Local force constants and charges of the nitrosyl ligand in photoinduced NO linkage isomers in a prototypical ruthenium nitrosyl complex.

Photoinduced linkage isomers (PLI) of the NO ligand in transition-metal nitrosyl compounds can be identified by vibrational spectroscopy due to the large shifts of the (NO) stretching vibration. We present a detailed experimental and theoretical study of the prototypical compound K2[RuCl5NO], where (NO) shifts by ≈150 cm-1 when going from the N-bound (κN) ground state (GS) to the oxygen-bound (κO) metastable linkage isomer MS1, and by ≈360 cm-1 when going to the side-on (κ2N,O) metastable linkage isomer MS2. We show that the experimentally observed N-O stretching modes of the GS, MS1, and MS2 exhibit strong coupling with the Ru-N and Ru-O stretching modes, which can be decoupled using the local mode vibrational theory formalism. From the resulting decoupled pure two-atomic harmonic oscillators the local force constants are determined, which all follow the same quadratic behavior on the wavenumber. A Bader charge analysis shows that the total charge on the NO ligand is not correlated to the observed frequency shift of (NO).

Pas de Deux of an NO Couple: Synchronous Photoswitching from a Double-Linear to a Double-Bent Ru(NO)2 Core under Nitrosyl Charge Conservation.

The {Ru(NO)2 }10 dinitrosylruthenium complex [Ru(NO)2 (PPh3 )2 ] (1) shows photo-induced linkage isomerism (PLI) of a special kind: the two NO ligands switch, on photo-excitation, synchronously from the ground state (GS) with two almost linear RuNO functions to a metastable state (MS) which persists up to 230 K and can be populated to ≈50 %. The MS was experimentally characterised by photo-crystallography, IR spectroscopy and DS-calorimetry as a double-bent variant of the double-linear GS. The experimental results are confirmed by computation which unravels the GS/MS transition as a disrotatory synchronous 50° turn of the two nitrosyl ligands. Although 1 shows the usual redshift of the N-O stretch on bending the MNO unit, there is no increased charge transfer from Ru to NO along the GS-to-MS path. In terms of the effective-oxidation-state (EOS) method, both isomers of 1 and the transition state are Ru-II (NO+ )2 species.

Solid-State Photo-NMR Study on Light-Induced Nitrosyl Linkage Isomers Uncovers Their Structural, Electronic, and Diamagnetic Nature.

A light-induced linkage NO isomer (MS1) in trans-[Ru(15NO)(py)419F](ClO4)2 is detected and measured for the first time by solid-state MAS NMR. Chemical shift tensors of 15N and 19F, along with nJ(15N-19F) spin-spin couplings and T1 relaxation times of MS1, are compared with the ground state (GS) at temperatures T < 250 K. Isotropic chemical shifts (15N and 19F) are well resolved for two crystallographically independent cations (A and B) [Ru(15NO)(py)419F]2+, allowing to define separately both populations of MS1 isomers and thermal decay rates for two structural sites. The relaxation times T1 of 19F in the case of GS (30/38.6 s for sites A/B) and MS1 (11.6/11.8 s for sites A/B) indicate that both isomers are diamagnetic, which is the first experimental evidence of diamagnetic properties of MS1 in ruthenium nitrosyl. After light irradiation (λ = 420 nm), the NO ligand rotates by nearly 180° from F-Ru-N-O to F-Ru-O-N, whereby the isotropic chemical shifts of δiso(15N) increase and those of δiso(19F) decrease. The nJ(15N-19F) couplings increase from 2J(15N-Ru-19F)GS = 71 Hz to 3J(15N-O-Ru-19F)MS1 = 105 Hz. These results are interpreted on the basis of DFT-CASTEP calculations including Bader-, Mulliken-, and Hirshfeld-charge density distributions of both states.

Photoinduced linkage isomers in a model ruthenium nitrosyl complex: Identification and assignment of vibrational modes.

