Nonlinear optical properties of Ni(Me6pzS2)MX (M=Ni, Pd, Pt;

X=Me2timdt, mnt)

P. Romaniello1,2, M. C. D’Andria3, and F. Lelj3

1Laboratoire des Solides Irradies UMR 7642, CNRS-CEA/DSM,

Ecole Polytechnique, F-91128 Palaiseau, France

2European Theoretical Spectroscopy Facility (ETSF), F-91128 Palaiseau, France and

3LaMI Dipartimento di Chimica and LaSCAMM,

INSTM Sezione Basilicata, Universita della Basilicata,

Via N. Sauro 85, Potenza 85100, Italy

(Dated: November 30, 2009)

Abstract

In this work we investigate the second-order response of complexes of formula Ni(Me6pzS2)MX

(M=Ni, Pd, Pt; X=Me2timdt, mnt=maleonitriledithiolate): by binding the porphyrazine to the

metal-dithiolene the electron asymmetry and π-conjugation of the latter is increased, and its second-

order response can result enhanced. By performing ab-initio calculations of the ground-state and

response properties of these compounds, we predict the molecular first hyperpolarizability, we elu-

cidate its electronic origin, and we illustrate its dependence on the metal and the dithiolene ligand.

Our study indicates that these complexes show a very high second-order response, comparable to

that of organic ’push-pull’ materials, and that the appropriate metal-dithiolene combination can

significantly enhance it.

1

I. INTRODUCTION

With their wide range of possible applications, such as information processing, optical

switching, optical frequency conversion, and telecomunications [1, 2], nowadays nonlinear

optical materials play an important role in the technological development [3, 4]. The proper-

ties of these materials have been studied experimentally and computationally with a major

focus on organic compounds. Recently, there has been increasing interest in organometallic

and coordination complexes [2].

Metal 1,2-dithiolenes represent a very interesting class of coordination complexes due

to their unique properties, such as high thermal and photochemical stabilities, reversibly

connected oxidation states, and a very intense vis-IR absorption [5–8]. In particular the

dithiolenes derived from the dmit ligand (dmit = C3 S25, 1,3-dithiole-2-thione-4,5-dithiolate)

together with the d8 metal ions are the most known due to their low temperature elec-

trical superconducting properties [9–16]. In the last decade numerous dithiolenes of for-

mula M(R,R′timdt)2x− (M=Ni, Pd, Pt; R,R′timdt= monoanion of N, N ′-disubstituted

imidazolidine-2,4,5-trithione; x=0, 1, 2) complexes have been synthesized and fully char-

acterized both experimentally and theoretically. In particular, the neutral form shows a

very intense near-infrared (NIR) absorption, which has been attributed to a π → π∗ elec-

tronic transition between the HOMO and the LUMO, and occurs at energy values depending

on the nature of the R and R′ substituents, the metal, and the environment [6, 17]. The

wavelength and the high intensity of this NIR absorption band together with the high ther-

mal and photochemical stability candidate this class of dithiolenes for laser applications (see

Mitsubishi patent [18]) [19–21]. In particular, the presence of an intense low-energy charge-

transfer band, which involves a large difference between the dipole moment of the ground

state and the excited state, could lead to a strong second-order response, as predicted by the

two-level model [22]. In this model, only one excited state is responsible for the second-order

response, and the first hyperpolarizability tensor (second-harmonic generation, see later in

the text) can be expressed as

βiii ∝~ωegfeg∆µi

eg

[(~ω)2eg − (2~ω)2][(~ω)2

eg − (~ω)2], (1)

(in atomic units) where βiii represents the dominant tensorial component, ~ωeg and feg are

the excitation energy and oscillator strength, respectively, of the transition to the selected

2

excited state, ∆µeg is the difference between the excited-state and the ground-state dipole

moments, and ~ω is the frequency of the external laser source.

In Ref. [19] the second-order response of M(R,R′timdt)2 metal-dithiolenes has been in-

vestigated. This study shows that these compounds have a promising second-order re-

sponse, which can be enhanced by increasing the charge-tranfer character of the NIR ab-

sorption. This is, indeed, the case in the MXY mixed-ligand compounds (M=Ni, Pd, Pt;

X,Y=R2timdt, dmit, mnt (maleonitriledithiolate); X 6=Y) [23], which exhibit an enhanced

second-order response. This is in line with the well-established empirical observations that

the second-order response can be enhanced by increasing the electronic asymmetry (stronger

donator and acceptor moieties) and/or the π-conjugation between the donor and acceptor

groups.

