Accepted Manuscript - Faizan Ullah · Accepted Manuscript Superalkalis as a source of diffuse...

Accepted Manuscript

Superalkalis as a source of diffuse excess electrons in newlydesigned inorganic electrides with remarkable nonlinear responseand deep ultraviolet transparency: A DFT study

Faizan Ullah, Naveen Kosar, Khurshid Ayub, Tariq Mahmood

PII: S0169-4332(19)31034-7DOI: https://doi.org/10.1016/j.apsusc.2019.04.042Reference: APSUSC 42350

To appear in: Applied Surface Science

Received date: 29 November 2018Revised date: 13 March 2019Accepted date: 3 April 2019

Please cite this article as: F. Ullah, N. Kosar, K. Ayub, et al., Superalkalis as a source ofdiffuse excess electrons in newly designed inorganic electrides with remarkable nonlinearresponse and deep ultraviolet transparency: A DFT study, Applied Surface Science,https://doi.org/10.1016/j.apsusc.2019.04.042

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https://doi.org/10.1016/j.apsusc.2019.04.042

https://doi.org/10.1016/j.apsusc.2019.04.042

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Superalkalis as a source of diffuse excess electrons in newly designed

inorganic electrides with remarkable nonlinear response and deep ultraviolet

transparency: A DFT study

Faizan Ullah, Naveen Kosar, Khurshid Ayub, Tariq Mahmood*

Department of Chemistry, COMSATS University Islamabad, Abbottabad Campus, Abbottabad-22060,

Pakistan

*To whom correspondence can be addressed: E-mail: [email protected] (T. M)

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Abstract

Recently, significant progress is observed in the design and synthesis of nonlinear optical

materials due to their optoelectronic and biomedical applications. In this report, a series of

inorganic electrides (Li2F@Al12P12, Li3O@Al12P12 and Li4N@Al12P12) are designed by doping of

Al12P12 nanocluster with superalkalis (Li2F, Li3O, Li4N) and studied through density functional

theory (DFT) for their geometrical, electronic and nonlinear optical properties. Computational

results indicated that these superalkalis doped complexes possess high stability and low HOMO-

LUMO gaps. Interaction energies reveal that adsorption of Li4N on Altop site of Al12P12 results in

highly stable structure (isomer J), where superalkali is strongly chemisorbed on the nanocage

(Eint = -105.13 kcal mol-1

). Moreover, the lowest HOMO-LUMO gap is also observed for J

isomer of Li4N@Al12P12 (0.44 eV), compared to 0.94 eV for alkali metal doped Al12P12 nanocage

and 3.36 eV for pure nanocage. Doping of superalkali on aluminum phosphide nanocage can

bring considerable increase in first hyperpolarizabilities (βo) response of the nanocage along with

deep ultraviolet transparency. The first hyperpolarizability (βo) for isomer J of Li4N@Al12P12 is

6.25 × 104 au. This study may provide an effective strategy to design high performance NLO

materials from stable inorganic electrides.

Keywords: Electrides; Aluminum phosphide; Superalkali; Nonlinear optical; DFT

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1. Introduction

In recent decades, many studies [1–7] have been focused on theoretical designing of novel

nonlinear optical (NLO) materials due to their extensive applications in optoelectronics. Up till

now, many design strategies have been proposed for efficient NLO materials; doping of metal

atoms [4,8–11], applying bond length alternation (BLA) theory[12], donor-π-conjugated-bridge-

acceptor (D-π-A) models [13,14], push-pull effects [15], decorating or changing sp2-hybridized

carbon nanomaterials [16], multidecker sandwiches clusters as building block [17], and octupolar

molecules [18] etc. Recently, delocalized π-conjugated surfaces are explored for their

applications as novel NLO materials. For example, graphene, graphyne and graphdiyne based

strong alkalides are recently designed by using alkali metals as source of excess electrons

[19,20]. Novel graphdiyne-based NLO materials are also designed by doping graphdiyne with

tetrahedral alkali-metal nitrides [21]. From literature, it is well known that introduction of

loosely bound excess electrons to a molecular system enhances nonlinear optical response and

many systems have been designed having excess electrons as nonlinear optical materials [22–

25].

Electrides are classified as ionic compounds consisting of positive and negative ions; however,

the negative ions are considered as simply electrons without nucleus [26–30]. These electrides

remained focus of several studies over the past years due to their potential applications in

nanodevices, catalysis, and functional materials [31–33]. Recent studies have found their

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potential applications as high performance nonlinear optical materials [22,34,35]. However, the

organic electrides presents major difficulties in their practical applications as they are sensitive

towards temperature and air [33]. In 2003, first inorganic electride was synthesized successfully

which made their use in practical applications possible, as inorganic electrides can withstand

exposure to air and remain stable at room temperature [36].

Usually, the electrides are designed by introducing excess electrons in organic systems via

doping alkali metals. As it is well-known that superalkalis have much lower ionization potential

compared to alkali metals and can donate electron more easily [37]. Therefore, it is expected

that superalkalis are better sources of excess electrons for designing electrides and other excess

electron systems for high nonlinear optical response. Recent studies have confirmed this by

designing alkalides and electrides with large nonlinear optical response using superalkalis as

source of excess electrons [38–40].

