Accepted Manuscript

Performance of the M06 family of functionals in predicting the charge transfer

transition energies of molecular complexes of TCNE with a series of methylated

indoles

Amit S. Tiwary, Kakali Datta, Asok K. Mukherjee

PII: S2210-271X(15)00272-8

DOI: http://dx.doi.org/10.1016/j.comptc.2015.06.033

Reference: COMPTC 1867

To appear in: Computational & Theoretical Chemistry

Received Date: 24 May 2015

Revised Date: 27 June 2015

Accepted Date: 27 June 2015

Please cite this article as: A.S. Tiwary, K. Datta, A.K. Mukherjee, Performance of the M06 family of functionals in

predicting the charge transfer transition energies of molecular complexes of TCNE with a series of methylated

indoles, Computational & Theoretical Chemistry (2015), doi: http://dx.doi.org/10.1016/j.comptc.2015.06.033

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1

Performance of the M06 family of functionals in predicting the charge transfer transition

energies of molecular complexes of TCNE with a series of methylated indoles

Amit S. Tiwarya, Kakali Datta

b and Asok K. Mukherjee*

c

aDepartment of Chemistry, Netaji Mahavidyalaya, Arambagh, Hooghly-712601, INDIA.

bDepartment of Chemistry, M. U. C. Womens College, B. C. Road, Burdwan-713104, INDIA

cDigital Computer System, 112 R.B. Ghosh Road, Burdwan 713101, INDIA.

Abstract:

Ground state intermolecular interactions in the molecular complexes of TCNE with a series of

methylated indoles have been predicted with almost equal efficiency by the B3LYP and the M06

family of functionals. However, TDDFT calculation with the B3LYP functional failed to find

any charge transfer (CT) absorption band of the complexes while each of the functionals M06,

M06-2X, M06-HF and M06-L succeeded; the calculated CT transition energies vary with the

calculated vertical ionization potentials of the indoles, complying with Mullikens theory of

charge transfer complexes and are fairly close to reported experimental values.

Key words: TDDFT, Charge transfer, Tetracyanoethylene, methylindoles, M06 functionals

---------------------------------

*Author for correspondence

Digital Computer System, 112 R.B. Ghosh Road, Burdwan-713101, INDIA.

Email: akm_13@rediffmail.com

2

1. Introduction

Properties of electronically excited states of broad classes of moderately large systems are

known to be predicted reliably [1-3] by the time-dependent density functional theory (TDDFT)

[4-7]. Charge transfer (CT) complexes are long known to be difficult for DFT [8,9] and use of

the traditional spatially local functionals in TDDFT calculations often fails to make satisfactory

prediction of CT excitation energies [10-13]. The sources of such failure are presumably the

spurious self-interaction [14] and missing derivative discontinuities [15,16] which, in some

applications, are eliminated by using a range-separated hybrid functional [17-19]. On the other

hand, the M06 family of functionals developed by Truhlar et. al.[20-23] are not range-separated

but reduce the errors of self-interaction and self-correlation by incorporating kinetic energy

density into the generalized gradient approximation (GGA) and in three of the cases by

also incorporating different extents of HartreeFock exchange; these functionals are of hybrid

meta-GGA type (i.e., they depend not only on the gradient of the charge density but also on the

kinetic energy of the electrons). In the M06 suite of functionals the percentages of HF exchange

are 0, 27, 54, and 100 for M06-L, M06, M06-2X, and M06-HF, respectively [24]. They are

showing improved performance when applied to a wide range of fields such as thermochemistry

of transition metal complexes [25], prediction of electronic excitation energies of main-group

compounds by TDDFT [23], description of NMR chemical shielding constants [26], adsorption

of gases on solids [27], weak intermolecular interactions involving charge transfer and H-

bonding in biomolecules [28-30] and electronic excitation energy of Rydberg and charge transfer

states [21, 31]. In a recent work [32] the M06 family of functionals were shown by TDDFT

calculation to yield two CT absorption bands for each of the complexes of tetracyanoethylene

(TCNE) with naphthalene and pyrene in satisfactory agreement with reported experimental