These findings suggested us that one could obtain large second-order response by com-

bining metal-dithiolenes with porphyrazines. The latter are molecules with high delocalised

electronic structure in which the four pyrrole moieties are linked to each other by four aza

bridges. Recently unsymmetrical porphyrazines bearing a peripheral functionality capable

of binding metal ions have been investigated [24–29]. The peripheral functionalities can

significantly influence the electronic structure of the π-system in the porphyrazine, and con-

sequently the optical spectrum. In this paper we focus mainly on the porphyrazine of the

kind Ni[pz(A;B3)], where A e B are functional groups directly bound at the β-positions of

the pyrroles. The peripheral B moieties involve alkyl groups. The peripheral A moieties can

be an heteroatom of the kind of N or S (in our study it is a sulphur atom), which can bind a

metal ions (M= Ni, Pd, Pt) coordinated to a dithiolene ( mnt and Me2timdt). These com-

plexes have features in the UV-vis spectra that depend on the metal coordinating the ’core’

of the porphyrazine and on the peripheral substitution of the complex, hence allowing a fine

tuning of the electronic properties. Moreover, these complexes have two metals linked by

a polarizable bridge. Similar push-pull bimetallic complexes have already been investigated

in literature for their nonlinear optical properties [30, 31].

To fully characterise these complexes and their possible applications we perform ab-initio

calculations of their ground-state and response properties. The paper is organized as follows.

In Sec. II we give some theoretical and computational details. In Sec. III we discuss the

results calculated for the geometry, electronic structure, electronic excitations, and second-

order response of these complexes, and we focus, in particular, on the role played by the

3

peripheral metal and the dithiolene ligand in the studied properties. We show, in particular,

that increasing the electron asymmetry, passing from Me2timdt to mnt, and red-shifting

the dominant low-energy excitation (if there is a dominant excitation that determines the

second-order response), passing from Pd to Pt and Ni, the second-order response is very large

and comparable to that of extended π-organics molecules. Finally we draw our conclusions.

II. METHOD AND COMPUTATIONAL DETAILS

All results showed in this paper refer to ab-initio calculations based on density-functional

theory. In particular, for the response calculations we used time-dependent density func-

tional theory (TDDFT). Within this approach, after the first order equations have been

solved, one can calculate the first hyperpolarizability tensors, which govern the second-

order properties. In this work we will consider only the case in which the frequency of the

external perturbation is either 0 or ω, which gives rise to the following first hyperpolariz-

ability tensors: the static tensor β(0; 0, 0), and the tensors β(−2ω; ω, ω), β(−ω; 0, ω), and

β(0;−ω, ω), which govern the second-harmonic generation (SHG), the ElectroOptic Pockels

Effect (EOPE), and the Optical Rectification (OR), respectively.

Since d-metals are involved, scalar relativistic effects are taken into account in all our

calculations [17] by using the zeroth-order regular approximation (ZORA) [32]. We used a

valence double-ζ STO (Slater-type orbital) basis set with one polarization function (DZP) for

main element atoms and a triple-ζ STO basis set with one polarization function (TZP) for the

transition metals. The cores (C, N, O: 1s; S, Ni: 1s-2p; Pd: 1s-3d; Pt: 1s-4d) have been kept

frozen. All the results are converged with respect to the basis set size. Geometries have been

optimized by using the exchange-correlation potential proposed by Becke [33] and Perdew

[34] (BP). Excited states have been computed by using the asymptotically correct potential

proposed by van Leeuwen and Baerends (LB94) [35] and the SAOP (statistical average

of orbital potentials) [36, 37], and the hyperpolarizabilities by using the LB94 potential.

The choice of these functionals has been motivated by our previous calculations on similar

compounds [17, 19, 20, 23, 38, 39].

All the calculations have been performed using the ADF2003 computational package [40].

4

III. RESULTS

In this section we present the results obtained for the geometry, the electronic structure,

the excited states, and the second-order response of the Ni(pzMe6S2)MX (M=Ni, Pd, Pt;

X=mnt, Me2timdt) complexes (see Fig. 1). For simplicity, in the following we will indicate

with A and B the series with X=Me2timdt and X=mnt, respectively, and with AM and BM

(M= Ni, Pd, Pt) the complexes of each series.

