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Manthos G. Papadopoulos

Institute of Organic and Pharmaceutical Chemistry.

National Hellenic Research Foundation

48 Vas. Constantinou Av.

Athens 11635

We will consider a series of derivatives,

which have interesting

linear and nonlinear optical properties

and possible applications

in the photonic industry

- Unifying features of this work:
- Molecules with large NLO properties
- and how these can be interpreted
- Discovery of mechanisms in order
- to modify the L&NLO properties

More specifically, we shall comment on the results

- of three projects:
- The L&NLO properties of derivatives
- involving noble gas atoms
- The L&NLO properties of [60]fullerene
- derivatives
- 3. The structure and properties of Ni-dithiolenes

Definition of the electric properties

E = E(0) -μαFα - (1/2)ααβFαFβ - (1/6)βαβγFαFβFγ

- (1/24)γαβγδFαFβFγFδ - ...

μα : Dipole moment

ααβ: Polarizability

βαβγ: First hyperpolarizability

γαβγδ:Second hyperpolarizability

Why the L&NLO properties are important:

- Theory
- Study of L&NLO processes (e.g. Kerr effect)
- Intermolecular interactions
- Applications
- Design and study of NLO materials

(optical processing of information,

optical computing)

Definition of the project:

We consider insertion of a noble gas atom, Ng,

in the chemical bond A-B, leading to A-Ng-B.

Specific examples we will consider involve insertion of:

Arin HFleading toHArF

Xe in HCnH leading to HXeCnH

Xe in AuF lading to AuXeF

Why are the noble gas derivatives interesting and significant?

- It is amazing what a noble gas atom, in the middle of a single bond can do, for example it leads to:
- large NLO properties,
- significant charge transfer etc

Which is the expanation?

A. Avramopoulos, H. Reis, J. Li and M. G. Papadopoulos, J. Am. Chem. Soc., 126, 6179 (2004).

- Synthesis of HArFa (argon fluoro-hydride)

[first covalent neutral cond. argon der.]

photolysis of HF in solid argon matrix

Point of interest:

The effect of Ar on the NLO

properties of the resulting derivative

a. L. Khriachtchev et al., Nature, 406, 874 (2000)

αzz

βzzz

Pol

HF

MP2

CCSD(T)

aug-cc-pV5Z

HF

MP2

3.139

2.691

2.578

3.085

2.653

37.61

55.37

59.80

37.80

54.01

-597.8

-1220.9

-1418.1

-578.7

-1102.5

The dipole moment, polarizability and

first hyperpolarizability of HArF (in a.u.)

μgg: ground state dipole moment

μee: excited state dipole moment

μge: transition dipole moment

Εge: transition energy

Rationalization ofβzzz

Comparison of

HArF withHF

μgg: 3.473/0.745 a.u.

μee: -0.814/-0.907 a.u.

μge: 1.419/-0.611a.u.

Εge: 0.276/0.570 a.u.

Method: HF/Pol, CIS/Pol

All the above properties contribute so that

βzzz of HArF is much larger than that of HF

HArF βzzz=-561.5 a.u. HF/Pol

-340.7 a.u. TSM

HF βzzz=-7.4 a.u. HF/Pol

-5.7 a.u. TSM

- Reliability of TSM
- Large effect of Ar

μz=0.983 a.u. (3.473 a.u.)

αzz=19.11 a.u. (34.25 a.u.)

βzzz= -35.09 a.u. (-561.5 a.u.) ratio=16

Charge of Ar: 0.02 (0.56) ratio=28

Method: HF/Pol

C6H6

Αzz = 44.74 a.u. (34.25 a.u.)

Method: MP4[SDQ]

P-nitro-aniline

βzzz = 797.5 a.u. ( -561.5 a.u.)

Method: HF/Pol

The first Xe derivative was reported by Bartlet in 1962

[Proc. Chem. Soc., 218(1962)]

- A large number of Xe compounds have been reported since then

F. Holka,A. Avramopoulos, O. Loboda, V. Kellö, M. G. Papadopoulos,

Chem. Phys. Letters, 472, 185 (2009)

- Effect of Xe
- Comparison of H with Au

HXeF, AuXeF: not synthesized yet

XeAuF: several NgMF have been synthesized

Ng: Ar, Kr, Xe

M: Cu, Ag, Au

X: F, Cl, Br

Xe - Au bond: covalent [1]

Au - Xe [AuXeF] bond: partially covalent

(AXe)+ F-: significant charge transfer

A= H, Au

The barrier height

AuXeF: 119 kJmol-1

separates

the global minimum (AuF+Xe)

from the local minimum

1. S. A. Cook and M. C. L. Gerry, J. Am Chem. Soc.126, 17000 (2004).

Method: HF/aug-cc-pVQZ

- Similar charges on F
- Quite different charges for Xe of XeAuF and AuXeF

Method: CCSD(T)