3

results while the B3LYP functional [33, 34] failed. In the present paper the efficiency of the four

above mentioned members of the M06 family as compared with the B3LYP functional has been

tested for predicting the CT excitation energies of the molecular complexes of TCNE with indole

and a series of methylated indoles in dichloromethane medium by using TDDFT in the

polarizable continuum model (PCM) [35, 36] for solvation. The CT transition energies of seven

complexes in the series have been computed by TDDFT and tested against Mullikens theory of

charge transfer complexes [37] and the computed values have been compared with

experimentally reported ones [38]. With this objective, ground state intermolecular interaction

(molecular complex formation) between TCNE and the indoles in dichloromethane solvent was

verified first by optimizing the geometries of the complexes (molecular adducts) and calculating

the electronic charge densities and 13

C and 15

N NMR chemical shifts of the atoms in TCNE

moiety and also of the indolic N atom in the complexed and isolated states. Formation of

molecular complexes in the ground state being thus established, TDDFT calculations were

performed on the optimized geometries (again in dichloromethane medium) for estimation of CT

transition energies of the complexes.

2. Computational Details

All computations were carried out by using the Gaussian 09 Revision A.02 suite of programmes

[39]. The functionals used were M06-L, M06, M06-2X and M06-HF and also B3LYP which is a

combination of Beckes three-parameter hybrid [33] exchange potential with the correlation

functional of Lee, Yang and Parr [34]. The 6-31++G** basis set was used throughout.

Optimization of the ground state geometry of each molecule under study was carried out in

dichloromethane solution, solvation effects being taken into account by the PCM. In this model

a solvent reaction field cavity is created by a series of overlapping spheres and the solute is

4

placed in the cavity. The 15

N and 13

C NMR chemical shifts and natural charges on the atoms of

the isolated indoles, TCNE and their complexes were calculated by using the ground state

optimized geometries obtained with all the above mentioned functionals. Electronic transition

energies were calculated by TDDFT using the universal force field radii scaled by 1.1 (default of

Gaussian 09) together with the linear response method [40] for taking solvation effect into

account.

3. Results and Discussion

3.1 Computational evidence for complex formation in the ground state

The molecules studied in the present work are TCNE, indole, monomethyl indoles with methyl

group at 1, 2 and 3- positions and dimethyl indoles with methyl groups at 1,2-, 2,3-, and 2,5-

positions. The molecular adduct of TCNE and each indole, considered as a single supermolecule,

was subjected to geometry optimization in vacuo. These optimized structures were then further

optimized in dichloromethane medium using the PCM model to incorporate the effect of solvent.

Absence of imaginary frequencies confirmed that the optimized geometries did correspond to

real minima and not to saddle points on the potential energy surface. Optimized structure of one

complex produced by the M06-2X functional is shown in Fig.1 as a typical case and coordinates

of the atoms in the optimized geometries of the other complexes are given in supporting

information (Tables ST1 ST7). In each complex the molecular plane of TCNE is parallel to the

indole ring, the interplanar separation being in the range 3.0-3.5, typical of -donor- -acceptor

complexes. The calculated dipole moment vectors (one being shown in Fig.1) are directed from

indole towards the TCNE moiety of each complex. This indicates that some amount of electronic

charge is transferred to TCNE even in the ground state of each complex (in the Gaussian, dipole

moments are taken from the negative to the positive end of the dipole). Calculated electronic

5

charges (obtained by natural population analysis, NPA) on the atoms of isolated TCNE are given

in Table 1; the charges are found to be grouped as demanded by symmetry. The calculated

electronic charges (NPA) on the atoms of the TCNE moiety in the optimized geometry of the

indole-TCNE complex are shown in Table 2 with reference to the atomic labels as in Fig.2. For

the other complexes these are given in supporting information (Tables ST8 ST13). The isolated

TCNE molecule has a symmetrical distribution of electronic charge, sum of the charges being

zero as expected. But in the ground states of the molecular adducts this symmetry of electronic

charge distribution is somewhat lost. Further, the sum of the natural charges on the atoms of the