A. Ground-state properties

1. Geometries

The geometries have been optimized assuming the system planar in the xz plane (see Fig.

1), with symmetry C2v and the singlet electronic ground state belonging to the A1 irreducible

representation. The dipole moments are along the z-axis, and they have opposite direction in

the two series. Although we have no experimental data for these complexes, the geometries

show that the bond lengths and bond angles are in agreement with the experimental data

found for similar complexes [24]. In Table I we compare the most representative bond

lengths and angles calculated for complex BPd with experimental data recorded for the

similar compound Ni[Pr6pz(NMe2)2]Pd(mnt) [24]: the agreement is in line with previous

studies on metal-dithiolenes [17, 19, 23, 38]. The geometry of the porphyrazine ring is not

influenced by the nature of the metal, as it is clear from the data reported in Table I, as

well as by the nature of the dithiolene ligand, since the bond lengths and angles of the

porphyrazine ring are similar in the two series. The M-S1 (S2) (and similarly the M-S3 (S4))

bond length is influenced both by the metal and by the dithiolene ligand. This bond length

increases passing from Ni to Pt, with a larger change from Ni to Pd than from Pd to Pt, as

already found in other metal-dithiolenes [17, 19, 23, 38]. The bond M-S3 is only marginally

affected by the nature of the dithiolene ligand: the variation between the two series are of

0.017 A , 0.008 A , and 0.007 A for Ni, Pd, and Pt, respectively, with series B showing the

largest values. The bond M-S1, instead, strongly feels the nature of the dithiolene ligand:

the variation between the two series are of 0.050 A, 0.035 A, and 0.037 A for Ni, Pd and Pt,

respectively, with series A showing the largest values. The remaining bond lengths as well

as the bond angles show in general small changes among the members of the two series.

5

2. Electonic structure

In order to better characterize these complexes we have analyzed the ground-state elec-

tronic structure in terms of the two ligand fragments Ni(Me6S2pz)x and Xy and the metal

M2+, with x =2-, y=0 for X=Me2timdt, and x =0, y =2- for X=mnt. This choice is based

on the Mulliken population analysis and on the calculated values of the ground-state dipole

moments (see later in the paper), which indicate as acceptor the porphyrazine ligand in

series A and the dithiolene ligand in series B. In Fig. 2 a schematic representation of the

energy levels of the two series is depicted. The analysis of this figure leads to the following

observations: the energy levels are similar within each series; in general, the energy levels of

series A are higher than those of series B, as it can be expected since each complex of the

former series has 8 electrons more than the corresponding complex of the latter series; the

LUMO is quite far from the LUMO+1 in both series; the HOMO tends to separate from the

other occupied MOs in series A, whereas it is quite close to the occupied MOs in series B;

the HOMO-LUMO energy gap of series A complexes is larger than that of the corresponding

series B complexes, with complexes APd and BPd showing the smallest gap (0.63 eV), and

complex ANi the largest gap (0.76 eV).

For both series the calculated MOs are, in general, mainly localized on the porphyrazine

ring. However, some of the orbitals that are involved in intense excitations of the systems, as

we will see in the next section, have large contributions from the peripheral metal and from

the dithiolene ligand as well. In Figs 3-4 we reported some selected orbitals (those which

will be mainly involved in the low-energy excitations) with the percentage compositions

in terms of the MOs of the fragments. In series A the HOMO (20b2) is delocalized both

on the porphyrazine ring and on the dithiolene ligand with a negligible contribution from

the peripheral metal. In series B, instead, the HOMO (13a2) is localized mainly on the

porphyrazine ring with a small contribution from the peripheral metal orbital ndxy, namely

9.8 %, 3.5 %, and 5.5 % for BNi, BPd, and BPt, respectively. The LUMO (21b2 for series

A and 19b1 for series B) is localized on the coordination sphere of peripheral metal, which

also contribute through the orbital ndyz with a percentage of 12.4 %, 8.9 %, and 10.6 %

for ANi, APd, and APt, respectively, and of 15.18 %, 10.5 %, and 13.4 % for BNi, BPd,

and BPt, respectively. The other selected orbitals in Figs 3-4 are mainly localized on the

porphyrazine ligand in both the series; the orbitals 17b1 and 18 b1 in series B have important

6

contributions also from the dithiolene ligand (> 20%).

