of other doped phases. On the one hand, we added a small charge fluctuation into K2C18H14 to form defect state, such as (K2C18H14)+0.1e and (K2C18H14)-0.1e. However, except for the small shift of peaks, this did not change the XRD spectrum in nature as shown in Fig. 1. On the other hand, we considered the fractional doping concentrations, such as K1.5C18H14 or K2.5C18H14, which can also understood as a mixed phase. In experiment, K1.5C18H14 may be obtained by mixing K1C18H14 and K2C18H14, while K2.5C18H14 can be formed by mixing K2C18H14 and K3C18H14. By subtracting and adding K atoms from/into K2C18H14, we have simply simulated the fractional doping levels in this calculation. Table II and Figure 2 present the optimized crystal lattice parameters and geometrical configurations, respectively. Both K1.5C18H14 and K2.5C18H14 are stabilized at $P1$ symmetry. The volumes of unit cell of doping cases of $x=$ 1, 1.5, 2, 2.5 and 3 does not satisfy the monotonically increasing trend due to the existence of phase transitions during the doping. As shown in Fig. 2(d), K1.5C18H14 is similar to K1C18H14. There are a visible herringbone feature and a big tilted angle between two successive benzene rings with respect to each other. The asymmetric distribution of K atoms in K2.5C18H14 (Fig. 2(e)) did not cause the big rotation between two successive benzene rings with respect to each other. However, the arrangement of organic molecules appears more arbitrary in K2.5C18H14. Comparing their XRD with the experiment one in Fig. 1, we were surprised to find that K2.5C18H14 produced some peaks fitting experiment near $2\theta=10.4^{\circ}$ and $2\theta=33.2^{\circ}$ and being not observed in K1.5C18H14. Of course, the XRD obtained from K2.5C18H14 can not completely match that of experiment, either. Seen from the XRD result, the superconducting phase observed in the experiment is more like a mixed phase by K2C18H14 and K3C18H14.

III.3 Stability

To examine the thermodynamic stability of these considered doping cases, we have calculated the formation energy $E_{f}$. The $E_{f}$ for the doping level $x$ is defined as the function of K chemical potential the following as

[TABLE]

where $E_{\text{doped}}$ and $E_{\text{pristine}}$ is the total energy of the doped and host crystal, respectively. $\mu_{\text{K}}^{\text{bulk}}$ can be obtained from the energy per K atom in the K metal with the $bcc$ structure. $x$ is the doping concentration. $\mu_{\text{K}}$ is the chemical potential of the K specie. $\mu_{\text{K}}=\mu_{\text{K}}^{\text{bulk}}$ means the element is so rich that the pure element phase can form. $E_{\text{f}}<0$ indicates that the doped compound can stably exist. From the calculated formation energy shown in Fig. 3, all of considered doped phases are able to exist as the chemical potential of K satisfying certain conditions. Comparing several doping levels, however, K2.5C18H14 is more stable since it has the lower formation energy than other phases in a wide range of chemical potential. This suggests that the experimentally observed superconducting phase of 7.2 K shall be K2.5C18H14 or a mixture phase.

III.4 Bonding character and charger transfer

Similar to other PAH superconductors, K-doped p-Terphenyl possesses the typical feature of charge transfer salt. Analyzing the interaction between K atoms and organic molecules, we can observe the clear ionic bonding characteristic. The different charge density $\Delta\rho$ [$\Delta\rho=\rho$(KxC18H${}_{14})-\rho$(C18H${}_{14})-\rho$(Kx)] shown in Fig. 4 graphically depicts the charge transferring between K atoms and organic molecules. The yellow and light blue areas define as the gain and loss of electrons, respectively. With the increase of doping content, the quantity of transferred charge is about 0.84, 1.24, 1.65, 1.99 and 2.44 e/f.u. for K1C18H14, K1.5C18H14, K2C18H14, K2.5C18H14 and K3C18H14, respectively. As mentioned above, the superconducting phase observed by experiment is predicted as a mixed phase such as the doping level around $x\sim 2.5$. Then the transferring charge of about two electrons is suggested. Another important information from $\Delta\rho$ is that it visibly shows the distribution of charge transferred to C atoms. As shown in Fig. 4, the transferred charge distribution is neither local nor homogeneous. The charge is distributed on part C atoms in certain an symmetrical ordering and highlights the distribution near bridge bonds. As a comparison, the added charge mainly concentrates on the middle benzene ring with the increase of K content. To K3C18H14, the distribution of transferred charge covers all C atoms.

