1

DFT Study of Hyperfine DFT Study of Hyperfine Interactions in Some Types of Interactions in Some Types of

the Complexesthe ComplexesOleg Poleshchuk, Natalya Khramova,

Alexander FateevTomsk State Pedagogical University,

Russia

2

Geometry optimizationGeometry optimizationSO3-B complexes

B3PW91/6-311+G(df,pd)BP86/TZ2P+ in ADF

XY-B complexes

BHandHLYP/aug-cc-pVTZ 3-21G*,DGDZVP (iodine)BP86E/TZ2P+(ZORA) in ADF

MHal-B complexes

B3LYP/SDD, B3LYP/DGDZVP BP86/TZ2P+(ZORA) in ADF

3

Bond LengthsBond Lengths Complex RD-A, Å Complex RD-A, Å

Exp. Cal. Exp. Cal.HCN.SO3 2.577 2.538 ICl.CO 3.011 2.960H3N.SO3 1.957 2.053 ICl.NH3 2.711 2.600Py.SO3 1.915 1.983 ICl.Py 2.290 2.519(CH3)3N.SO3 1.912 1.997 I2

.Py 2.310 2.644Cl2

.NH3 2.730 2.685 AuCl.CO 2.217 2.259SbCl5

.OPMe3 1.94 2.11 AuCl.Ar 2.198 2.261SnCl4

.(OSMe2)2 2.11 2.24 AgBr.CO 2.373 2.400TiCl4

. (CH3CN)2 2.21 2.28 AgBr.Ar 2.393 2.427TiCl4

. (OPCl3)2 2.22 2.20 CuF.CO 1.736 1.758ICl.Ar 3.576 3.761 CuBr.CO 2.182 2.225

4

• A comparison of the geometrical para-meters calculated by us with the experimental data of free molecules and complexes displays that the bond lengths have been overestimated.

• Analysis leads to the following corre-lations between the calculated and experimental bond lengths and valence angles for the compounds studied.

5

SOSO33-В-В complexes complexes

1,9 2,0 2,1 2,2 2,3 2,4 2,5 2,6 2,71,9

2,0

2,1

2,2

2,3

2,4

2,5

2,6SO3HCN

SO3HCCCN

SO3(HCN)2

SO3MeCN

(HCN)2

(HCN)3

SO3PySO3NMe3

SO3NH3

Calc

ulat

ed b

ond

leng

th, А

Experimental bond length, А

R(cal.) = 0.46 + 0.79 R(exp.) (r=0.991; s=0.03; n=9)

Correlation between experimental and calculated at B3PW91/6-311+G(df,pd) level bond lengths.

92 94 96 98 100

92

93

94

95

96

97

98

99

SO3NMe3

SO3Py

SO3NH3

SO3(HCN)2

SO3MeNSO3HCN

SO3HCCCNCalc

ulat

ed d

egre

e NS

O,

0

Experimental degree NSO, 0

NSO(cal.) = 23.3 + 0.75 NSO(exp.) (r=0.999; s=0.16; n=7)

Correlation between experimental and calculated at B3PW91/6-311+G(df,pd) level valence degree.

6

Dependence between experimental and calculated at BHandHLYP/aug-cc-pVTZ level bond lengths.

XYXY--B complexesB complexes

1,6 1,8 2,0 2,2 2,4 2,6 2,8 3,0 3,2

1,6

1,8

2,0

2,2

2,4

2,6

2,8

3,0

3,2

Rcal. = 0,13 + 0,94 Rexp. (r=0,994; s=0,04; n=21)

Calc

ulat

ed b

ond

leng

th, А

Experimental bond length, А

7

HalM-L complexesHalM-L complexes

1,6 1,8 2,0 2,2 2,4 2,6 2,8 3,01,6

1,8

2,0

2,2

2,4

2,6

2,8

3,0

Rcal.=0.13+0.92Rexp. (r=0.999; s=0.01; n=27)

Calc

ulat

ed b

ond

leng

th,A

Experimental bond length,A

Dependence between experimental andcalculated at B3LYP/dgdzvp level bondlength in Au,Ag,Cu complexes

8

HalM-L complexes

2,10 2,15 2,20 2,25 2,30 2,35 2,40 2,45 2,50 2,552,05

2,10

2,15

2,20

2,25

2,30

2,35

2,40

2,45

Rcal.=0.2+0.89Rexp. (r=0.982; s=0.02; n=22)

Calc

ulat

ed b

ond

leng

th,A

Experimental bond length,A

Correlation between the calculated atB3LYP/DGDZVP and experimental bond lengthsfor the Nb, Sb and Ta compounds

9

Rotational constantsRotational constantsComplex В0, MHz Complex В0, MHz

Exp. Cal. Exp. Cal.