From the analysis of the bonding energy in terms of the fragments [42] it results that

these complexes are very stable (the total bonding energy being -3339.8, -3303.8, and -3463.9

kJ/mol for ANi, APd, and APt, respectively, and -3457.1, -3411.1, and -3577.2 kJ/mol for

BNi, BPd, and BPt, respectively), which is an essential requirement for laser applications.

B. Electronic spectra

We have calculated the excitation energies for the Ni(Me6S2pz)MX ( M=Ni, Pd, Pt;

X=mnt, Me2timdt) complexes in the range around 300-1000 nm using both the LB94 and

SAOP xc functionals. This choice of the functionals is justified by previous studies on

metal-dithiolenes and porphyrazines [17, 38, 39, 41]: in that case the two functionals give

substantially the same overall picture of the spectra, with the LB94 better describing the

high wavelength range and the SAOP the lower wavelength range. The symmetry point

group of these complexes is the C2v, with the singlet ground-state belonging to the A1

irreducible representation. The spin- and symmetry-allowed excitations are those to the

singlet excited states belonging to the A1, B1, and B2 irriducible representations. In Figs 5-

6 we reported the calculated excitation energies. All the complexes show a similar spectrum.

Considering only the most dominant transitions (oscillator strength ≥ 0.1, mainly belonging

to the A1 representation), the spectra can be arbitrarily separated in three main regions:

the first two in the ranges 300-400 nm and 400-650 nm, which can be identified with the

N,B and Q bands, respectively, of the porphyrazine, and the third region at wavelengths

higher than 650 nm, which can be identified with the excitations of the metal-dithiolene.

Furthermore, for the near infrared (NIR) peaks we observe within each series the same

trend found for other metal-dithiolenes: a blue-shift of the peaks in the complex with Pd

with respect to the complexes with Ni and Pt. The analysis of the main excitations in

terms of monoelectronic transitions reveals a similar nature of the spectra with the two xc

functionals, although SAOP yields in general a stronger multiconfigurational character of

the spectra, specially for low wavelengths. In general the spectra of these complexes show

strong charge transfers (CT) from/to the metals to/from the ligands, and inter/intraligands

CT. Large charge transfers from one side of the molecule to another can result in a large

change in the dipole moment, which, in turn, can play an important role in the second-order

7

response. Therefore, the analysis of the excitation energy spectrum and of the nature of

the predominant transitions can give a first insight in the second-order response of these

complexes. In particular, in Table II we reported the major monoelectronic transitions

contributing to the LB94 excitations for λ > 650 nm (SAOP compositions are essentially

similar).

1. Uv-vis-IR spectrum of Ni(Me6S2pz)M(Me2timdt])complexes

We first analyze the spectrum of complexes ANi, APd, and APt. In general, the spectrum

of complex ANi has a dominant ligand-to-ligand (both inter and intraligand) and metal-to-

ligand charge transfer character. However, due to the complexity of the molecules, also

metal-to-metal and ligand-to-metal charge transfers are present. In the low-energy region

(λ > 650 nm) there are three main excited states responsible for the absorption, namely 1

A1, 2 A1, and 3 A1. Intra/interligand and metal-to-ligand charge transfers are predominant,

as it becomes clear from Table II and from the MOs depicted in Fig. 3. In particular, we

observe that there are two opposite tendencies in the one-electron excitations involved in

the low-energy absorption: charge transfers from the porphyrazine ligand towards the metal

and the dithiolene ligand (namely 19b2 → 21b2), but also the viceversa (namely 20b2 →

22b2). This might result in a small dipole moment in the related excited state. Furthermore,

only the one-electron excitation 20b2 → 21b2 (HOMO→LUMO) involves MOs with large

overlap, which explains also why the excited state 2 A1 shows the largest oscillator strength.

Note also that, unlike the corresponding symmetric metal-dithiolenes, the NIR absorption is

not predominantly due to the HOMO→ LUMO transition. Complexes APd and APt show

similar spectral features, in particular the low-energy region has essentially a similar nature

as in complex ANi.