Basis set: aug-cc-pVQZ

ECP: Au(60), Xe(28)

The position of Xe has a great effect on αzz and βzzz

βzzz(AuXeF) / βzzz (AuF) = 6.0

- βzzz(XeAuF) / βzzz (AuF) = 0.7

Method: CCSD(T)

Basis set: aug-cc-pVQZ

- βzzz(HXeF) / βzzz (HF) = 57.0

Xe may greatly affect βzzz

AuXeF

Methods: CCSD(T), Douglas-Kroll

Basis sets: PolX, PolX_DK

βzzz = great effect of relativistic contribution

Xe inserted into HC2H and HC4H:

L&NLO properties

A.Avramopoulos, L. Serrano-Andres, J. Li, H. Reis and M. G. Papadopoulos,

J. Chem. Phys., 127, 214 (2007).

HXeC2H and HXeC2XeH:

They are prepared in a low-temperature Xe matrix using UV

photolysis of C2H2 and subsequently annealing at 40-45K

[JACS, 125, 4696 (2003)]

HXeC4H:

Tanskanen et al. reported its preparation

[JACS, 125, 16361 (2003)]

HC2XeC2H:

Ansbacher et al. predicted that the diacetylide Xe exists

as a metastable chemically-bound compound

[PCCP, 8, 4175 (2006)]

Resonance structures of HXeC2H

Structures Weight (%)a

H–Xe+C–CH (I) 44

H·Xe·CCH (II) 26

H–Xe+–CCH (III) 14

H–Xe2+C–CH (IV) 11

H+XeC–CH (V) 5

Method:CASVB(6,4)/3-21G*

- Intra-molecular
- Inter-molecular

- 1 and 2 Xe atoms:
- Approx. the same charge
- The chain length does not appear to have an effect

- End:0.79 e
- Middle:1.02 e
- 3 Xe atoms:
- The middle one has much larger charge

Method:HF/aug-cc-pVZ

Inter-molecular charge transfer

- {Xe matrix}/HXeC2H
- Two models
- 6 Xe atoms octahedrally placed around HXeC2H
- A1A2=7.56 a.u.
- A2A3=9.45 a.u.
- Method:MP2/aug-cc-pVDZ

(b) 8 Xe atoms arranged in a cube

A1A2=15.12 a.u.

insignificant CT takes place from the Xe environment to HXeC2H:

0.02e in the first model and

0.002e in the second model

in connection with effect

of the chain length

H2C2H

H2C4H

Δγzzzz = 30 000 au (approx.)

H2XeC2H

H2XeC4H

Δγzzzz = 340 000 au (approx.)

H-Xe-CC-CC-H γzzzz =111 190 a.u

- H-CC-Xe-CC-H γzzzz =28 488 a.u.
- H-CC-CC-H γzzzz = 31 224 a.u.
- Xe leads to a reduction of γzzzz !
- The position of Xe has a significant effect on γzzzz
- Method: MP2/aug-cc-pVDZ

Decomposition channels of HXeC2H

H+ Xe + C2H

HXeC2H

Xe + HC2H

34 kcalmol-1

104 kcalmol-1

The barrier to this exothermic reaction is very high, 64.6 kcalmol-1

and prevents the molecule from dissociation

T. Ansbacher et al., PCCP, 8, 4175 (2006)

Example: HXeC2H

αpvzz = [μ2](0,0)=60.13 a.u

Vibrational Modes:

H-Xe: 1681cm-1 [μ2](0,0)=13.1 a.u

Xe-C: 313 cm-1 [μ2](0,0)=46.8 a.u

The other modes have a negligible contribution (0.23 a.u.)

Method:MP2/aug-cc-pVDZ

βpvzzz = [μα](0,0) = -835 a.u.

Vibrational Modes:

H-Xe: 1681cm-1 [μα](0,0)=1212 a.u

Xe-C: 313 cm-1 [μα](0,0)=-2079a.u

The other modes have a very small contribution (32 a.u.)