III.5 Electronic structures

The pristine p-terphenyl is a wide-gap semiconductor with the bandgap of 3.3 eVref43 . The charge transferring from K atoms to organic molecules makes Fermi level shift toward to higher energy, which results in a transition from insulator to metal. Figure 5 and 6 respectively show the band structure and the total density of states (DOS) for each doping level at non-magnetic (NM) state. Under $P2_{1}$ symmetry, the conjugated molecules splits each orbital into a pair of partly degenerate bands in K1C18H14. As shown in Fig. 5(a), two partly degenerate bands forming the first group conduction band cross Fermi level. However, transforming to K1.5C18H14 with $P1$ symmetry (Fig. 5(b)), the coupling between the two conjugated molecules is weakened, which leads to a bigger splitting of bands. These former two doping levels both drive the high DOS at Fermi level ($N_{E_{F}}$) as shown in Fig. 6(a) and 6(b). The values of $N_{E_{F}}$ are 10.25 and 10.43 states/eV/f.u. for K1C18H14 and K1.5C18H14, respectively. More electrons transferring to organic molecules, in K2C18H14 shown in Fig. 5(c), the Fermi level moves into the overlap region of two group of conduction bands formed by two molecular orbitals. K2C18H14 exhibits the weak metallic feature with a small $N_{E_{F}}$ value of 1.28 states/eV./f.u. as shown in Fig. 6(c). In K2.5C18H14 (Fig. 5(d)), more electrons transferring to organic molecules rises Fermi level into the second group of conduction band. However, the conjugated character of organic molecules completely disappears, which further weakens the coupling among bands. One band crosses Fermi level, differing from the two-band model in other doping cases. The Fermi level is localized at a DOS peak (Fig. 6(d)) which results in a slightly big $N_{E_{F}}$ value of 5.1 states/eV/f.u.. For K3C18H14 with $P2_{1}/c$ symmetry, as shown in Fig. 5(e), the Fermi level moves into the second group of conduction band. The interactions between K atoms and molecules strengthen which makes bands become more extended. As shown in Fig. 6(e), a stronger metallic feature (3.57 states/eV/f.u. for $N_{E_{F}}$) is observed in K3C18H14 than K2C18H14. The result of electronic structures also indicates that we can obtain higher $N_{E_{F}}$ value by tuning the chemical potential of K to realize the high superconductivity, which is consistent with Mazziotti’s suggestionref44 .

Previous studies have pointed out that doped PAHs are often at the AFM ground stateref10 ; ref11 ; ref12 ; ref13 . Hence, we have investigated the magnetism of K-doped p-terphenyl. It was found that both K1C18H14 and K1.5C18H14 are at the AFM ground state. The total energy of AFM state is respectively 40.4 meV for K1C18H14 and 9.2 meV for K1.5C18H14 less than that of their NM state. The local magnetic moment are respectively 0.57 and 0.22 $\mu_{B}$/f.u. for K1C18H14 and K1.5C18H14, respectively. The electronic states at Fermi level shown in Fig. 7 visibly decrease, and the values of $N_{E_{F}}$ reduce to 1.6 and 5.5 states/eV/f.u. for K1C18H14 and K1.5C18H14, respectively. Interestingly, all of K2C18H14, K2.5C18H14 and K3C18H14 are stabilized at NM state. Comparing these magnetic structures in K-doped p-terphenyl, the difference of magnetism possibly results from the distortion in organic molecular plane. As shown in Fig. 2, the tilt between two successive benzene rings drives the spin ordering of electrons transferred to C atoms from K atoms. With the increase of charge transferring, the spin ordering disappears in systems while the superconductivity occurs.