H3N.SO3 4378 4189 ClF.CH3CN 919 919

(CH3)3N.SO3 1633 1585 ICl.CO 903 888

HCN.SO3 409 445 ICl.NH3 1608 1604

CH3CN.SO3 1016 1038 AuCl 3519 3306

HCCCN.SO3 655 665 AuClCO 1404 1367

(HCN)2.SO3 409 419 CuClCO 1563 1527

Cl2.NH3 1895 1890 CuBrCO 1034 1011

ClF.NH3 3316 3328 AgClCO 1316 1299

BrCl.NH3 1801 1815 AgBrCO 852 840B0(cal.) =-38 + 1.05 B0(exp.) (r=0.9999; s=14; n=7)

for SO3 complexes

B0(cal.) = 10.7 + 0.99 B0(exp.) (r=0.9999; s=34; n=22) for halogen complexes

В0(cal.) = 15.1 + 0,95 В0(exp.) (r = 0.998; s = 49; n = 13) for metal complexes

10

0 200 400 600 800 1000 1200 14000

200

400

600

800

1000

1200

1400

(cal.)=9+1.04(exp.) r=0.999;s=20;n=24

Calc

ulat

ed fr

eque

ncy,

cm-1

Experimental frequency,cm-1

Correlation between experimental and calculated at B3LYP/dgdzvp level IR-frequencies in SO3and halogen complexes

11

• The halogen, metal and nitrogen nuclear quadrupole coupling constants obtained by these calculations substantially corresponded to the data of microwave spectroscopy in the gas phase. An analysis of the quality of the calculations that employ the pseudo-potential and the expanded basis set for the halogen compounds was carried out. The ZORA model is

• shown to be a viable alternative to the computa-• tionally demanding pseudo-potential model for

the calculation of the iodine and metal (Nb, Au, Sb) quadrupole coupling constants in molecules.

12

NQCC NQCC 1414N inN in SOSO33 complexes complexes

0

1

2

3

4

5

HCN HCCCN СН3CN H3N Py (CH3)3N

Bases

NQ

CC

N, M

Hz

Exp.GaussADF

NQCC nitrogen changing by complex formation

0

1

2

3

4

5

HCN HCCCN СН3CN H3N Py (CH3)3N

NQCC

N b

ase

min

us c

ompl

ex

Exp.

Gauss

ADF

-6 -5 -4 -3 -2 -1

-6

-5

-4

-3

-2

-1

NH3

MeCNHCCCN

(HCN)2Py

NMe3

SO3HCN

(HCN)3

SO3(HCN)2

SO3HCCCN

SO3MeCN

SO3NH3

SO3NMe3

SO3Py

e2 Qq zz

-14N(

cal.)

,MHz

e2Qqzz-14N(exp.),MHz

Correlation between experimental and calculated at B3PW91/6-311+G(df,pd) level 14N-NQCC in SO3 complexes.

e2QqzzN(cal.) =-0.09 + 1.05e2Qqzz

N(exp.) (r=0.989; s=0.2; n=18)

e2QqzzN (cal.) =-0.05 + 0.96 e2Qqzz

N (exp.)

(r = 0.970; s = 0.3; n = 11)from ADF calculations

13

1414N-NQCC in nitrogen moleculesN-NQCC in nitrogen molecules

Dependence between experimental and calculated at BP86/TZ2P+ level NQCC values of N nuclei in nitrogen molecules

e2Qq(exp.) = -0.3 + 0.94 e2Qq (cal.)

(r = 0.997; s = 0.2; n = 27)

-8 -6 -4 -2 0 2 4 6-8

-6

-4

-2

0

2

4

6

Expe

rimen

tal 14

N- N

QCC

,MHz

Calculated 14N- NQCC,MHz

14

1717O-NQCC in oxygen moleculesO-NQCC in oxygen molecules

Dependence between experimental and calculated at BP86/TZ2P+ level NQCC values of O nuclei in oxygen molecules

e2Qq(exp.) = 0.1 + 0.99 e2Qq (cal.)

