88
2 Actual Potentials of Theoretical Chemistry: What Can Be Obtained
molecules have two SOMO’s being nearly degenerated. As a matter of fact, the
calculated E ST values of these become positive guaranteeing stability of the triplet
state as listed in Table 2.24. Atomic spin densities listed in Table 2.25 show alternative spin alignment due to spin polarization in the both MQDM and MPD
2+ where
C
1 , C
3 , C
5 , C
11 (N
11 in MPD
2+ ), and C
12 (N
12 in MPD
2+ ) possess large α spins as
expected in this molecular design. It is rather interesting that N
11 and N
12 in MPD
2+
have negative atomic net charges in spite of dicationic species. Instead, the hydrogen
atoms H
7 , H
9 , and H
10 attached to nitrogen atoms are rather protonic, the tendency
of which is also seen in MQDM. Distribution of the atomic spin densities is shown
in Fig. 2.84. Basic idea presented here can be applicable to molecular design toward
higher spin state. In fact, attempt to obtain higher spin state such as quartet state has
been published elsewhere (Yoshizawa et al. 1993; Ito et al. 1998). Further extensive
Table 2.24 Comparison of the singlet and triplet states of MQDM and MPD 2+ based on
DFT/B3LYP/6-31+G** calculations
Multiplicity
Symmetry
Electronic state
E ST (kcal/mol) a
MQDM
Closed-shell singlet
C 2v
1 A 1
29.50
Open-shell triplet
C 2v
3 B 2
MPD 2+
Closed-shell singlet
C 2v
1 A 1
8.53
Open-shell triplet
C 2v
3 B 2
a Positive value signifies stabilization of the triplet state (see text)
Table 2.25 Atomic net charges and atomic spin densities of MQDM and MPD 2+ based on
DFT/B3LYP/6-31+G** calculations a
Atom No.
MQDM
MPD 2+
Atomic net charge
Atomic spin
density
Atomic net charge
Atomic spin
density
C 1 , C 3
−0.2018
0.3801
−0.1226
0.3863
C 2
−0.2585
−0.1637
−0.1672
−0.1070
C 4 , C 6
−0.1449
−0.1780
0.1888
−0.0340
C 5
−0.1642
0.4491
−0.0388
0.6171
H 7 , H 9
0.2415
−0.0116
0.3112
−0.0116
H 8
0.2497
0.0047
0.3289
0.0027
H 10
0.2351
−0.0135
0.2940
−0.0178
C 11 , C 12
(N 11 , N 12 ) b
−0.3604
0.7103
−0.5685
0.4344
H 13 , H 16
0.2173
−0.0196
0.4944
−0.0114
H 14 , H 15
0.2171
−0.0195
0.4881
−0.0112
Total
0
2
2
2
a From natural population analyses
b For MPD 2+
2 Actual Potentials of Theoretical Chemistry: What Can Be Obtained
molecules have two SOMO’s being nearly degenerated. As a matter of fact, the
calculated E ST values of these become positive guaranteeing stability of the triplet
state as listed in Table 2.24. Atomic spin densities listed in Table 2.25 show alternative spin alignment due to spin polarization in the both MQDM and MPD
2+ where
C
1 , C
3 , C
5 , C
11 (N
11 in MPD
2+ ), and C
12 (N
12 in MPD
2+ ) possess large α spins as
expected in this molecular design. It is rather interesting that N
11 and N
12 in MPD
2+
have negative atomic net charges in spite of dicationic species. Instead, the hydrogen
atoms H
7 , H
9 , and H
10 attached to nitrogen atoms are rather protonic, the tendency
of which is also seen in MQDM. Distribution of the atomic spin densities is shown
in Fig. 2.84. Basic idea presented here can be applicable to molecular design toward
higher spin state. In fact, attempt to obtain higher spin state such as quartet state has
been published elsewhere (Yoshizawa et al. 1993; Ito et al. 1998). Further extensive
Table 2.24 Comparison of the singlet and triplet states of MQDM and MPD 2+ based on
DFT/B3LYP/6-31+G** calculations
Multiplicity
Symmetry
Electronic state
E ST (kcal/mol) a
MQDM
Closed-shell singlet
C 2v
1 A 1
29.50
Open-shell triplet
C 2v
3 B 2
MPD 2+
Closed-shell singlet
C 2v
1 A 1
8.53
Open-shell triplet
C 2v
3 B 2
a Positive value signifies stabilization of the triplet state (see text)
Table 2.25 Atomic net charges and atomic spin densities of MQDM and MPD 2+ based on
DFT/B3LYP/6-31+G** calculations a
Atom No.
MQDM
MPD 2+
Atomic net charge
Atomic spin
density
Atomic net charge
Atomic spin
density
C 1 , C 3
−0.2018
0.3801
−0.1226
0.3863
C 2
−0.2585
−0.1637
−0.1672
−0.1070
C 4 , C 6
−0.1449
−0.1780
0.1888
−0.0340
C 5
−0.1642
0.4491
−0.0388
0.6171
H 7 , H 9
0.2415
−0.0116
0.3112
−0.0116
H 8
0.2497
0.0047
0.3289
0.0027
H 10
0.2351
−0.0135
0.2940
−0.0178
C 11 , C 12
(N 11 , N 12 ) b
−0.3604
0.7103
−0.5685
0.4344
H 13 , H 16
0.2173
−0.0196
0.4944
−0.0114
H 14 , H 15
0.2171
−0.0195
0.4881
−0.0112
Total
0
2
2
2
a From natural population analyses
b For MPD 2+