Photoinduced NO-linkage isomers were investigated in the solid state of labelled trans-[Ru(14/15NO)(py4)F](ClO4)2 complex by combined IR-spectroscopy and DFT calculations. Based on the experimental data and the DFT calculations of this isotopically labelled 14/15NO nitrosyl compound, we present a complete assignment of the vibrational bands of three nitrosyl linkage isomers in a range from 4000 to 200 cm-1. The calculated IR-spectra match well with the experimental data allowing reliable assignment of the vibrational bands. The structural change from the Ru-NO (GS) to the Ru-ON (MS1) and Ru-η2-(NO) (MS2) linkage configuration leads to the downshift of the ν(NO) and ν(Ru-(NO)) bands, and a corresponding increase of the energy of the ν(Ru-F) band. The shift of the bands corresponds to the change of the Ru-(NO) and Ru-F bond lengths: increase of the Ru-(NO) bond length leads to the decrease of the energy of the ν(Ru-(NO)) band; decrease of the Ru-F bond length leads to the increase of the energy of the ν(Ru-F) band. These observations can be extrapolated to the family of related nitrosyl complexes and therefore be used for the qualitative prediction of the Ru-(NO) and Ru-Ltrans-to-NO bond lengths of different linkage isomers in the framework of one complex. While the formation of linkage isomers is a reversible process, long-time irradiation sometimes induces irreversible reactions such as the release of NO. Here, we show that the photolysis of trans-[Ru(14/15NO)(py4)F](ClO4)2 in KBr pellets may lead to the release of nitrous oxide N2O, conceivably through the formation of a {Ru-(κ2-ONNO)} intermediate.

Combining photoinduced linkage isomerism and nonlinear optical properties in ruthenium nitrosyl complexes.

The complex trans-[RuNO(NH3)4F]SiF6 was synthesized in quantitative yield and the structure was characterized by X-ray diffraction and spectroscopic methods. The complex crystallizes in the non-centrosymmetric space group Pn. Hirshfeld surface analysis revealed that the dominant intermolecular interactions are of types H...F and F...O, which are likely to be responsible for the packing of the molecules in a non-centrosymmetric structure. Irradiation with blue light leads to the formation of Ru-ON (metastable state MS1) and Ru-η2-(NO) (metastable state MS2) bond isomers, as shown by IR and UV-Vis spectroscopy. The structural features of the MS1 isomer were elucidated by photocrystallography. The complex exhibits exceptionally good thermal stability of the metastable state MS1, such that it can be populated by light at 290-300 K, which is important for potential applications. The second harmonic (SH) emission can be generated by femtosecond-pulsed irradiation of the complex. The generated SH is rather efficient and stable under long-term exposure. Finally, since both metastable states and harmonic generation can be generated at room temperature, an attempt to drive the SH response by photoisomerization of the nitrosyl ligand was made and is discussed.

{FeNO}7 -Type Halogenido Nitrosyl Ferrates: Syntheses, Bonding, and Photoinduced Linkage Isomerism.

Mononitrosyl-iron compounds (MNICs) of the Enemark-Feltham {FeNO}7 type can be divided into a doublet (S=1/2) and a quartet (S=3/2) spin variant. The latter relies on weak-field co-ligands such as amine carboxylates. Aqua-only co-ligation appears to exist in the long-known "brown-ring" [Fe(H2 O)5 (NO)]2+ cation, which was prepared originally from ferrous salts and NO in sulfuric acid. A chloride variant of this species, the green [FeCl3 (NO)]- ion, was first prepared analoguosly by using hydrochloric instead of sulfuric acid. As a tetrahedral species, it is the simple prototype of sulfur-bonded {FeNO}7 (S=3/2) MNICs of biological significance. Although it has been investigated for more than a century, neither clean preparative routes nor reliable structural parameters were available for the [FeCl3 (NO)]- ion and related species such as the [FeCl2 (NO)2 ]- ion, a prototypical dinitrosyliron species (a "DNIC"). In this work, both issues have been resolved. In addition, we report on a computational study on the ground- and excited-state properties including an assignment of the chromophoric transitions. Photoinduced metastable isomers were characterised in a combined experimental and computational approach that resulted in the confirmation of a single photoinduced linkage isomer of the paramagnetic nitrosyl-metal coordination entity.

Photocrystallography and IR spectroscopy of light-induced linkage NO isomers in [RuBr(NO)2(PCyp3)2]BF4.

One single photo-induced linkage NO isomer (PLI) is detected and characterized in the dinitrosyl pentacoordinated compound [RuBr(NO)2(PCyp3)2]BF4 by a combination of photocrystallographic and IR analysis. In the ground state, the molecule adopts a trigonal-bipyramidal structure with the two NO ligands almost linear with angles Ru-N1-O1 = 168.92 (16), Ru-N2-O2 = 166.64 (16)°, and exactly equal distances of Ru-N = 1.7838 (17) and O-N = 1.158 (2) Å. After light irradiation of 405 nm at T = 10 K, the angle of Ru-N2-O2 changes to 114.2 (6)° by rotation of the O atom towards the Br ligand with increased distances of Ru-N2 = 1.992 (6) and N2-O2 = 1.184 (8) Å, forming a bent κN bonded configuration. Using IR spectroscopy, the optimal wavelength and maximum population of 39 (1)% of the PLI is determined. In the ground state (GS), the two symmetric νs(NO) and asymmetric νas(NO) vibrations are measured at 1820 and 1778 cm(-1), respectively. Upon photo-irradiation, the detection of only one new vibrational ν(NO) stretching band at 1655 cm(-1), assigned to the antisymmetric coupled vibration mode and shifted to lower wavenumbers by -123 cm(-1), supports the photocrystallographic result. These experimental results are supported by additional DFT calculations, which reproduce the structural parameters and vibrational properties of both the ground state and the photo-induced linkage isomer well. Especially the experimentally characterized molecular structure of the PLI state corresponds to an energy minimum in the calculations; the stabilization of the bent κN bonded configuration of the PLI state originates from specific intramolecular orbital overlap.

