Table.1. Bond distances (Å) of bi-metal doped alkali metal atoms with nearest boron atom (dM-B) and phosphorus atom (dM-P) and NBO charges (q) of both doped alkali metal atoms.
Complexes
|
dM-B
|
dM-P
|
dM-B
|
dM-P
|
NBO charges
|
|
M25
|
M26
|
M25
|
M26
|
Li2@b64
|
2.17
|
2.55
|
2.11
|
2.67
|
0.86
|
0.91
|
Li2@b66
|
2.5
|
2.46
|
2.16
|
2.51
|
0.92
|
0.85
|
Li2@r6
|
2.52
|
2.48
|
2.52
|
2.48
|
0.91
|
0.91
|
Li2@B
|
2.11
|
2.51
|
2.50
|
2.46
|
0.85
|
0.92
|
Li2@P
|
3.73
|
2.41
|
3.73
|
2.41
|
0.71
|
0.71
|
Na2@b66
|
2.46
|
2.98
|
2.46
|
2.98
|
0.90
|
0.91
|
Na2@r6
|
2.98
|
2.83
|
2.98
|
2.83
|
0.91
|
0.91
|
Na2@r4
|
2.99
|
2.74
|
2.99
|
2.74
|
0.87
|
0.87
|
Na2@P
|
4.15
|
2.79
|
4.15
|
2.79
|
0.56
|
0.57
|
K2@b64
|
2.86
|
3.38
|
2.86
|
3.37
|
0.91
|
0.91
|
K2@b66
|
2.86
|
3.38
|
2.86
|
3.38
|
0.92
|
0.92
|
K2@r6
|
3.41
|
3.22
|
3.41
|
3.22
|
0.94
|
0.94
|
Table.2. Interaction energies (Eads), dipole moment (µ) and symmetry of pristine and bi-metal doped nanocage
|
Eads (kcal/mol)
|
Dipole moment (Debye)
|
Symmetry
|
Complexes
|
Li
|
Na
|
K
|
Li
|
Na
|
K
|
Li
|
Na
|
K
|
M2@b64
|
-43.2
|
-
|
-31.7
|
7.33
|
-
|
11.18
|
C1
|
-
|
C1
|
M2@b66
|
-49.4
|
-20.4
|
-31.9
|
3.85
|
0.14
|
0.02
|
C1
|
C1
|
C1
|
M2@r6
|
-43.4
|
-22.6
|
-34.7
|
0.0004
|
0.001
|
0.01
|
C1
|
C1
|
C1
|
M2@r4
|
-
|
-18.5
|
-
|
-
|
0.03
|
-
|
-
|
C1
|
-
|
M2@B
|
-49.3
|
-
|
-
|
3.85
|
-
|
-
|
C1
|
-
|
-
|
M2@P
|
-22.6
|
-12.4
|
-
|
0.001
|
0.01
|
-
|
C1
|
C1
|
-
|
Table.3. Energy of HOMO and LUMO (EHOMO), ELUMO), Fermi levels (EFL) and HOMO-LUMO gap (Eg) of bare and bi-metal doped boron phosphide complexes.
Complexes
|
EHOMO (eV)
|
ELUMO (eV)
|
EFL (eV)
|
Eg (eV)
|
B12P12
|
-6.83
|
-3.13
|
-4.9
|
3.7
|
|
Li
|
Na
|
K
|
Li
|
Na
|
K
|
Li
|
Na
|
K
|
Li
|
Na
|
K
|
M2@b64
|
-4.06
|
-
|
-3.016
|
-2.53
|
-
|
-1.84
|
-3.29
|
-
|
-2.42
|
1.53
|
-
|
1.17
|
M2@b66
|
-4.48
|
-3.38
|
-2.97
|
-2.47
|
-2.21
|
-1.87
|
-3.5
|
-2.80
|
-2.42
|
2.01
|
1.16
|
1.09
|
M2@r6
|
-3.74
|
-3.50
|
-2.95
|
-2.15
|
-1.91
|
-1.80
|
-2.95
|
-2.71
|
-2.37
|
1.6
|
1.58
|
1.15
|
M2@r4
|
-
|
-3.19
|
-
|
-
|
-2.24
|
-
|
-
|
-2.71
|
-
|
-
|
0.95
|
-
|
M2@B
|
-4.48
|
-
|
-
|
-2.47
|
-
|
-
|
-3.47
|
-
|
-
|
2.01
|
-
|
-
|
M2@P
|
-3.15
|
-3.18
|
-
|
-2.51
|
-2.62
|
-
|
-2.83
|
-2.90
|
-
|
0.63
|
0.56
|
-
|
Table.4. Polarizability (α), first hyperpolarizability (βₒ) and crucial transition state composition of complexes (CT).