2. Uv-vis-IR spectrum of Ni(Me6S2pz)M(mnt) complexes

In general, ligand-to-ligand and metal-to-ligand charge transfers are predominant in the

spectra of series B, as in series A. However, the nature of the low-energy region is different

from series A. First, there exist a net charge transfer from the porphirazine ligand to the

peripheral metal and dithiolene ligand; this can yield a large dipole moment in the related

8

excited state. Second, no HOMO→LUMO transition is involved in the low-energy region.

In fact the lowest excitation energies for these complexes (related to the excited state 1B2)

is a pure HOMO→LUMO transition; it is, however, very weak (oscillator strength <10−3)

and hence not appearing in Fig. 6. We also notice that the lowest-energy absorption falls at

λ > 1000 nm in these complexes, whereas it falls at λ < 1000 nm in series A.

C. Second-order response

The analysis of the excitation energies in the previous section showed that combining

a metal-dithiolene with a porphyrazine one build complexes in which there can be intense

excitations that fall at low energies and for which the difference in the dipole moment

between the ground-state and the relative excited state (∆µeg) can be large. According to

the two-level model (see in the Introduction) this could lead to a large second-order response.

Therefore, we have calculated the off-resonance (0.35 eV) second-order response of these

complexes. In Table III the vector component of the β tensors along the dipole moment

direction (the z axes in the studied complexes) and the predominant tensorial component βzzz

are reported. We have also indicated the value of the dipole moment, in order to indicate the

electronic asymmetry in the ground-state. The studied complexes show a significant second-

order response, much larger than that calculated for the (quasi)symmetric- and mixed-ligand

dithiolenes previously investigated [19, 23]. Series B shows a larger second-order response

than series A, with complex BPd having the largest values of β (βSHGvec =355.5 · 10−30 esu).

The low-energy excitations are probably the main responsible for the second-order response

in these complexes, since they fall at very low energies and they can have strong oscillator

strengths. Moreover, these excitations are characterized by ∆µeg values that can be expected

larger in series B than in series A, in line with the larger β values calculated in the former.

The trend of the β values within series B seems to be explained by the two-level model,

assuming that the excited state 3 A1, which has the largest oscillator strength in the low-

energy region, gives the dominant contribution to the first hyperpolarizability. To show this,

we stress that the three main excitations in the low-energy region have similar nature (hence

one could assume a similar ∆µeg ) and similar oscillator strengths among the complexes of

the series. Furthermore, for each complex of the series the three excitations show a similar

nature, whereas the oscillator strengths are very different, with the excited state 3 A1 showing

9

a much larger oscillator strength than 1 A1 and 2 A1. If one assumed this excited state as

the main responsible for the second-order response in series B, then complex BPd, which

has the lowest-energy excitation, would have the largest β vector according to the two-level

model and in line with the values of β reported in Table III.

The two-level model, instead, does not explain the trend of the β values in series A. In

this case, assuming a predominant excitation in the low-energy region and using the same

arguments valid for series B, one would get the largest second-order response for complex

APd, whereas the results in Table III show the trend βAPt> βANi

> βAPd. The ”failure” of

the two-level model may be explained by the fact that the nature of the three main excited

states in the low-energy region is not as uniform as in series B and not coherent with the

trend of the oscillator strengths and excitation energies. To be more specific, the excited

states 1 A1 and 3 A1 show a stronger CT character than the excited state 2 A1, but a lower

oscillator strength. Therefore, there might not be a predominant excitation, but rather the

whole region at λ > 700 nm could be responsible of the second-order response.

IV. CONCLUSIONS

We investigated the ground state and response properties of Ni(Me6pzS2)MX (M=Ni,

Pd, Pt; X=Me2timdt, mnt) complexes within (time-dependent) density functional theory.