(r = 0.997; s = 0.5; n = 17)

-10 -5 0 5 10 15-10

-5

0

5

10

15

Expe

rimen

tal 17

O- N

QCC

,MHz

Calculated 17O- NQCC,MHz

15

NQCC in XY-B complexesNQCC in XY-B complexes

Dependence between experimental and calculated at BHandHLYP/aug-cc-pVTZ level NQCC values of Cl, Br, N nuclei in XY-B complexes

e2Qq(cal.) = 0.7 + 1.005 e2Qq (exp.)

(r = 0.9999; s = 3.4; n = 35)

-200 0 200 400 600 800 1000

-200

0

200

400

600

800

1000

Calc

ulat

ed 14

N- N

QCC

,MHz

Experimental 14N- NQCC,MHz

16

-3000 -2500 -2000 -1500 -1000

-3600

-3400

-3200

-3000

-2800

-2600

-2400

-2200

NQCC(cal.)=-1475+0.65NQCC(exp.)r=0.961;s=125;n=12

e2 Qq zz

(cal

.) M

Hz

e2Qqzz (exp.) MHz

Dependence between calculated and experimental 127I-NQCC values of the XY...B(XY=I) complexes at B3LYP/dgdzvp level

NQCC iodine nucleiNQCC iodine nuclei

Dependence between calculated and experimental 127I-NQCC values of the XY...B(XY=I) complexes at ZORA in ADF

-3200 -3000 -2800 -2600 -2400 -2200 -2000 -1800

-3000

-2500

-2000

-1500

-1000

NQCC(cal.)=1600+1.6NQCC(exp.)r=0.992;s=75;n=17

e2 Qqz

z (c

al.)

MHz

e2Qqzz (exp.) MHz

17

3535Cl- NQCC in XY-B complexesCl- NQCC in XY-B complexes

Dependence between experimental and calculated at BP86/TZ2P+ level NQCC values of Cl and Br nuclei in XY-B complexes

e2Qq(exp.) = -5.1 + 1.05 e2Qq (cal.)

(r = 0.997; s = 3.5; n = 48)

0 50 100 150 200

0

50

100

150

200

250

n35Cl

,79Br

(exp

.),M

Hz

n35Cl,79Br(cal.),MHz

18

50 100 150 200 250 300 350 400 450 500

50

100

150

200

250

300

350

400

450

QCC Sb(exp)=-13+0.9QCC Sb(cal.)r=0.994;s=11;n=11

e2 Qq zz

121 Sb

(exp

.),M

Hz

e2Qqzz121Sb(cal.),MHz

Calculated at B3LYP/dgdzvp versusexperimental 121Sb compounds

19

40 60 80 100 120 140 160 180 200100

150

200

250

300

350

400

QCC Sb(exp)=35+1.8QCC Sb(cal.)r=0.992;s=10;n=13

e2 Qq zz

121 Sb

(cal

.),M

Hz

e2Qqzz121Sb(exp.),MHz

Calculated at BP86/TZ2P+(ZORA) versusexperimental 121Sb compounds

20

60 80 100 120 14020

40

60

80

100

120

QCC Nb(exp)=-44+1.1QCC Nb(cal.)r=0.993;s=4;n=6

e2 Qq zz

93Nb

(exp

.),M

Hz

e2Qqzz93Nb(cal.),MHz

Calculated at B3LYP/dgdzvp versusexperimental 93Nb compounds

21

-1000 -500 0 500 1000 1500 2000

-1000

-500

0

500

1000

1500

2000

QCC Nb,Ta(exp)=2.9+1.01QCC Nb,Ta(cal.)r=0.9999;s=13;n=14

e2 Qq zz

93Nb

,181 Ta

(cal

.),M

Hz

e2Qqzz93Nb,181Ta(exp.),MHz

Calculated at BP86/TZ2P+(ZORA) versusexperimental 93Nb and 181Ta compounds

22

-1200 -1000 -800 -600 -400 -200 0 200-700

-600

-500

-400

-300

-200

-100

0

QCC Au(cal.)=2.9+1.01QCC Au(exp.)r=0.992;s=30;n=12

e2 Qq zz

197 Au

(cal

.),M

Hz

e2Qqzz197Au (exp.),MHz

Calculated at BP86/TZ2P+(ZORA) versusexperimental 197Au compounds

23

NQCC in Xe-B complexesNQCC in Xe-B complexes

Dependence between experimental and calculated at B3LYP/DGDZVP level NQCC values of Xe nuclei in Xe-B complexes

e2Qq(exp.) = -0.3 + 0.9 e2Qq (cal.)