|
(au)
|
βₒ (au)
|
CT
|
B12P12
|
402
|
-
|
|
Complexes
|
Li
|
Na
|
K
|
Li
|
Na
|
K
|
Li
|
Na
|
K
|
M2@b64
|
522.20
|
-
|
634.69
|
1.4×103
|
-
|
1.4×104
|
H→L
|
|
H→L
|
M2@b66
|
455.58
|
595.06
|
632.89
|
1.47×103
|
6.1×102
|
62.93
|
H→L+4
|
H→L
|
H→L
|
M2@r6
|
534.73
|
577.65
|
602.45
|
2.14
|
21.73
|
65.72
|
H→L+7
|
H→L+8
|
H→L+8
|
M2@r4
|
-
|
668.95
|
-
|
-
|
3.2×102
|
-
|
-
|
H→L
|
-
|
M2@B
|
1016.21
|
595.29
|
-
|
1.6×103
|
39.89
|
-
|
H→L+4
|
-
|
-
|
M2@P
|
996.52
|
1300.37
|
-
|
39.29
|
469.14
|
-
|
H→L
|
H→L
|
|
Table.5. The largest oscillator strength (f0), transition energy (ΔE) and maximum absorption wavelength (λmax) of complexes
Complexes
|
f0
|
λmax (nm)
|
ΔE(eV)
|
|
Li
|
Na
|
K
|
Li
|
Na
|
K
|
Li
|
Na
|
K
|
M2@b64
|
0.122
|
|
0.201
|
984.24
|
|
1122.69
|
1.25
|
|
1.10
|
M2@b66
|
0.033
|
0.097
|
0.147
|
532.46
|
1384.5
|
1272.3
|
2.32
|
0.89
|
0.97
|
M2@r6
|
0.097
|
0.110
|
0.118
|
710.21
|
712.37
|
720.92
|
1.75
|
1.74
|
1.71
|
M2@r4
|
|
0.156
|
|
|
1185.85
|
|
|
1.04
|
|
M2@B
|
0.033
|
|
|
532.59
|
|
|
2.32
|
|
|
M2@P
|
0.176
|
0.399
|
|
2359.1
|
1980.5
|
|
0.52
|
0.62
|
|
Table.6.The AIM topological variables of bi-metal doped complexes.
Structure
|
Metal
|
Interaction
|
ρ
|
∇2 ρ
|
G(r)
|
V(r)
|
H(r)
|
-G(r)/V(r)
|
Li2@b64
|
A
|
Li-B
|
0.2395
|
0.1064
|
0.2514
|
-0.2367
|
0.1474
|
1.0621
|
B
|
Li-B
|
0.2578
|
0.1174
|
0.2775
|
-0.2613
|
0.1619
|
1.0620
|
Li2@b66
|
A
|
Li-P
|
0.1623
|
0.7708
|
0.1680
|
-0.1434
|
0.2461
|
1.1715
|
Li-P
|
0.1457
|
0.6938
|
0.1494
|
-0.1254
|
0.2403
|
1.1913
|
Li-P
|
0.1607
|
0.7641
|
0.1656
|
-0.1402
|
0.2539
|
1.1811
|
B
|
Li-B
|
0.2476
|
0.1141
|
0.2668
|
-0.2483
|
0.1845
|
1.0745
|
Li2@r6
|
A
|
Li-P
|
0.1578
|
0.7477
|
0.1621
|
-0.1372
|
0.2481
|
1.1814
|
Li-P
|
0.1578
|
0.7478
|
0.1621
|
-0.1373
|
0.2481
|
1.1806
|
Li-P
|
0.1578
|
0.7480
|
0.1621
|
-0.1373
|
0.2482
|
1.1806
|
B
|
Li-P
|
0.1579
|
0.7483
|
0.1622
|
-0.1374
|
0.2483
|
1.1804
|
Li-P
|
0.1577
|
0.7474
|
0.1620
|
-0.1372
|
0.2481
|
1.1807
|
Li-P
|
0.1578
|
0.7478
|
0.1621
|