TCNE moiety of each complex is negative, thereby confirming the transfer of some electronic

charge to the TCNE moiety even in the ground states of the complexes. Thus, with the M06-2X

functional, 0.118 a.u. of electronic charge is transferred to TCNE. The large dipole moments of

the complexes in spite of small charge separation are due to large interplanar separation. 15

N and

13C NMR chemical shifts were calculated with the optimized geometries in CH2Cl2 medium

using all the functionals mentioned. Unfortunately the results cannot be compared with

experiment owing to non-availability of data. However, it transpires from the calculations

(Tables ST14-ST16 in supporting information) that the changes in chemical shift () of the

indolic N on complexation (all with increasing ) are in conformity with the changes in

electronic charges (Q) on this N (all with decreasing Q, deshielding). Molecular complex

formation between TCNE and each of the indoles is thus indicated by all the functionals used

including B3LYP.

3.2 TDDFT calculation of CT transition energies of the indole-TCNE series of complexes

Attempts were made to calculate the vertical CT excitation energies of the complexes by the

linear response TDDFT method using all the four members of the M06 family of functionals

6

mentioned earlier and also with the commonly used B3LYP. In each case, the same functional

and basis set as used for geometry optimization of the complexes were used for the

corresponding TDDFT calculations. It was found that B3LYP failed to predict any CT transition

with non-vanishing oscillator strength (i.e., the experimentally observed CT absorption band

could not be found by simulation with TDDFT calculation using B3LYP), although this

functional did establish some intermolecular interaction between each indole and TCNE in the

ground state. Success in finding CT absorption band, however, was achieved with all the four

M06-type of functionals for the seven molecular complexes under study. Results are given in

Table 3 together with reported [38] experimental values for comparison. The results obtained

from the four M06 type of functionals and the experimental values are more easily compared in a

bar diagram (Fig. 3). A typical CT absorption spectrum, simulated by TDDFT, is shown in Fig.4

where epsilon in the abscissa means molar absorptivity of the complex. The individual

molecules (indoles and TCNE) were also subjected to similar TDDFT calculation for their

valence transition energies in CH2Cl2 medium. It was found that each molecular complex

exhibits an absorption peak in the UV-Vis range different from those of the component

molecules (indoles and TCNE) in the series under study. That these new absorption peaks are

really CT peaks is established by the fact the transition electric dipole moment has major

component(s) along the axis/axes directed from indole to TCNE moiety in each complex. Also,

according to Mullikens theory of CT complexes [37] the following relation between CT

transition energy (hCT) and vertical ionization potential of the donor (IdV) must hold:

hCT = IdV C1 + C2/( Id

V C1) (1)

C1 = EAV + G1 + G0 (2)

7

Here, EAV

is the vertical electron affinity of the acceptor (here, TCNE), G0 is the sum of several

energy terms ( like dipole-dipole, van der Waals interaction, etc.) in the no-bond state; in most

cases G0 is small. G1 is largely the energy of electrostatic attraction between D+ and A

- (the

positively charged donor and the negatively charged acceptor) in the dative state of the

complex . The term C2 in eqn. (1) is related to the resonance energy of interaction between the

no-bondand dative forms in the ground and excited states and for a given acceptor it may be

supposed constant [37]. In summary, C1 and C2 are constants for a given solvent and a given

electron acceptor in a series of complexes with structurally similar donors. A rearrangement of

eqn.(1) gives

2 IdV hCT = (1/ C1) Id

V(Id

V hCT) + C1 + ( C2/ C1) (3)

The CT transition energies and the ionization potentials (= negative of the highest occupied

orbital energies, according to Koopmans theorem) computed using the M06-2X functional give

an excellent linear plot (Fig. 5) as expected from eqn. (3) and the linear regression equation,

2IDv hCT = (0.186 0.005) ID

v(ID

v - hCT) + (5.625 0.139) ... (4)

is obtained with a correlation coefficient of 0.999. This establishes the CT nature of the

calculated absorption band. The CT nature of the transitions is revealed more convincingly when

the concerned orbitals of the complexes are considered. In all the cases under study, the long

wavelength absorption bands which have been assigned as CT are due to transitions from the

second highest occupied to the lowest unoccupied orbital of the molecular complexes. The

electron density plots (Gaussview pictures) of these orbitals are shown in Fig.6 for one typical

complex. It is clear that before transition electron density is concentrated mostly on the indole

(donor) moiety of the complex and after (vertical) transition it is concentrated mostly on the

acceptor (TCNE) moiety. Regarding quality of the results, M06-2X overestimates the CT

8

transition energies by about .07 to 0.5 eV while M06-HF overestimates it by 0.4 to 1.1 eV as

compared with experimental values; the functionals with lower HF exchange, namely, M06 and

M06-L, underestimate the same by about 0.005 to 0.7 eV and 0.4 to 0.75 eV respectively.