Practical applications of nonlinear optical materials depend on their stability and transparency in

the applied laser wavelength. It is well-known that inorganic compounds possess better stability

and transparency than organic compounds. Therefore, much research is going on finding and

exploring possibilities of using superalkalis in the design of more efficient and enhanced

inorganic nonlinear optical materials. The above discussion indicates that superalkalis have a

significant role in designing of nonlinear optical materials, with dramatically large nonlinear

optical responses (electrides). But one is uncertain which type of modification in these materials

would further increase the nonlinear optical response. In this study, we have performed

systematic study of superalkali doped on aluminum phosphide nanocage (AlP) for nonlinear

optical response and to understand which type of modification in these electrides would further

increase the nonlinear optical response. The fullerene-like X12Y12 nanocages were theoretically

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predicted to be the most stable nanocages among the several (XY)n clusters [41,42] and a study

has shown that phosphide nanocages are better than nitride nanocages for nonlinear optical

applications [43]. We intend to design series of inorganic electrides by doping this cage with

superalkalis e.g. Li2F, Li3O, and Li4N, respectively. By doping these superalkalis Li2F, Li3O, and

Li4N on aluminum phosphide (Al12P12) nanocage we are mainly focusing on these main issues.

(a) can inorganic electrides systems having loosely bound excess electrons be obtained by

doping superalkalis e.g. Li2F, Li3O, and Li4N on Al12P12 nanocage? (b) To perform systematic

study of superalkali doped phosphide nanocage for NLO response. (c) Do these inorganic

electrides possess better stability and large hyperpolarizability than previously reported

electrides? (d) How the nature of different superalkali affect the hyperpolarizability and

nonlinear optical response?

2. Computational methodology

Geometries of pure nanocage (Al12P12) and superalkali doped nanocage are optimized by using

the combination of Becke’s hybrid 3-parameter exchange functional and Lee-Yang-Parr’s

correlation functional (B3LYP) with 6-31+G (d) basis set. B3LYP in conjunction with 6-31+G

(d) basis set is proved as a reliable level for the geometry optimization of similar systems in the

previous studies [21,44,45].

In addition, interaction energies, natural bond orbital (NBO), highest occupied molecular orbital-

lowest unoccupied molecular orbital (HOMO-LUMO) energy gap are calculated on the same

level of theory as used for optimization (B3LYP/6-31+G(d). The interaction energy is defined as:

Eint = Esuperalkali@Al12P12 - (EAl12P12 + Esuperalkali) Equation 1

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where E(Al12P12), E(superalkali), and E(superalkali@Al12P12) are the total energies of the undoped Al12P12

nanocage, corresponding superalkali unit (Li2F, Li3O, and Li4N), and doped system, respectively.

The time-dependent density functional theory (TD-DFT) calculations are performed at the TD-

B3LYP/6-311+G(d) level to get the crucial excited states and ultraviolet-visible-nearinfrared

(UV-VIS-NIR) absorption spectra of the optimized structures. All the above calculations are

performed using Gaussian 09 [46] and results are visualized by using GaussView 5.0 [47]

CAM-B3LYP [48] and LC-BLYP [49,50] methods are used for calculation of dipole moment,

polarizability (αo) and first hyperpolarizability (βo) as these methods provide excellent balance

between computational cost and accuracy [51]. CAMB3LYP is a highly reliable method for

calculating hyperpolarizabilities. Range separation is quite important for accurate calculations of

hyperpolarizabilities. CAM-B3LYP has 0.65 fraction of nonlocal exchange at asymptotic

distance. Full range-separated functionals such as LC-BLYP have the correct 1.00 fraction of

nonlocal exchange. Previous studies have found that a full range-separated functional has been

shown to give even better nonlinear optical properties compared to CAM-B3LYP.

6-311++G(2d,2p) basis set is chosen with both CAM-B3LYP and LC-BLYP methods. This

basis set is adequate to calculate the molecular nonlinear optical properties and is widely used in

recent works on nonlinear optical materials [52].

The static mean polarizability (αo) and mean first hyperpolarizability (βo) are defined as follows:

αo = 1/3(αxx+ αyy+ αzz)

βo = [βx2 + βy

2 + βz

2]

1/2

where βx = βxxx + βxxy + βxxz, βy = βyyy+ βyzz+ βyxx and βz = βzzz+ βzxx+ βzyy

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3. Results and discussion

3.1 Optimized geometries

Initially, the optimized structure of aluminum phosphide (Al12P12) nanocage is obtained with no

symmetry constraints at UB3LYP/6-31+G (d) level of theory and is shown in Figure 1. The

optimized geometry of Al12P12 nanocage has C2H point group symmetry and comprises of six

tetragons and eight hexagons. Two distinct types of Al-P bonds are present in pristine Al12P12

nanocage, one connecting two hexagonal rings (b66) and the other connects hexagonal ring with

tetragonal ring (b64). The bond lengths of the b66 and b64 bonds in Al12P12 nanocage are 2.29 Å

and 2.34 Å, respectively, which is consistent with earlier reports [53]. Three sets of geometries

are optimized for Al12P12 nanocage by doping with superalkalis e.g. Li2F, Li3O and Li4N at

different orientations.

Figure 1: Side and top view of optimized structure of pristine Al12P12 nanocage.