-0.1373
|
0.2482
|
1.1806
|
Li2@B
|
A
|
Li-P
|
0.1625
|
0.7719
|
0.1683
|
-0.1437
|
0.2464
|
1.1711
|
Li-P
|
0.1461
|
0.6957
|
0.1498
|
-0.1257
|
0.2407
|
1.1917
|
Li-P
|
0.1607
|
0.7642
|
0.1656
|
-0.1402
|
0.2541
|
1.1811
|
B
|
Li-B
|
0.2477
|
0.1141
|
0.2670
|
-0.2485
|
0.1843
|
1.0744
|
Li2@P
|
A
|
Li-P
|
0.2358
|
0.9555
|
0.2191
|
-0.1994
|
0.1970
|
1.0988
|
B
|
Li-P
|
0.2358
|
0.9556
|
0.2192
|
-0.1995
|
0.1970
|
1.0987
|
Na2@b66
|
A
|
Na-B
|
0.1900
|
0.8372
|
0.1916
|
-0.1739
|
0.1768
|
1.1017
|
B
|
Na-B
|
0.1898
|
0.8381
|
0.1916
|
-0.1737
|
0.1786
|
1.1030
|
Na2@r6
|
A
|
Na-P
|
0.1218
|
0.5468
|
0.1185
|
-0.1004
|
0.1815
|
1.1802
|
Na-P
|
0.1218
|
0.5467
|
0.1185
|
-0.1003
|
0.1814
|
1.1814
|
Na-P
|
0.1216
|
0.5459
|
0.1183
|
-0.1002
|
0.1812
|
1.1806
|
B
|
Na-P
|
0.1216
|
0.5460
|
0.1183
|
-0.1002
|
0.1813
|
1.1806
|
Na-P
|
0.1218
|
0.5467
|
0.1185
|
-0.1003
|
0.1814
|
1.1814
|
Na-P
|
0.1218
|
0.5471
|
0.1186
|
-0.1004
|
0.1815
|
1.1812
|
Na2@r4
|
A
|
Na-P
|
0.1522
|
0.6833
|
0.1501
|
-0.1295
|
0.2063
|
1.1590
|
Na-P
|
0.1069
|
0.4849
|
0.1042
|
-0.8732
|
0.1695
|
0.1193
|
B
|
Na-P
|
0.1526
|
0.6853
|
0.1506
|
-0.1299
|
0.2068
|
1.1593
|
Na-P
|
0.1507
|
0.6761
|
0.1485
|
-0.1280
|
0.2047
|
1.1601
|
Na2@P
|
A
|
Na-P
|
0.1754
|
0.6739
|
0.1495
|
-0.1306
|
0.1891
|
1.1447
|
B
|
Na-P
|
0.1752
|
0.6724
|
0.1492
|
-0.1303
|
0.1887
|
1.1450
|
K2@b64
|
A
|
K-B
|
0.1531
|
0.5273
|
0.1227
|
-0.1136
|
0.9108
|
1.0801
|
B
|
K-B
|
0.1532
|
0.5275
|
0.1227
|
-0.1136
|
0.9101
|
1.0801
|
K2@b66
|
A
|
K-B
|
0.1546
|
0.5259
|
0.1228
|
-0.1141
|
0.8675
|
1.0762
|
B
|
K-B
|
0.1547
|
0.5264
|
0.1229
|
-0.1142
|
0.8673
|
1.0761
|
K2@r6
|
A
|
K-P
|
0.1060
|
0.3856
|
0.8218
|
-0.6796
|
0.1421
|
1.2092
|
K-P
|
0.1063
|
0.3866
|
0.8243
|
-0.6821
|
0.1421
|
1.2084
|
K-P
|
0.1061
|
0.3857
|
0.8221
|
-0.6799
|
0.1421
|
1.2091
|
B
|
K-P
|
0.1064
|
0.3866
|
0.8245
|
-0.6823
|
0.1421
|
1.2084
|
K-P
|
0.1060
|
0.3855
|
0.8217
|
-0.6795
|
0.1421
|
1.2092
|
K-P
|
0.1059
|
0.3851
|
0.8207
|
-0.6785
|
0.1421
|
1.2095
|