These compounds combine together a porphyrazine, which has a very delocalized π-system,

with a metal-dithiolene, which, with their intense π → π∗ NIR band and high thermal

and photochemical stabilities, are promising candidates for laser applications. From the

analysis of the ground state it results that, whereas in the complexes with X=Me2timdt

(series A in the article) the charge is quite uniformly distributed (small dipole moment) in

the molecules, in the complexes with X=mnt (series B in the article) there is a net tendency

of the porphirazine ligand to behave as donor and the dithiolene ligand as acceptor, which

resembles the structure of nonlineral push/pull organic materials. The calculation of the

excitation energies shows that also these complexes exhibit intense low-energy absorptions

with strong change transfers between the two ligands and between the ligands and the

peripheral metal. Series A shows charge transfers from the porphyrazine ligand to the metal

and dithiolene ligand and viceversa, which can result in a small dipole moment in the exited

states; series B, instead, shows a net CT from the porphyrazine to the metal and dithiolene

10

ligand, which can be a signal of large dipole moment in the excited states. All these features

can lead to a large second-order response. Indeed our values of the first hyperpolarizability

tensors, calcuclated off-resonance (0.35 eV) for the second-harmonic generation(SHG), the

ElectroOptic Pockels Effect (EOPE), and the Optical Rectification (OR), respectively, show

that all the complexes have a second-order response comparable to the typical push/pull

organic molecules. In particular, the response is strongly enhanced in series B (βvec >

100 · 10−30), with the complex of palladium showing the largest values of the β tensors

(βSHGvec =355.5 · 10−30). The trend of the β values in series B can be explained by the

two-level model, assuming one of the low-energy excitations as the main responsible for the

second-order response. In series A, instead, all the main low-energy excitations are probably

responsible for the second-order response.

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13

TABLE I: Selected bond lengths (A) and angles (◦) calculated for complexes BM (M=Ni, Pd, Pt).

For comparison, experimental data for the similar compound Ni[Pr6pz(NMe2)2]Pd(mnt) are also

reporteda.

Bond lengths (A) (s.r.) ZORA

and Angles (◦) Ni Pd Pt Expa

M-S1 2.138 2.275 2.282 2.246

Ni-N1 1.882 1.883 1.883 1.898

Ni-N2 1.885 1.887 1.887 1.85

Ni-N3 1.886 1.886 1.886 1.894

S1-M-S2 93.13 88.47 89.20 89.9

N1-Ni-N2 90.25 90.30 90.27 90.5

N2-Ni-N3 89.74 89.71 89.73 89.5

aExperimental data for Ni[Pr6pz(NMe2)2]Pd(mnt) reported in Ref. [24]

14

TABLE II: Low-energy excitations (λ > 650 nm) and major one-electron transition contributions

calculated for complexes AM and BM (M=Ni, Pd, Pt) using the LB94 xc functional. In brackets

the oscillator strengths are reported as well.

State ANi APd APt BNi BPd BPt

1 A1 926 (0.12) 941 (0.14) 945 (0.07) 1049 (0.04) 1100 (0.05) 1057 (0.05)

76% 20b2 → 22b2 79% 20b2 → 22b2 88% 20b2 → 22b2 61% 17b1 → 19b1 70% 17b1 → 19b1 60% 17b1 → 19b1

21% 20b2 → 21b2 19% 20b2 → 21b2 10% 20b2 → 21b2 35% 18b1 → 19b1 26% 18b1 → 19b1 37% 18b1 → 19b1

2 A1 885 (0.23) 923 (0.24) 890 (0.29) 836 (0.02) 875 (0.06) 833 (0.03)

49% 20b2 → 21b2 51% 20b2 → 21b2 57% 20b2 → 21b2 88% 16b1 → 19b1 80% 16b1 → 19b1 86% 16b1 → 19b1

30% 19b2 → 21b2 34% 19b2 → 21b2 34% 19b2 → 21b2 15% 18b1 → 19b1 8% 18b1 → 19b1

15% 20b2 → 22b2 11% 20b2 → 22b2

3 A1 776 (0.15) 808 (0.13) 780 (0.24) 713 (0.26) 798 (0.24) 726 (0.32)

58% 19b2 → 21b2 58% 19b2 → 21b2 56% 19b2 → 21b2 47% 18b1 → 19b1 52% 18b1 → 19b1 47% 18b1 → 19b1

20% 20b2 → 21b2 23% 20b2 → 21b2 28% 20b2 → 21b2 28% 17b1 → 19b1 21% 17b1 → 19b1 29% 17b1 → 19b1

8% 16b1 → 19b1 18% 16b1 → 19b1 12% 16b1 → 19b1

TABLE III: βvec(10−30esu)a values calculated for complexes AM and BM (M=Ni, Pd, Pt) at 0.35

eV (3.50 µm) using the LB94 xc functional. The calculated dipole moments along the z-axis, µz

(D), are also reported.