Method:MP2/aug-cc-pVDZ

- The Xe derivatives have been synthesized in a Xe matrix
- Thus it would be useful to compute the effect of the Xe environment on the L&NLO properties
- Example: HXeC2H
- The discrete local field approximation has been applied
- Only the dipole and induced dipole interactions between HXeC2H and the Xe environment are considered

,

Where

N is the number of molecules in the cell

Vcell is the volume of the cell

ε0is the permitivity of vacuum

α,β,γ are the Cartesian components

Fk’α is the permanent local field effect on molecule k’ due to the surrounding molecules

μk’βis the dipole moment of the free molecule k’

αk’αβis the polarizability of the free moleculek’

L(11) is the Lorentz-factor tensor

HXeC2H: Dipole moment and polarizability of at the CCSD(T) level and

Xe: experimental polarizability value (27.10 au)

Results:

Local field: Fz=-4.4x10-3 au

μz:50.5%

αzz:2.5%

βzzz:20.2%

γzzzz: 12.7%

Changes of properties

Insertion of Xe in HCnH leads to a large increase of γzzzz

For example:

γzzzz(HXeC2H)=38740 au γzzzz(HC2H)=3380 au

Ratio=11.5

Why?

Method: CASSCF/CASPT2

Basis set:ANO-RCC

Xe:7s6p4d2f1g

C:4s3p2d1f

H:3s2p1d

CASSSF(10,14)

The computations have shown that insertion of Xe leads to:

(a) Excited states of lower energy

(b) An electronic spectrum which is more dense in low lying states

(c) Many non-zero contributions to the transition dipole moment matrix

- The NLO properties are:
- proportional to products of TDM matrix elements and
- inversely proportional to products of energy differences
- Therefore an enhancement to NLO properties is expected

HC2H HXeC2H

αzz = 11.07 au αzz = 26.51 au

γzzzz = 3473au γzzzz = 9102 au

The SOS model reflects the expected trend

On the electronic structure of H-Ng-Ng-F

(Ng=Ar, Kr, Xe) and the L&NLO properties

of HXe2F

A.Avramopoulos, L. Serrano-Andre, J.Li, M. G. Papadopoulos,

J. Chem. Theory Comput. 6, 3365 (2010).

Electronic ground state description

HArArF: 38%σ2 + 56%σσ*

HΚrΚrF: 53%σ2 + 39%σσ*

HΧeXeF: 58%σ2 + 35%σσ*

Increase of the closed shell character:

Xe > Kr > Ar

Method: MS-CASPT2/ANO

CASVB computations show:

The total weight of the resonance structures

with diradical character is approx.:

99% for HArArF

97% for HKrKrF

87% for HXeXeF

The singlet-triplet (3Σ+) gap (STG)

provides an indication for the diradical

character of the system:

STG

HAr2F 4.7 kcal/mol

HKr2F 14.7 kcal/mol

HXe2F 28.7 kcal/mol)

Wirz suggested that a diradical is a molecule with

STG which does not differ by much more than

≈ 2kcal/mol.

The expression “diradicaloid”

would then extend this range to ≈24 kcal/mol.

So, all the HNg2F are diradicaloids.

Stability, Electronic Structure

and L&NLO Properties of

HXeOXeF and FXeOXeF

A.Avramopoulos, J. Li, G. Frenking, M. G. Papadopoulos,

J. Phys. Chem. A, 115, 10226 (2011)

HXeOXeF (FXeOXeF) results

from introduction of 2 Xe atoms

in HOF (FOF)

- We have shown that the novel derivatives

HXeOXeF and FXeOXeF

can be synthesized, because they are

protected by high energy barriers

Description of the ground state

HXeXeF 58.0% σ2 + 35% σσ*

HXeΟXeH77.0% σ2 + 9% σσ*

FXeΟXeF76.5% σ2 + 10% σσ*

Insertion of O increases

the closed character

E2 = 25.5

E3 = 90.3

Units: kcal/mol

Dissociation paths of HXeOXeF calculated at

the CASPT2/ANO level.

ZPE has been taken into account

Reactants and products were connected through

Intrinsic Reaction Coordinate (IRC) calculations

E4 = 50.1 kcal/mol

E5 = 31.9 kcal/mol

E6 = 20.1 kcal/mol

HOXeF is another novel derivative

HXeOXeF is a local minimum and is higher in energy

than several of its dissociation products:

E(HXeOXeF) – E(HOF + 2Xe) = 125.4 kcal/mol

E(HXeOXeF) – E(HO + F + 2Xe) = 85.2 kcal/mol

E(HXeOXeF) – E(OF + H + 2Xe) = 9.0 kcal/mol

HXeOXeF: Metastable

E2= 40.5 kcal/mol

E3= 32.1 kcal/mol

Dissociation paths of FXeOXeFcalculated at

the CASPT2/ANO level

Frenking et al. [1] found that HArArF and HKrKrF

are associated with low-energy barriers.

Thus, they can NOT be observed.

But,

HXeXeF 13.1 kcal/mol

HXeOXeF 14.9 kcal/mol

FXeOXeF 40.5 kcal/mol

Thus O and F increase the barrier

and thus

FArOArF and FKrOKrF

may be observed.