As a result of doping of Li2F on the Al12P12 nanocage, four isomers (A-D) are obtained based on

different orientations of Li2F (Figure 2). The most stable isomer A has C1- symmetric structure,

in which Li2F is chemisorbed on the Altop position of the nanocage. F atom of superalkali

interacts with Al atom of the nanocage and each Li atom of the superalkali is directed towards P

Side view Top view

vvview

2.29

2.34

Å

Å

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atoms of the nanocage. Since the two Li atoms of Li2F are confined by two P atoms of the

nanocage, the (∠LiFLi) is reduced from 177.75° to 126.31°. Also, the Li-F bond is weakened

and elongated to 1.69 Å compared to 1.67 Å in bare Li2F superalkali. Isomer B is generated

where Li2F is present in the center of 4-membered ring (r4). The average Li-P bond length and

∠LiFLi are almost unchanged from isomer A however, F atom of superalkali does not show

interaction with Al atom of the nanocage in isomer B. Isomer C is also Altop but with orientation

different than isomer A. The ∠LiFLi is enlarged to 147.97° and Li-F bond is elongated to 1.8 Å.

Another stable isomer D with Cs-symmetry is obtained in which Li2F is present on top of r4 ring

like isomer B however, Li2F adopted planar orientation and its F atom is fixed on top of Al atom

in isomer D. The average Li-P and Li-F bond lengths are same as in isomer C. (see Table 1).

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Figure 2: Optimized geometries of Li2F@Al12P12 (A-D), Li3O@Al12P12 (E-I) and Li4N@Al12P12

(J-L) isomers.

Five isomers (E-I) are also observed for doping Li3O on Al12P12 nanocage (Figure 2). Quite

similar to Li2F@Al12P12, the most stable isomer of Li3O@ Al12P12 (E) is also designated as Altop.

Li3O is chemisorbed on Altop position (in isomer E) of the nanocage via one O-Al and three Li-P

bonds. The structural integrity of superalkali and nanocage is preserved. The ∠LiOLi is slightly

B C A D

E F G H I

J K L

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increased from 120° to 121.94° and Li-O bond is elongated to 1.81 Å compared to Li-O bond

length (1.68 Å) of isolated Li3O.

Table 1: Relative energies Erel (in kcal mol-1

), symmetry, first frequency v1 (in s-1

), average bond

length between Li and P (XLi-P in Å), average bond length between F/O/N and Li (XX-Li in Å),

bond angle between Li, F/O/N and Li (∠LiXLi in degree), HOMO-LUMO gaps (EH-L) in eV and

interaction energy (Eint.) in kcal mol-1

of all optimized isomers (A-L).

Li2F@Al12P12

Isomers Erel. Symmetry ν1 XLi−P XF−Li ∠LiFLi EH-L Eint.

A 0 C1 22.18 2.46 1.69 126.31 1.86 -50.42

B 0.81 C1 10.61 2.45 1.69 123.94 1.88 -49.60

C 2.18 C1 73.47 2.39 1.80 147.97 1.51 -48.24

D 3.64 Cs 76.68 2.39 1.80 137.93 1.56 -46.77

Li3O@Al12P12

Isomers Erel Symmetry ν1 XLi−P XO−Li ∠LiOLi EH-L Eint.

E 0 Cs 89.14 2.44 1.81 121.94 1.42 -86.49

F 18.78 C1 51.34 2.55 1.82 100.53 1.62 -67.71

G 33.53 C1 66.39 2.54 1.69 114.09 1.79 -52.95

H

I

39.14 C1 34.07 2.52 1.86 85.69 2.19 -47.34

39.20 C1 11.13 3.47 1.69 104.02 1.79 -47.29

Li4N@Al12P12

Isomers Erel Symmetry ν1 XLi−P XN−Li ∠LiNLi EH-L Eint.

J 0 C1 79.09 3.10 1.89 115.12 0.44 -105.13

K 5.89 C1 35.40 2.60 1.92 103.12 1.49 -99.24

L 36.98 C1 60.08 3.28 1.79 103.57 1.76 -68.16

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The next stable isomer (F) is Altop for Li3O@Al12P12, quite contrary to the Li2F@Al12P12 series

where the second most stable isomer is r4. Isomer (F) has geometry similar to isomer E but one

Li atom of Li3O occupies the position above r4 ring of the cage. The superalkali in this isomer

suffers from relatively large structural distortion. Another isomer (G) is generated where Li3O

occupies central position of the r6 ring. Three of the Li atoms of superalkali are directed towards

the top of the P atoms (three) of six-membered ring while O atom is present in the mid of the r6

ring. During capping of Li3O on the mid of the four-membered ring, a new isomer H is obtained,

due to the large size of the Li3O, distortion of the nanocage is observed. One of the Li atoms of

superalkali occupies the central position of r4 ring of the cage. The bond angle (∠LiOLi) is

reduced to 85.69° whereas average bond length of Li-O is increased to 1.86 Å. The vertical

placement of Li3O on nanocage generates another isomer I, in which the two Li atoms of

superalkali are directed towards the P atoms of the r4 ring. Both superalkali and nanocage

sustains their structural integrity in isomer I.