4. Conclusion:

Owing to their wrong asymptotic behavior, standard exchange functionals (like B3LYP)

significantly underestimate CT excitation energies [14] in TDDFT calculation. In the present

case the B3LYP functional fails to detect any CT absorption band by TDDFT calculation for all

the seven molecular complexes studied. Each of the four members of the M06 family of

functionals, however, is successful in this respect; a CT absorption band, very close to the

experimental one, is found by simulation using each of the M06 functionals separately. The

vertical CT transition energies obtained by TDDFT comply with Mullikens theory of charge

transfer complexes.

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14

Figure Captions:

Fig. 1. Optimized Structure of Indole-TCNE complex with dipole moment, calculated at

DFT/M06-2X/6-31++G(d,p) level in dichloromethane medium using PCM. Arrow

shows the direction of calculated dipole moment.

Fig.2. Labels for atoms in the TCNE moiety of the complexes and also in isolated

TCNE molecule

Fig.3. Comparison of theoretically obtained and experimental CT transition energies of the

TCNE complexes with (1) indole, (2) 1-methyl indole (3) 2-methyl indole (4) 3-methyl

indole (5) 1,2-dimethyl indole (6) 2,3-dimethyl indole (7) 2,5-dimethyl indole.

Fig. 4. UV-Vis spectrum of 2,5-dimethyl indole-TCNE complex in CH2Cl2 medium

calculated at TDDFT/M06-2X/6-31++G(d,p) level of theory using the polarizable

continuum model.

Fig. 5. Correlation between the vertical ionization potentials of the indoles (donors)

calculated by DFT/M06-2X/6-31G** and CT transion energies of the indole-TCNE

complexes calculated by TDDFT/M06-2X/6-31G**, both in dichloromethane medium

using the PCM formalism. (Verification of Mullikens theory using theoretical hCT

values).

Fig. 6. Gaussview pictures of (a) the second highest occupied and (b) lowest unoccupied orbitals

of the 2,3-dimethyl indole-TCNE complex.

15

Table 1. Natural charges (q/a.u.) on relevant atoms of isolated (i.e., uncomplexed) TCNE

molecule in CH2Cl2 medium calculated using different functionals.

Functional N atoms C atoms

Ethylenic Cyano

M06-2X -0.22 -0.11 0.27

M06-L -0.24 -0.12 0.30

M06-HF -0.19 -0.11 0.24

M06 -0.24 -0.12 0.23

B3LYP -0.22 -0.11 0.28

16

Table 2. Natural charges (q/a.u.) on the atoms of TCNE moiety in Indole-

TCNE complex (in CH2Cl2 medium); atom labels refer to Fig. 2

Functional N atoms C atoms

M06-2X

qc = - 0.24, qf = - 0.24

qe = - 0.23, qd = - 0.25

qg = 0.28, qh= 0.28

qj = 0.28, qj = 0.28

qb = - 0.14, qa = - 0.13

M06-L

qd= - 0.29, qe = - 0.28

qc = - 0.29, qf = - 0.29

qg= 0.30, qi= 0.30,

qj = qh = 0.30,

qa = qb = - 0.17

M06-HF

qe = -0.20, qf = -0.21

qc = -0.21, qd= -0.21

qh= 0.25, qg= 0.26,

qi = 0.25, qj = 0.26,

qa = -0.11, qb = -0.14

M06

qc = qf = - 0.28,

qd = qe = - 0.28,

qg = qi = qh = qj = 0.31

qa = - 0.12, qb = - 0.16

B3LYP

qe = -0.25, qc= - 0.26,

qd = qf = - 0.26

qj = 0.30, qi = 0.29

qg = qh = 0.29

qa = qb = - 0.15

17

Table 3. CT transition energies of the complexes of TCNE (acceptor) with indole and

methylindoles (donors) calculated in dichloromethane medium at TDDFT/6-31++G(d,p)

level of theory using the PCM formalism and the M06 family of functionals; in parenthesis

are given the calculated values of IDv; experimental CT transition energies are taken from

literature (ref. [37]) for comparison.