(r = 0.987; s = 0.8; n = 6)

-10 -8 -6 -4 -2 0 2 4 6-10

-8

-6

-4

-2

0

2

4

6

Calculated 131Xe- NQCC,MHz

Expe

rimen

tal 13

1 Xe- N

QCC

,MHz

24

Energy decomposition analysis (kcal/mol)Energy decomposition analysis (kcal/mol) Complex Eprep. EPauli Eelectr. Eorb. De

ADF/D0gauss

HCN.SO3 0.86 22.44 -13.25 -10.57 0.5/4.2

HCCCN.SO3 0.94 23.4 -13.57 -11.13 0.4/3.5

(HCN)2.SO3 0.67 31.42 -18.79 -16.08 2.8/7.0

СН3CN.SO3 1.72 35.15 -21.05 -18.22 2.4/7.8

H3N.SO3 6.51 125.26 -76.37 -71.53 16.1/18.4

Py.SO3 9.98 153.33 -90.53 -89.73 17.0/23.1

(СН3)3N.SO3 11.55 162.94 -97.37 -97.49 20.4/28.7

25

• The Eelstat. term in all complexes is close to the Eorb term, although for weakly bound complexes the electrostatic interactions tend to be slightly larger than the covalent ones.

• The calculated values of the bonding energy in these complexes using the ADF package differ from those obtained at the B3PW91/6-311+G(df,pd) level. However, the variation from one system to another is similar:

• DeADF = -4.5 + 0.83 D06-311+G(df,pd) (r=0.990; s=1.4; n=7)

26

NBO analysis for SONBO analysis for SO33 complexes complexesComplex Orbital Occupaid Hybridization of S

atom (%)Eij

(2) (kcal/ mol)

Interaction between bonding and anti-bonding orbitalss p d

HCN.SO3 LP(N) 1.942 33.1 65.3 1.6 8.1 LP(N)BD*(S-O)

HCCCN.SO3 LP(N) 1.937 32.1 66.3 1.6 8.6 LP(N)BD*(S-O)

(HCN)2.SO3 LP(N) 1.920 31.2 67.0 1.8 13.1 LP(N)BD*(S-O)

СН3CN.SO3 LP(N) 1.906 33.0 65.3 1.7 15.4 LP(N)BD*(S-O)

H3N.SO3 BD(N-S) 1.888 17.7 43.5 38.8 93.1 BD(N-S)BD*(S-O)

Py.SO3 BD(N-S) 1.851 16.4 46.8 36.8 105.4 BD(N-S)BD*(S-O)

(СН3)3N.SO3 LP(O) 1.751 12.5 85.1 2.4 142.8 LP(O)BD*(N-S)

27

SO3…B complexes

• NBO second-order interaction energies of n-complexes shown that the LP(N) → π*SO3 (LP=lone electron pair) donor-acceptor interaction is the source of such intermolecular charge transfer.

• DeADF/kcal/mol = 5.4 + 0.2 Eij(2)/kcal/mol (r=0.998; s=0.7; n=7)

28

0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,350

5

10

15

20

25

30SO3NMe3

SO3Py

SO3NH3

SO3MeCN

SO3(HCN)2

SO3HCCCN

SO3HCN

D 0, kc

al/m

ol

charge transfer q(B--->X),eBonding energy versus charge transfer (NAO) for SO3 complexes

D0 = 2.3 + 70.4 q(r=0.985; s=1.9; n=7)

29

Bonding energy by ADF is close to outcomes at the BHandHLYP/aug-cc-pVTZ De

ADF =-0.1 + 0.9 Deaug-cc-pVTZ (r=0.995; s=0.5; n=7)

 Complex Eprep. EPauli Eelectr. Eorb. De RB-Ycal. Eij

(2)

IClAr 0.0 0.1 0.0 -0.2 0.1 4.433 1.0

IClCO 0.7 67.8 -34.3 -36.5 2.3 2.413 13.5

I2Py 0.4 48.6 -32.1 -25.6 8.7 2.564 36.4

IBrPy 1.7 44.9 -31.3 -24.9 9.6 2.576 45.2

I2N(СН3)3 1.8 50.0 -33.2 -28.4 9.7 2.601 40.2

IClNH3 1.3 45.2 -32.6 -24.1 10.1 2.576 53.5

IClPy 1.9 59.4 -40.9 -31.5 11.1 2.475 56.8

Energy decomposition and NBO analysis (kcal/mol)Energy decomposition and NBO analysis (kcal/mol)

30

ICl…B complexes• The Eelstat. term in all complexes is larger than the

Eorb term. This suggests that the Y-B bonding in these complexes is more electrostatic than covalent.