Three isomers (J-L) are obtained by doping of Li4N on Al12P12 nanocage, all the isomers have C1

symmetry. The most stable isomer of Li4N@Al12P12, J, is generated by doping Li4N at the Altop

site of Al12P12 via three Li-P bonds and one N-Al bond. Structural integrity of nanocage is

preserved whereas, Li4N unit suffers distortion to chemisorb on the nanocage. The Li-N and

∠LiNLi angle are elongated to 1.89 Å and 115. 12°, respectively compared to 1.82 Å and 90° in

the isolated Li4N cluster. Capping the planar Li4N on the Altop of the nanocage results in another

isomer K where the Li atoms of Li4N are directed towards the P atoms of the cage whereas N of

Li4N occupies the Altop position. The N-Al bond length of isomer K is same as that of isomer J

whereas Li-P bond length of isomer K is shortened by 0.5 Å than that of isomer J. Doping Li4N

on the center of six-membered ring (r6) generates isomer L. The Li-P bond length of isomer L is

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3.28 Å which is higher compared to the most stable isomer J. Above discussion reveals that

structural integrity of the cage is retained whereas superalkali adopts the shape of cage according

the doping position. The interaction involves strong chemisorption through stable F/O/N----Al

and P-Li bonds. In some cases, F/N/O---Al interactions are absent. Among all doping sites, it is

observed that Altop of Al12P12 is the most favorable position for doping of superalkali on the

Al12P12 nanocage.

3.2 Thermodynamic stability of the complexes

For practical applications of nonlinear optical materials and their synthetic utility in laboratory,

the thermodynamic stability is very important. For analyzing the stability of all optimized

isomers (A-L), the interaction energies are studied and listed in Table 1. Interaction energy

define the stability of the complexes. Thus, the larger the Eint. value, the stronger is the

interaction between two subunits and greater is the stability of resultant complex. All the

observed isomers (A-L) exhibit much larger Eint. values which lie in the range of -46.77−-105.13

kcal mol-1

. The large Eint values indicate stronger interaction between superalkalis (Li2F, Li3O

and Li4N) and Al12P12 nanocages. The interaction energies of superalkali@Al12P12 are also

compared with those of M@Al12P12 (M = Li, Na and K). The interaction energies for

superalkali@Al12P12 are in the range of -46.77−-105.13 kcal mol-1

whereas the interaction

energies of M@Al12P12 are in the range of -12.05−-30.27 kcal mol-1

[54]. Eint. indicates that the

superalkalis Li2F, Li3O and Li4N interact more strongly with Al12P12 nanocage than alkali metal

atoms. Thus, comparing with the alkali metal atom doped Al12P12 complexes, doping of

superalkali Li2F, Li3O and Li4N on the Al12P12 nanostructure not only brings structural diversity

but also produces more stable species. Moreover, these Eint values -46.77−-105.13 kcal mol-1

are

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comparable to similar electrides Li3O@Al12N12 already reported in the literature (-52−-118 kcal

mol-1

) [40].

Two isomers (J and K) of Li4N@Al12P12 have the highest Eint. values and ultimately are more

stable as compared to all other isomers. The stability is attributed to higher number of

interactions between superalkali (Li4N) and nanocage. In Li4N@Al12P12 complexes, isomer J is

the most stable isomer (-105.13 kcal mol-1

) followed by isomer K (-99.24 kcal mol

-1) and L (-

68.16 kcal mol-1

). The increasing trend of Eint. in Li4N@Al12P12 isomers is J > K > L. Among

five isomers of Li3O@Al12P12, E has more Eint (-86.49 kcal mol-1

) value than other isomers. Eint.

values for isomers F, G, H and I are -67.71 kcal mol-1

, -52.95 kcal mol-1

, -47.34 kcal mol-1

and -

47.29 kcal mol-1

, respectively. The increasing trend of Eint. in Li3O@Al12P12 isomers is E > F >

G > H > I. For Li2F@Al12P12 isomers, the highest Eint. of -50.42 kcal mol-1

is observed for

isomers A. The Eint. values of the isomers B, C and D, are -49.6 kcal mol-1

, -48.24 kcal mol-1

,

and -46.77 kcal mol-1

, respectively. The increasing trend of Eint. in Li3O@Al12P12 isomers is A >

B > C > D. Collectively, the trend of increasing stability based on the Eint. of isomers is

Li4N@Al12P12 > Li3O@Al12P12 > Li2F@Al12P12.

3.3 Frontier molecular orbitals (FMOs) analysis and electride characteristics

To evaluate the electronic stability of these three sets of superalkali doped Al12P12 complexes (A-

L), the energy gap between HOMO and LUMO is also calculated via FMOs analysis and is

summarized in Table 2.

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Li2F@Al

12P

12

Li3O@Al

12P

12

HOMO LUMO HOMO LUMO

HOMO LUMO HOMO LUMO

C

B A

D

E

G H

F

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Figure 3: HOMOs and LUMOs of superalkali doped Al12P12 nanocage (A-L) (isovalue = 0.04)

Generally, Al12P12 nanocage is a semiconductor having EH-L of 3.37 eV. Relatively large energy

gap hinders its application in optical devices [54]. For the enhancement of conducting properties

of Al12P12 nanocage, different superalkalis (Li2F, Li3O and Li4N) are doped. EH-L is significantly

reduced for doped systems which is attributed to the increase in the energies of HOMOs and

decrease in the energies of LUMO. The reason for increase in energies of HOMO is the presence

Li4N@Al

12P

12

HOMO LUMO HOMO LUMO

I

J K

L

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of excess electrons. The excess electrons occupy the new HOMOs which are now known as

HOMO and the old one becomes HOMO-1 [43].