Donor Calculated CT transition energy/eV; in parenthesis, calculated IDv/eV

M06 M06-HF M06-L M06-2X Expt.

Indole 1.861(6.117) 2.932 (8.794) 1.769 (5.198) 2.543 (7.107) 2.472

1-methyl indole 1.912 (6.019) 3.036 (8.600) 1.660 (5.097) 2.466 (6.989) 2.364

2-methyl indole 1.997 (5.968) 3.060 (8.630) 1.790 (5.070) 2.487 (6.966) 2.230

3-methyl indole 1.864 (5.942) 3.064(8.590) 1.704 (5.006) 2.430 (6.929) 2.359

1,2-dimethyl indole 1.893 (5.886) 2.902 (8.483) 1.680 (4.973) 2.384 (6.863) 2.051

2,3-dimethyl indole 1.817 (5.799) 2.941 (8.463) 1.690 (4.870) 2.407 (6.792) 1.880

2,5-dimethyl indole 1.954 (5.925) 3.045 (8.585) 1.781(5.006) 2.389 (6.922) 2.149

18

Fig. 1. Optimized Structure of Indole-TCNE complex with dipole moment, calculated at

DFT/M06-2X/6-31++G(d,p) level in dichloromethane medium using PCM. Arrow

shows the direction of calculated dipole moment.

19

Fig.2. Labels for atoms in the TCNE moiety of the complexes and also in isolated

TCNE molecule

C

C

C

N

C

C C

NN

N

(a)

(b)

(c)

(d)

(e)

(f)

(i)

(j)

(g)

(h)

20

Fig.3. Comparison of theoretically obtained and experimental CT transition energies of the

TCNE complexes with (1) indole, (2) 1-methyl indole (3) 2-methyl indole (4) 3-methyl

indole (5) 1,2-dimethyl indole (6) 2,3-dimethyl indole (7) 2,5-dimethyl indole.

1 2 3 4 5 6 70.0

0.5

1.0

1.5

2.0

2.5

3.0

h

CT/e

V

Donors (1 to 7)

Expt

M06

M06-HF

M06-L

M06-2X

21

Fig. 4. UV-Vis spectrum of 2,5-dimethyl indole-TCNE complex in CH2Cl2 medium

calculated at TDDFT/M06-2X/6-31++G(d,p) level of theory using the polarizable

continuum model; Epsilon in abscissa means molar absorptivity.

22

Fig.5. Correlation between the vertical ionization potentials of the indoles (donors)

calculated by DFT/M06-2X/6-31G** and CT transion energies of the indole-TCNE

complexes calculated by TDDFT/M06-2X/6-31G**, both in dichloromethane

medium using the PCM formalism. (Verification of Mullikens theory using

theoretical hCT values).

29.5 30.0 30.5 31.0 31.5 32.0 32.5

11.1

11.2

11.3

11.4

11.5

11.6

11.7

2I D

V-h

CT

ID

V(I

D

V-h

CT)

23

Fig. 6 Gaussview pictures of (a) the second highest occupied and (b) lowest unoccupied

orbitals of the 2,3-dimethyl indole-TCNE complex.

(a) (b)

24

Graphical Abstract

25

Highlights

CT bands & NMR chemical shifts of complexes of TCNE with a series of methylated indoles were found by TDDFT/PCM.

B3LYP cannot predict CT absorption bands for these complexes.

M06, M06-2X, M06-HF and M06-L predict one CT band for each complex in the series.

The predicted CT excitation energies comply with Mullikens theory of Charge Transfer

B3LYP and the M06 family predict 13C and 15N NMR chemical shifts almost equally.