III.6 Discussions

With regard to the superconductivity of K-doped p-terphenyl, more data and analysis are yet to come. The complexity of superconducting mechanism in K-doped p-terphenyl is evidented by recent reported three critical temperatures, 7.2, 43 and 123 Kelvin, in the same materialref22 ; ref23 ; ref24 . In previous studies, however, we have pointed out that there is a common phase to show $T_{c}$ in the range of $5<T_{c}<7$ Kelvin in all K-doped aromatic compoundsref9 . The existed superconductivity of 7.2 Kelvin in K-doped p-terphenyl just confirms that prediction. For this low $T_{c}$ phase, the electron-phonon coupling mechanism is enough to describe this superconductivity. From previous investigationsref9 ; ref45 , the phonons with low and middle frequency mainly contribute to electron-phonon interaction. The maximum value of our calculated the middle frequency of K2C18H14 is about 1574 cm*-1* which is almost equal to that of K-doped piceneref45 and also comparable with that of K2C6H6ref9 . At the same time, the $N_{E_{F}}$ can change with the doping content around 5.1 states/eV/f.u. for K2+δC18H14 ($0<\delta<1$) due to the charge fluctuations. Based on the comparable $N_{E_{F}}$ of K-doped p-terphenyl with K-doped benzene and picene in the range of $4-6$ states/eV/f.u.ref9 ; ref45 , and combining with the similar feasible screened Coulomb pseudopotential $\mu^{\star}$ of 0.1, we can predict that the $T_{c}$ of K-doped p-terphenyl is in the range of $5<T_{c}<7$ Kelvin, which is according with the experimental observationref23 . In other words, the observed superconducting phase is a mixed compound in the doping range of $2<x<3$ instead of pure K1C18H14 of K1.5C18H14 phase, which is just what we predicted by XRD, thermodynamic stability, electronic and magnetic properties.

With regarded to higher transition temperature, the experimental investigations presented unknown peaks in Raman spectra. These unknown peaks are possibly induced by graphite, C60 and other modesref23 ; ref24 . On the one hand, therefore, we infer that the two higher transition temperatures may be from other new superconducting modes such as CKx, KHx and K-CHx compounds induced by the reconstruction. On the other hand, as our previous studiesref9 ; ref19 , some internal and external factors can be the cause of high superconducting transition temperature, such as electronic correlations and pressure. The strong electronic correlations in K-doped p-terphenyl were implied by Baskaranref46 and Fabrizio et al.ref47 . In this kind of low dimensional organic system, therefore, the high superconductivity may be related with the electronic correlations effects. To clarify the matter, more efforts in the future are surely needed.

IV Conclusions

In conclusion, with the aim of exploring the structural and bonding characteristics of K-doped p-terphenyl which has been discovered to be a superconductor with $T_{c}=7.2-123$ Kelvin, we have carried out the first-principles calculations based on vdW-DF2 functional. Considering five doping levels of $x=$ 1, 1.5, 2, 2.5 and 3 in KxC18H14, we have predicted the optimized crystal structures at each doping level, calculated the XRD spectra, and investigated the thermodynamic stability, ionic bonding characteristics, charge transfer, electronic and magnetic properties. All of these five doping phases are able to exist in experiment based on the negative formation energy, but K2.5C18H14 or say a mixed phase by K2C18H14 and K3C18H14 is more stable in a wide range of chemical potential. The XRD summarized by K2C18H14, K2.5C18H14 and K3C18H14 can almost match that of experiment. The charge transfer from K atoms to organic molecules results in the insulator-metal transition. However, both K1C18H14 and K1.5C18H14 are stabilized at AFM ground state, while the latter three compounds exhibit the non-magnetic behavior. The superconducting phase observed in experiment should be a mixture phase with doping level in range of $2<x<3$. However, the multiformity of band structures near Fermi level indicates that the driving force for superconductivity is complicated. Future works are needed to understand the superconductivity especial for the transition temperature above 40 Kelvin.

V ACKNOWLEDGMENTS

The work was supported by the National Natural Science Foundation of China (Grant Nos. 61574157 and 61774164) and the Basic Research Program of Shenzhen (Grant nos. JCYJ20160331193059332, JCYJ20150529143500956 and JCYJ20150401145529035). H. Q. Lin, X. H. Wang, J. X. Han and G. H. Zhong acknowledge support from NSAF U1530401 and computational resource from the Beijing Computational Science Research Center. The partial calculation was supported by the Special Program for Applied Research on Super Computation of the NSFC-Guangdong Joint Fund (the second phase) under Grant No. U1501501.