ANi APd APt BNi BPd BPt

βstaticvec 68.8 (69.8)b 39.4 (40.6) 82.5 (83.3) 136.4 (-134.7) 166.4 (-163.7) 140.7 (-138.9)

βSHGvec 78.2 (80.2) 33.5 (36.0) 94.3 (95.9) 270.1 (-257.5) 355.5 (-333.6) 280.1 (-268.8)

βEOPE/ORvec 71.7 (72.9) 38.4 (39.8) 86.1 (87.1) 165.7 (-162.8) 205.2 (-201.0) 171.6 (-168.6)

µz 1.95 1.93 1.73 -14.28 -14.84 -14.49

aHere βvec = µz·βz

|µ| , with βz = 13

∑i(βzii + βizi + βiiz), (i=x,y,z), and z the axis of the dipole moment.

bIn brackets the dominant component of the hyperpolarizability tensor, i.e. βzzz, is reported.

15

Ni

N2

N4

N3 N1 M

NN

N N

S3 S2

S4 S1

CH3

CH3H3C

H3C

H3C

H3C

R

R

R

R

S

S=

S

S

CN

CN

S

SS

CH3N

CH3

N

x

z

FIG. 1: Structure of the Ni(Me6pzS2)MX (M=Ni, Pd, Pt; X=mnt, Me2timdt) complexes. The

system is placed in the xz plane, with the dipole moment along the z-axis. For simplicity, we

enumerated only the atoms involved in the bond lengths and angles discussed in the paper.

16

-7.0

-6.5

-6.0

-5.5

-5.0

-4.5

-4.0

MO

s en

ergy

(eV)

ANi APd APt BNi BPd BPt

20b2

21b2

22b241b1

14a2

13a2

50a1

19b2

20b2

21b2

22b2

14a2

15a2

13a2

50a119b2

20b2

21b2

22b2

15a2

14a2

13a2

50a119b2

13a2 13a213a2

19b1

39b2

14a2

15a2

12a2

18b1

47a1

17b1

12a218b1

47a1

17b1

19b1

14a2

20b1

15a2

12a2

18b1

47a1

17b1

19b1

14a2

20b1

15a2

11a2 16b2 16b2

FIG. 2: Energy level scheme for complexes AM and BM (M=Ni, Pd, Pt). Only some selected

molecular orbitals are depicted. For the sake of homogeneity here and in the following the orbital

numbering of complexes APt and BPt does not include the 4f valence orbitals of Pt.

17

FIG. 3: Selected MOs and main percentage contributions from the peripheral metal (M), por-

phyrazine ligand (pz), and dithiolene ligand (X) for complexes AM (M=Ni, Pd, Pt). Each per-

centage value is the sum of the main contributions from the MOs of each fragment. Where missing,

the contributions are meant negligible. Notice that the orbitals 20b2 and 21b2 are the HOMO and

the LUMO, respectively.

18

FIG. 4: Selected MOs and main percentage contributions from the peripheral metal (M), por-

phyrazine ligand (pz), and dithiolene ligand for complexes BM (M=Ni, Pd, Pt). Each percentage

value is the sum of the main contributions from the MOs of each fragment. Where missing, the

contributions are meant negligible. Notice that the orbitals 13a2 and 19b1 are the HOMO and the

LUMO, respectively.

19

0.8

0.6

0.4

0.2

0.0

12001000800600400! (nm)

0.8

0.6

0.4

0.2

0.0

f

0.8

0.6

0.4

0.2

0.0

Ni

Pd

Pt

— SAOP— LB94

Ni(Me6S2pz)M(Me2timdt)

FIG. 5: Excitation energies of complexes AM (M=Ni, Pd, Pt) calculated using the LB94 (violet

lines) and SAOP (blue lines) xc functionals.

20

0.8

0.6

0.4

0.2

0.0

12001000800600400! (nm)

0.8

0.6

0.4

0.2

0.0

f

0.8

0.6

0.4

0.2

0.0

Ni

Pd

Pt

— SAOP— LB94

Ni(Me6S2pz)M(mnt)

FIG. 6: Excitation energies of complexes BM (M=Ni, Pd, Pt) calculated using the LB94 (violet

lines) and SAOP (blue lines) xc functionals.

21