Among four isomers of Li2F@Al12P12 (A-D), EH-L is in the range of 1.51 eV-1.86 eV. Energies of

HOMOs (LUMOs) are -2.55(-4.41), -2.50(-4.38), -2.30(-3.81) and -2.37(-3.93) for isomers A, B,

C, and D, respectively. The Lowest EH-L (1.51 eV) in this series is obtained for isomer C. EH-L

for isomers D, A and B are 1.56, 1.86 and 1.88 eV, respectively. The trend of decreasing order of

EH-L is C < D < A < B. In case of Li3O@Al12P12 isomers (E-I), energy gap ranges from 1.42 eV-

2.19 eV. Energies of HOMOs (LUMOs) for isomers E, F, G, H, and I are -2.27(-3.69), -2.63(-

4.25), -2.50(-4.29), -2.64(-4.82) and -2.24(-4.03), respectively (Table 2). Here, the lowest EH-L is

observed for isomer E which is 1.42 eV. EH-L for isomers F, G, I and H are 1.62, 1.79, 1.79 and

2.19 eV, respectively. The decreasing trend of EH-L in Li3O@Al12P12 series is E < F < G ⁓ I < H.

Lastly, isomers J-L have EH-L of 0.44 eV to 1.76 eV, where isomer J has the lowest EH-L of 0.44

eV. EH-L of isomer K is 1.49 eV, whereas EH-L of isomer L is 1.76 eV. Energies of HOMOs

(LUMOs) are -2.99(-3.43), -2.25(-3.74) and -2.34(-4.1) for isomers J, K, and L, respectively.

Overall, doping of superalkalis narrows down the EH-L but the lowest gap is observed for isomer

J and the trend of decreasing EH-L is J < K < L. The EH-L of isomer J is lower than the previously

reported energy gap for C60, alkali, alkaline and transition metals doping on aluminum/boron

phosphide and nitride nanosheets and aluminum phosphide nanocages[44,55–57]. The lower

energy gap of isomer J reflects the metallic properties of this isomer. The doping of superalkalis

on Al12P12 nanocage results in the reduction of energy gap irrespective of the nature of

superalkalis. Under the influence of lone pair of electrons on phosphorus atom, s electrons of the

Li atoms of the superalkali units are pulled towards the cage as diffuse excess electrons. As a

result, the energy of the new HOMO increases which results in decrease of energy gap. In this

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study, moving from Li2F to Li4N as the number of alkali metals increases the energy gap

decreases. Due to the pulling effect of the cage, the electronic density in HOMOs mostly reside

in the cage. Although doping of superalkalis on aluminum phosphide nanocage increased the

energies of HOMOs of all isomers from A to L. Yet the contribution from different superalkalis

in HOMOs is different for all the isomers. These doped nanocage act as n-type semiconductors.

The distribution and shapes of HOMOs and LUMOs are depicted in Figure 3. In isomers A, B,

D, G, H, I, and L, the density in HOMOs reside outside any atom. Based on the distributions of

densities in HOMOs, the above isomers are characterized as new types of inorganic electrides. In

these electrides, the density is present mainly in the center of the cage. Exceptional behavior is

observed in electride J where the density in HOMOs is located near the superalkalis (more

contribution from superalkalis compared to cage). Conclusively, the contributions of superalkalis

as well as nanocage in HOMOs of these isomers is expected to significantly enhance the

electronic and nonlinear optical properties of doped aluminum phosphide nanocages.

3.4 Charge analysis

To investigate the interaction of superalkali and nanocage, charge analysis of all geometries is

investigated. The charge analysis provides important information about the net charge transfer

after doping. Charge analysis data from NBO analysis confirmed the charge transfer from the

superalkali unit to the nanocage in all the superalkalis doped isomers. The charge transfer is

evident from the positive charges present on the alkali metal atoms in the superalkali unit and the

overall positive charge on the superalkali unit.

The total NBO charges on superalkali unit in Li2F series is observed between 0.866 to 0.949 |e|,

while in case of Li3O series and Li4N series, it is observed between 0.585 to 0.974 |e| and 0.422

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to 1.007 |e|, respectively (see Table 2). The highest charge transfer is observed for isomer K and

the lowest charge transfer is observed for isomer J of Li4N@Al12P12, respectively. The charge

analysis revealed the charge transfer from superalkali to the nanocage. Under the influence of

lone pairs of the P atoms, electrons are pushed out from outer s valence orbital of alkali atoms of

the superalkali units and are pulled towards the nanocage. These results are also justified from

the fact that the charges on the superalkali units in all isomers (A-L) are much more compared

to the previously reported charges (0.531–0.634 |e|) on alkali metal atoms doped M@Al12N12 (M

= Li, Na, K) complexes [44], suggesting that more charges are transferred from the superalkali

units to the phosphide nanocage in these compounds (Except isomer J where charge is 0.422 |e|.

The excess electrons are derived from the superalkali to form excess electron cloud in isomers A,

B, D, G, H, I, and L. The excess electrons do not belong to any atom which reflect the electride

characteristics of these isomers.

Table 2: NBO charges on superalkalis (Q in |e|), Energies of HOMOs (in eV), energies of

LUMOs (in eV), HOMO-LUMO gaps (in eV) and wavelength (λmax in nm) of isomers (A-L).