G. Frenking et al., Angew. Chem. Int. Edition,

48, 366 (2009).

The L&NLO properties of some

Ni-Dithiolene derivatives

Luis Serrano-Andrés, A. Avramopoulos, J. Li, P. Labéquerie, D. Begué,

V. Kellö, M. G. Papadopoulos, J. Chem Phys., 131, 134312 (2009).

Points of interest:

- The low-lying excited states of NiBDT
- The impressive NLO properties and their interpretation

ΔE/eV

Main configuration

11Ag ( diradicaloid)a

−0.004b

… (π2)2(π3)0 - (π2)0(π3)2

11B1u (pp*)c

0.000b

… (π2)1 (π3)1

.

. 14 states

.

31B3u (σSNi ππ *π *)

3.064

… (σSNi)1 (π 1)1 (π 2)2 (π 3)2

13B1u (diradical)d

0.612

… (π 2)1 (π 3)1

Excited states structure of Ni(S2C2H2)2

a 11Ag [71% (p2)2(p3)0−21% (p2)0(p3)2].

b The energy difference is within the method accuracy. For simplicity the 11Ag state will be considered the ground state at this level.

c 11B1u state 65% [(π 2)1(π 3)1].

d13B1u state 92% [(π 2)1(π 3)1].

Basis set: ANO-RCC

Method: CASSCF/CASPT2

The main findings of the CASSCF/CASPT2 computations are:

The quasidegenaracy of 11Ag and 11B1u and the large number of low lying excited states.

These features are very likely to lead to large NLO properties

Table 4. A Basis set study of NiBDTa. The UBHandBHLYP functional was employed. All values are in au.

Property

Basis set

αzz

γzzzzx10-4

6-311G*

222.0

68.1

SDD[Ni]/6-31G*

221.9

55.8

ZPolX

245.3

67.7

aug-cc-pVDZ

244.7

71.9

aug-cc-pVTZ

245.2

68.0

aug-cc-pVQZ

245.4

67.6

Properties of Ni(S2C2H2)2

Method: UBHandHLYP

a The B3LYP/SDD optimized geometry was employed to all calculations.

Method

αzz

γzzzzx10-4

UBHandHLYP

245.3

67.7

UCCSD

300.5

72.4

UCCSD(T)

364.3

119.0

CASSCF/CASPT2

m/a1b1b2a2b

12/4242 (4s2p,4s*2p*)

67.9/282.2

1647.5/216.0

16/4444 (4s4p,4s*4p*)

243.2/340.7

1102.7/184.7

20/4646 (4s6p,4s*6p*)

309.3/363.8

869.5/153.1

aThe properties were computed numerically. Base field: 0.005 au.

bm: Number of active electrons; a1b1b2a2: Number of orbitals

in subspaces of C2v symmetry.

Basis set: ZPolX

6-31G*

- The big second hyperpolarizability of NiBDT

has been interpreted in terms of the

quasidegeneracy of the 11Ag and 11B1u states.

As well as the many low lying excited states.

- The considered Ni-dithiolene derivatives have

very big NLO properties.

The L&NLO properties of [60]fullerene

derivatives

- Points of interest:
- Selection of the appropriate method (e.g. functional)
- Computation of the electronic and vibrational contributions
- Selection of functional groups

O. Loboda, R. Zalesny, A. Avramopoulos, J. –M. Luis, B. Kirtman, N. Tagmatarchis, H. Reis and M. G. Papadopoulos, J. Phys. Chem. A, 113, 1159 (2009).

2

Comment: The substituents were selected according to increasing

Hammett σp constant, which may be used as a measure

of their electron donating capabilities.

Methods: BLYP and HF(it does not have the overshoot problem).

41

Remark:The ratio of the BLYP and the HF values increases monotonically and becomes

quite large for the strongest donors.

Concluding remarks

- Mechanisms which lead to large NLO properties have been discussed
- Novel derivatives with possible photonic applications have been proposed

Colleagues who contributed to this work:

Dr Aggelos Avramopoulos, NHRF, Greece

Dr Heribert Reis, NHRF, Greece

Dr Luis Serrano Andrés, Universitat de València, Spain

Dr Jiabo Li, SciNet Technologies, USA

Dr Robert Zalesny, NHRF, Greece

Dr Oleksandr Loboda, NHRF, Greece

Professor B. Kirtman, University of California, USA

Dr Josep Maria Luis, University of Girona, Spain

Dr Nikos Tagmatarchis, NHRF, Greece

Professor Vladimir Kellö, Comenius University, Slovakia

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