4P090

Density matrix renormalization group method for prediction ofhyperfine structure
Tran Nguyen Lan,1 Yuki Kurashige,1,2 and Takeshi Yanai1,2
1The Graduate University for Advanced Studies, Okazaki, Aichi 444-8585
2Institute for Molecular Science, Okazaki, Aichi 444-8585
E-mail: lantran@ims.ac.jp

Despite all recent progress, the accuracy of hyperfine coupling constants (HFCCs) is stillchallenging for quantum chemistry. In this work, we have performed the density matrix
renormalization group (DMRG) calculations to predict the HFCCs of several π−radicals: BO,
CO+, CN, and AlO. The DMRG algorithm used herein was considered as a near fullconfiguration interaction (FCI) method and the electron correlation effects weresystematically investigated using the complete active space (CAS) procedures, i.e CASSCF
and CASCI. The geometry of radicals has been adapted from experiments. The EPR-III basis
set was used for C, O, and N elements, while the IGLO-III basis set was used for Al element.
Although the HFCCs of BO and CO+ calculated by conventional methods, i.e. density
functional theory (DFT) and coupled cluster (CC), were already in the acceptable agreementswith experimental values, our DMRG calculations have pushed the accuracy of HFCCsfurther. For CN radical, our DMRG calculation has captured the high-order effect ofcorrelation treatment. Regarding AlO radical, our DMRG calculation properly described themulti-reference problem resulting from the balance between ionic states. Therefore, theHFCCs of C center in CN and Al center in AlO are in the good agreements with experimentalvalues.
Concerning the CAS-type procedure, most CASCI calculations provided the poor agreementswith experimental values, while the quite accurate HFCCs of less electronegative centers canbe found when the orbital optimization procedure was employed with the same CAS. Thesesituations can be attributed to the nature of one-particle bases in which the DMRG
calculations were performed. The canonical Hatree-Fock (HF) orbitals were used as theorbital bases for the DMRG-CASCI calculation. Whereas, the DMRG calculation inconjunction with CASSCF procedure was performed on much more compact orbitals whichwere obtained through orbital optimization procedure.
In summary, our results have confirmed that it is critical to correlate the core electrons tocorrectly obtain the spin density at the nucleus. Additionally, the inclusion of polarization
shells is necessary for describing the dynamical correlation, which makes the proper spinpolarized effects. Finally, the assessment for the convergence of HFCCs with respect to thenumber of renormalized states M indicates that the acceptable result can be obtained even if
total energy is not converged with respect to M.

Table 9: Hyperfine coupling constants (in MHz) for 2 AlO molecule. The IGLO-III and EPR-III
basis sets were used for Al and O, respectively. The total number of AOs is of 84. For comparison,
we also adapted the CCSD and CCSD(T) results calculated by Kossmann and Neese.
27 AlMethods

17 O

A(K;c)

A(K;d)
11

A(K;d)
22

A(K;d)
33

A(K;c)

A(K;d)
11

A(K;d)
22

A(K;d)
33

DMRG-CASCI(21e,36o)

710.91

46.45

46.62

93.06

1.82

44.98

44.89

89.87

DMRG-CASSCF(21e,36o)

722.73

54.19

54.09

109.28

15.06

50.73

50.43

101.16

B3LYP

512.2159.9759.97

119.93

8.17

66.22

66.22

132.43TPSS

656.79

56.10

56.10

112.21

9.52

59.91

59.91

119.83

BP

653.71

56.86

56.86

113.72

14.21

59.60

59.60

119.20

CCSD

482.40

57.20

57.20

114.30

18.10

63.80

63.80

127.70

CCSD(T)

565.30

56.20

56.20

112.40

19.30

58.90

58.90

117.80Exp

gas-phase

738

5656

112

Exp

Ne-matrix

766

52

52

104

50

100n/a250

HFCCs (in MHz) for AlO radical. The IGLO-III and EPR-III basis sets were used for Aland O, respectively. The total number of AOs is of 84.
Table 11: The convergence of total energy, Fermi contact term, and spin-dipole term at C centerwith respect to number of renormalized states M. For the spin-dipole term we only present the firstelement. The active space is CAS(13e,30o). The convergent MOs of DMRG-CASSCF(13e,30o)
calculation with M = 512 was used as the reference for the other DMRG calculations 0.7
and only
AlDMRG-CASSCF(15e,33o)
CASCI procedure was performed for these calculations.
0.6
Energy (Eh )A(K;c) (MHz)A(K;d)
11 (MHz)128

92.570835

576.8053.18

25692.575539563.79

52.97

51292.577510

561.95

52.92

1024

92.578114

559.4452.86

0.5

ρα -β (a.u.)M

DMRG-CASSCF(21e,31o)
DMRG-CASSCF(21e,36o)

0.4
0.3
0.2

O

0.1

The convergence of total energy, Fermi
0contact term, and spin-dipole term at C-1
01
23
4
center (CN) with respect to number ofz-axis (a.u.)
renormalized states M. The active space is↵
Figure1: Spin density distribution of SNO with largest ni of AlO radical. The results were calcuCAS(13e,30o). The EPR-III basis setwasSpin density distribution of spin natural
lated by DMRG-CASSCF(15e,33o), DMRG-CASSCF(21e,31o), and DMRG-CASSCF(21e,36o).
used.	  orbital (SNO) with largest spin
occupation number of AlO radical. The
geometry of AlO radical (in Bohr) are:O(0.000, 0.000, 0.000) and Al(0.000,0.000, 3.057)

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