Li2F@Al12P12

Isomers Q HOMO LUMO EH-L λmax.

Al12P12 - -6.75 -3.38 3.37 -

A 0.872 -4.41 -2.55 1.86 738

B 0.866 -4.38 -2.50 1.88 742

C 0.949 -3.81 -2.30 1.51 957

D 0.937 -3.93 -2.37 1.56 887

Li3O@Al12P12


E 0.974 -3.69 -2.27 1.42 963

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F 0.82 -4.25 -2.63 1.62 628

G 0.831 -4.29 -2.50 1.79 807

H 0.585 -4.82 -2.64 2.19 663

I 0.847 -4.03 -2.24 1.79 790

Li4N@Al12P12


J 0.422 -3.43 -2.99 0.44 674

K 1.007 -3.74 -2.25 1.49 937

L 0.785 -4.10 -2.34 1.76 842

3.5 TD-DFT analysis

Materials with large first hyperpolarizability values are mainly used in second harmonic

generation (SHG) for doubling frequency. Therefore, good NLO materials should have

transparency under the utilized laser light besides having large NLO response [58]. For this

purpose, the ultraviolet visible near-infrared (UV-VIS-NIR) absorption analysis of the proposed

superalkali doped structures is also performed and UV-Vis spectra of each series is shown in

Figure 4. The main absorption region of all isomer A-L lies in the range above UV-Vis region

i.e. from 628 to 957 nm. The highest λmax (957 nm) is observed for the isomer C, whereas lowest

λmax (628 nm) is observed for the isomer F. All isomers have weak absorption in the visible and

ultraviolet region which indicates sufficient transparency for the routinely used laser. Also, these

electrides are fully transparent in deep ultraviolet region (≤200 nm). Therefore, these electrides

may be considered as new candidates for deep ultraviolet NLO materials.

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Figure 4: UV-Vis spectra of stable isomers (A-L) of Li2F/Li3O/Li4N@Al12P12.

Transparent region

Transparent region

Transparent region

Li2F@Al

12P

12

Li3O@Al

12P

12

Li4N@Al

12P

12

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3.6 PDOS and TDOS analysis

For further confirmation of the electronic behavior of these superalkali doped isomers, partial

density of states (PDOS) and total density of states (TDOS) analysis are also performed. PDOS

and TDOS of the most stable superalkali doped nanocages are plotted in Figure 5 and SI. 1-3.

Doping superalkali on Al12P12 nanocage results new energy levels, as a result of the transfer of

excess electrons from superalkalis (Li2F, Li3O and Li4N) to Al12P12 nanocage. The newly

generated HOMOs have higher energy compared to the pure nanocage HOMOs which results in

decrease of the HOMO-LUMO gap. The formation of new HOMO energy levels and decreased

HOMO-LUMO gap revealed that the conducting properties of the nanocage are changed as a

result of the excess electrons introduced by superalkali. PDOS plots also confirmed the presence

of excess electrons in the system.

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Figure 5: TDOS and PDOS spectra of the most stable complexes of superlaklis@Al12P12 (A, E,

J)

Li4N@Al

12P

12 (J)

Li3O@Al

12P

12 (E)

Li2F@Al

12P

12 (A)

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3.7 Dipole Moment

The product of charge and distance among the charge particles is known as dipole moment (µo).

Therefore, high charges and more separation between these charges results in higher µo value.

Analysis of superalkali doped Al12P12 nanocages produces similar trend i.e. isomers having

higher charges on superalkalis and higher separation of charges showed higher dipole moment.

At CAM-B3LYP method, in a series of Li2F@A112P12 complexes (isomers A-D) the highest µo of

15.4D is observed for isomer C followed by 14.55D for isomer D. As the bond length of Li-F

increases, the dipole moment increases. The highest charge transfer of 0.949 |e| is overall

obtained for isomer C which also supports its higher µo value. The value of µo for isomer B is

7.54D while isomer A has µo of 6.89D. E-I isomers of Li3O@A112P12 complex have µo in the

range of 6.52D -17.64D. Here, the highest µo of 17.64D is obtained for isomer E. Among three

isomers (J-L) of Li4N@A112P12 complex, isomer K has the highest µo of 16.23D, whereas µo of

isomers J and L are 0.86D and 11.44D, respectively. Similar to first series, in last two series, the

charges on isomer E and K are 0.974 |e| and 1.007 |e| respectively, which elucidated the higher

µo of these respective isomers.

Similar trend of µo values are obtained at LC-BLYP for all three series of superalkalis doped

Al12P12 as are observed in case of CAM-B3LYP method. For Li4N@Al12P12 series, µo is 16.57D

for isomer K, followed by 11.44D for isomer L, and 0.39D for isomer J. Additionally, µo values

of isomers F-I showed similarity to CAM-B3LYP except isomer E where µo is 17.97D (higher

than previous results). In Li2F@Al12P12 series, isomers C (15.68D) and D (14.68D) have slightly

higher µo values compared to µo at CAM-B3LYP method.

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3.8 Nonlinear optical (NLO) properties

Literature reveals that the NLO response of a system can be enhanced effectively by introducing

excess electrons in a system. The excess electrons occupy the high energy HOMOs which results

in decrease of EH-L and increase of first hyperpolarizabilities (βo). Previously, doping of alkali

and transition metals is described as an effective strategy for enhancing NLO response [44,54].