• NBO second-order interaction energies of n-complexes shown that the LP(B)*XY (LP=lone electron pair, B=N, C, Ar coordinated atom) donor-acceptor interaction is the source of such intermolecular charge transfer.

• DeADF/kcal/mol = 0.2 + 0.2 Eij

(2)/kcal/mol (r=0.978; s=1.0; n=7)

31

-0,02 0,00 0,02 0,04 0,06 0,08 0,10 0,12 0,14 0,16-2

0

2

4

6

8

10

12

14

De= 0,01 + 78,8 q (r=0,980; s=0,9; n=26)

D e, kc

al/m

ol

charge transfer q(B--->X),e

Dependence between De and electron transfer (NAO) in XY...B complexes

32

• The calculated bonding energies for both complexes are strongly correlated with the extent of electron transfer from base to the acceptor from the natural atomic charges.

• These correlations contrasts with the different situation found for the main group and transition metal complexes.

• Apparently, related to this is the observation that, according to our calculations, the electronic charge changes are significant only on the two atoms immediately involved in the intermolecular bond, while in metal chloride complexes such changes are appreciable on all atoms.

33

Complex ΔЕprep. ΔЕPauli ΔЕelectr. ΔЕorb. DeADF De

Gauss ΔЕij(2)

OC-CuCl 0.0 96.0 -80.5 -56.7 41.2 36.0 110

OC-AgCl -0.1 99.7 -77.6 -44.5 22.5 24.6 103

OC-AuCl -0.2 176.9 -139.4 -86.0 48.7 46.4 256

Py-CuCl 0.7 77.4 -80.5 -33.9 36.3 38.3 66

Py-AgCl 0.4 68.7 -66.2 -24.7 21.8 27.5 56

Py-AuCl 0.7 111.1 -102.6 -46.5 37.3 40.7 119

(СН3)3PO-CuCl 1.7 60.3 -63.6 -28.6 30.2 36.2 79

(СН3)3PO-AgCl 1.0 49.6 -49.5 -20.2 19.1 26.0 23

(СН3)3PO-AuCl 1.9 72.8 -67.4 -34.6 27.3 33.6 58

Energy decomposition analysis,kcal/molEnergy decomposition analysis,kcal/mol

34

Decomposition of the formation energy of the complexes by ADF, kcal/mol

Complex Eprep EPauli Eelstat Eorbtot Eint De/D0Gauss

SbCl5SMe2 7.9 83.2 -54.3 -48.9 -20.0 12.1/13.5

SbCl5OPMe3 11.1 128.0 -94.0 -65.7 -31.7 20.6/25.4

SbCl5NCCH3 4.8 72.4 -49.1 -34.1 -10.8 6.0/9.9

SbCl5OPCl3 4.1 46.2 -30.7 -20.9 -5.4 1.3/5.3

SbCl5OSCl2 2.2 15.7 -10.0 -6.2 -0.5 1.7/0.7

SbCl5Py 9.4 109.3 -79.6 -56.6 -26.9 17.5/20.0

35

0 5 10 15 20 25 30-5

0

5

10

15

20

25

30

35

40

-DH=-4.1+1.5Der=0.974;s=2.7;n=11

-DH(

exp.

),kca

l/mol

De(cal.),kcal

Calculated bonding energy at PB86/TZ2P+(ZORA) versusexperimental enthalpy values for Sb complexes

36

MCln…B complexes

• The Eelstat. term in all complexes is larger than the Eorb term. This suggests that the M-B bonding in these complexes is more electrostatic than covalent.

• NBO second-order interaction energies of nv-complexes shown that the LP(B)*MCl (LP=lone electron pair, B=N, O, S, P coordinated atom) donor-acceptor interaction is the source of such intermolecular charge transfer.

• DeADF/kcal/mol = 19.6 + 0.12 Eij

(2)/kcal/mol (r=0.80; s=6.0; n=12)

37

Conclusions• The calculations clearly show that the calculated by

Gaussian and ADF bond lengths, IR-spectra correlate with the experimental values.

• The halogen, nitrogen and metal NQCC’s obtained by both calculations substantially corresponded to the data of microwave and NQR-spectroscopy.

• The calculated by both methods stabilization energies are close to the experimental values.

• We have found the correlations between charge donation and the calculated bonding energies of the halogen and SO3 complexes contrasts with the different situation found for the main group and transition metal complexes.

• From EPA scheme follows that for all complexes the electrostatic bonding is a little bit more than covalent bonding.