In the current study, the stable inorganic superalkali doped Al12P12 nanocages are studied for

large NLO response at LC-BLYP and CAM-B3LYP. In this regard, the dipole moments (µo),

polarizabilities (αo), and first hyperpolarizabilities (βo) of these superalkali@Al12P12

nanostructures are calculated and summarized in Table 3. For better visualization of the results,

the dependences of the polarizability (αo) and first hyperpolarizability (βo) values on the

electronic and geometric structures of most stable isomers from each series are shown in Figure

6. The first hyperpolarizability (βo) and dipole moment of pure nanocage are zero since Al12P12 is

centrosymmetric. Doping of superalkali brings significant enhancement of the dipole moment

(µo) and first hyperpolarizability (βo) for the Al12P12 nanocage because the introduction of

superalkali (Li2F, Li3O and Li4N) not only distorts the symmetry of nanocage but also provides

the excess electrons into the doped system.

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Figure 6: Polarizability α0 and first hyperpolarizability (βo) of most stable isomers of

Li2F@Al12P12 (A), Li3O@Al12P12 (E) and Li4N@Al12P12 (J). The orbitals shown are HOMOs of

the corresponding isomers.

Both LC-BLYP and CAM-B3LYP revealed similar trends of hyperpolarizability. However, the

calculated values are slightly higher in CAM-B3LYP than LC-BLYP which is consistent with

the literature [59]. The polarizability (αo) value of all these superalkali doped aluminum

phosphide nanocage are in the range of 669 au to 911 au (at CAM-B3LYP). The Li4N doped

Al12P12 isomers (J-L) show comparatively better αo values. Isomer J shows highest polarizability

value of 911 au. Other isomers K and L of this series have values of 751 and 746 au,

respectively. Calculated αo values for Li3O@Al12P12 structures are 729 au, 674 au, 697 au, 674

au and 699 au for isomers E, F, G, H and I, respectively. Li2F@Al12P12 structures show

comparatively lower polarizability values of 669 au, 671 au, 712 au and 699 au for isomers A, B,

0

10000

20000

30000

40000

50000

60000

70000

200

275

350

425

500

575

650

725

800

875

950

A E J

Hyp

erp

ola

riza

bil

ity, β

o (au

)

Pola

riza

bil

ity, α

0 (

au

)

Isomers

Polarizability Hyperpolarizability

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C, and D, respectively. The trend of increasing polarizability is in the order of Li2F@Al12P12 <

Li3O@Al12P12 < Li4N@Al12P12.

The trend of polarizability (αo) of all superalkali doped Al12P12 complexes at LC-BLYP is similar

to results of CAM-B3LYP method. However, the values are slightly lower than αo values at

CAM-B3LYP method. Highest αo are 877.64 au, 702. 25 au and 688.34 au for isomers J, E and

C of Li4N@Al12P12, Li3O@Al12P12 and Li2F@Al12P12, respectively.

Table 3: Oscillator strength (fo), crucial excitation energy (ΔE) in eV, dipole moment (µo) in

debye, polarizabilities (αo) in au and first hyperpolarizability (βo) in au of isomers (A-L) of

Li2F@Al12P12, Li3O@Al12P12 and Li4N@Al12P12 complexes.

Li2F@Al12P12

Isomers CAM-B3LYP LC-BLYP

fo ΔE µo αo βo µo αo βo

Pure Al12P12 0.00 595 0.00 0.00 578 0.00

A 0.039 1.68 6.89 669 2.11×103 6.84 645 3.01×10

3

B 0.035 1.67 7.54 671 1.96×103 7.47 646 3.22×10

3

C 0.044 1.29 15.40 712 9.93×103 15.68 697 5.90×10

3

D 0.043 1.39 14.55 699 9.12×103 14.68 674 6.17×10

3

Li3O@Al12P12

E 0.039 1.28 17.64 729 1.18×104 17.97 711 8.38×10

3

F 0.038 1.97 11.96 674 6.47×103 11.97 642 4.90×10

3

G 0.038 1.53 6.52 697 2.46×103 6.47 675 3.48×10

3

H 0.010 1.87 9.52 674 1.98×103 9.50 645 1.60×10

3

I 0.039 1.56 15.76 699 2.40×103 15.73 674 4.67×10

3

Li4N@Al12P12

J 0.062 1.83 0.86 911 6.03×104 0.39 880 2.03×10

4

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K 0.036 1.32 16.23 751 8.96×103 16.57 731 7.87×10

3

L 0.035 1.47 11.44 746 1.54×103 11.54 717 3.26×10

3

At CAM-B3LYP method, the highest first hyperpolarizability (βo) value of 6.03×104 au is

observed for isomer J of Li4N@Al12P12 complexes, followed by 8.96×103

au and 1.54×103

au for

isomer K and L, respectively. βo is inversely related to EH-L (vide supra). Therefore, the lowest

EH-L of isomer J is the main reason for its highest βo. For Li3O doped Al12P12 series, highest βo

value of 1.18×104

au is observed for isomer E. βo values are 6.47×103, 2.46×10

3, 1.98×10

3 and

2.40×103

au for isomers F, G, H and I, respectively. Again, a monotonic relation of EH-L and βo

is observed for these isomers (E-I). C has the highest βo value of 9.93×103

au among

Li2F@Al12P12 isomers. βo values are 2.11×103, 1.96×10

3 and 9.12×10

3 au for isomers A, B and

D, respectively.

The βo results at LC-BLYP revealed that Li4N@Al12P12 complexes have higher βo than

Li3O@Al12P12 and Li2F@Al12P12 complexes. Comparing the βo of different superalkali doped

Al12P12 complexes, βo values are in the range of 1.60×103

au to 2.03×104

au. The highest βo is

2.03×104

au is observed for isomer J of Li4N@Al12P12 complex, followed by 8.38×103 au for

isomer E of Li3O@Al12P12 complex and 6.17×103

au for isomer D of Li2F@Al12P12. The βo

increases from Li2F to Li4N doped Al12P12 complexes.

βo of a system can be affected by many factors, such as the internuclear distance between the

dopant and the nanocage and ionization potential. The shorter the interaction distance between

superalkali and nanocage, the higher will be the hyperpolarizability. The lower the ionization

potential, the higher is the hyperpolarizability. Moreover, the number of alkali metal atoms also

affect the βo of the doped system through the number of excess electrons (vide supra) which are

provided by the superalkali unit to the nanocage. Since the number of alkali metal atoms are

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higher in Li4N, it provides more excess electrons which result in higher hyperpolarizability (in

our case) by reducing EH-L. In case of Li3O and Li2F the number of alkali metal atoms are less as

compared to Li4N and Li3O, their corresponding hyperpolarizability values are also lower.

Conclusively, both methods LC-BLYP and CAM-B3LYP showed remarkable increase in

hyperpolarizability of all three considered superalkali doped aluminum phosphide nanocages.

Both methods also revealed that increasing the numbers of alkali metals in superalkali unit

results in the increase of the first hyperpolarizability.

To gain insight into the factors responsible for affecting hyperpolarizability, crucial excitation

energies and oscillator strength of crucial excited states are calculated. In literature it has been

previously reported that the small transition energy (ΔE) of the crucial excited state leads to large

βo value. Our calculated results reveal that, in contrast to the pristine nanocage with large ΔE, the

superalkali doped cages exhibit much smaller ΔE values of 1.28–1.97 eV, which are comparable

to the previously reported Li3O doped Al12N12 electrides [40]. The small transition energies of

crucial excited states of these isomers are responsible for the large first hyperpolarizability

response. As shown in Table 3, In Li2F@Al12P12 series, isomers C (1.29 eV) and D (1.39 eV)

have lower crucial excitation energies than isomers A (1.68 eV) and B (1.67 eV). Thus, the

smaller ΔE of isomer C and D is the main controlling factor for the larger first

hyperpolarizability (βo) value as compared to the other two isomers. Similarly, in Li3O@Al12P12

series, isomer E has much smaller ΔE of 1.28 eV than others (1.53-1.97 eV). Therefore, isomer

E exhibits much larger hyperpolarizability response compared to other isomers. Isomer J of

Li4N@Al12P12 series is an exception as it exhibits much larger hyperpolarizability as well as

larger crucial excitation energy. In Li4N@Al12P12 series oscillator strength of crucial excited

state is the dominant factor affecting hyperpolarizability response.

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4. Conclusions

A series of superalkalis (Li2F, Li3O and Li4N) doped aluminum phosphide (Al12P12) nanocages

are designed and investigated through density functional theory method. It is found that these

doped systems with electride feature have maintained structural integrity of nanocage. The

electride features of these species are verified from the analysis of electronic structures and

HOMOs. These inorganic electrides, superalkali@Al12P12 clusters are thermodynamically highly

stable as evident from their large interaction energies (Eint). The highest interaction energy (Eint =

-105.13 kcal mol-1

) is calculated for the isomer J of Li4N@Al12P12 complex. The doping of

superalkali on nanocage dramatically reduces the HOMO-LUMO energy gap (EH-L). The EH-L of

the most stable cluster J is only 0.44 eV which suggests its conductivity is comparable to metals.

This reduced EH-L leads to prominent changes in the nonlinear optical response. A quite

remarkable nonlinear optical response is observed for isomer J (first hyperpolarizability βo =

6.25 x 104 au). Regardless of the nature of superalkali doped, the HOMO-LUMO gaps of all

complexes are reduced significantly compared to pure nanocage as well as βo values of the

considered structures increases up to several orders of magnitude. Also, it was observed that

Li4N gives better hyperpolarizability enhancement with Al12P12 nanocage as compared to Li3O

and Li2F.

ACKNOWLEDGEMENT

This study was supported by Higher Education Commission of Pakistan under HEC indigenous

fellowship to Faizan Ullah (315-19560-2PS3-146).

Supplementary information

Supplementary data associated with current article can be found online at http://dx.doi.org/

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Graphical abstract

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Highlights

Li2F@Al12P12, Li3O@Al12P12 and Li4N@Al12P12 complexes are investigated for

electronic and NLO properties.

FMOs and charge analyses are indicative of resultant isomers can act as inorganic

electrides and transparent in deep UV region.

HOMO-LUMO gap of Li4N@Al12P12 is decreased up to 0.44eV, which suggests its

conductivity comparable to metals.

Polarizability and hyperpolarizability values of Li4N@Al12P12 are 899.06 au and

6.25×104

au, respectively.

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Accepted Manuscript - Faizan Ullah · Accepted Manuscript Superalkalis as a source of diffuse...

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