Multiple light-induced NO linkage isomers in the dinitrosyl complex [RuCl(NO)2(PPh3)2]BF4 unravelled by photocrystallographic and IR analysis.

Multiple light-induced reversible metastable NO linkage isomers (PLIs) have been detected in the dinitrosyl compound [RuCl(NO)2(PPh3)2]BF4 by a combination of photocrystallographic and IR analysis. The IR signature of three PLI states has been clearly identified, with estimated populations of 59% (PLI-1), 8% (PLI-2) and 5% (PLI-3) for a total population of the metastable state of 72%. The structural configuration of the major component (PLI-1) has been derived by X-ray photocrystallography. In the ground state, the structure is characterized by a bent and a linear nitrosyl, the bent one being oriented towards the linear equatorial nitrosyl with an Ru-N-O angle of 133.88 (9)°. X-ray Fourier difference maps indicate a selectivity of the photo-isomerization process in PLI-1: only the bent NO ligand changes its position, while the linear NO is unaffected. After irradiation at 405 nm, the orientation is changed by rotation towards the Cl ligand opposite the linear NO, with an Ru-N-O angle in this new position of 109 (1)°. The photocrystallographic analysis provides evidence that, in the photo-induced metastable state, the bent NO group is attached to the Ru atom through the N atom (Ru-N-O), rather than in an isonitrosyl Ru-O-N binding mode. In the IR spectra, the asymmetric NO vibrational band shifts by -33 cm(-1) to a lower value, whereas the symmetric band splits and shifts by 5 cm(-1) to a higher value and by -8 cm(-1) to a lower value. The down shift is a clear indication of the structural change, and the small upward shift in response to the new electronic configuration of the metastable structure. Variable-temperature IR kinetic measurements in the range 80-114 K show that the decay of the PLI-1 state follows an Arrhenius behaviour with an activation energy of 0.22 eV.

NO-binding in {Ru(NO)2}8-type [Ru(NO)2(PR3)2X]BF4 compounds.

Two different structure types were found for a series of mononuclear dinitrosyl complexes of the general formula [RuL2(NO)2X]BF4 (L = monodentate phosphane, X = Cl, Br, I). The {Ru(NO)2}(8)-type target compounds were prepared by the reduction of the respective {RuNO}(6) precursors and subsequent oxidative addition of (NO)BF4. About one half of the new compounds share their molecular structure with the hitherto only representative of this class of dinitrosyls, Pierpont and Eisenberg's [RuCl(NO)2(PPh3)2]PF6·C6H6 (Inorg. Chem., 1972, 11, 1088-1094). The Cs-symmetric cations exhibit both a linear and a bent Ru-N-O fragment, in line with a formal 6 + 2 split of the {Ru(NO)2}(8) electron sum in the sense of a [Ru(II)(NO(+))((1)NO(-))](2+) bonding. The coordination entity's configuration in this subgroup is described by IUPAC's polyhedral symbol SPY-5. Continuous shape measures (CShM) as defined by Alvarez et al. (Coord. Chem. Rev., 2005, 249, 1693-1708) reveal a uniform deviation from the L-M-L angles expected for SPY-5, in a narrower sense, towards a vacant octahedron (vOC-5). DFT calculations confirmed that Enemark and Feltham's analysis (Coord. Chem. Rev., 1974, 13, 339-406) of the electronic situation of the {Ru(NO)2}(8) group remains adequate. The same holds for the second subclass of new compounds the existence of which had been predicted in the same paper by Enemark and Feltham, namely C(2v)-symmetric, TBPY-5-type cations with two almost equally bonded nitrosyl ligands. In agreement with an 8 + 0 distribution of the relevant electrons, the formal [Ru(0)(NO(+))2](2+) entities are found for L/X couples that donate more electron density on the central metal. Two solid compounds (8a/b, 12a/b) were found in both structures including the special case of the P(i)Pr3/Br couple 12a/b, which led to crystals that contained both structure types in the same solid. Conversely, four compounds showed a single form in the solid but both forms in dichloromethane solution in terms of the solutions' IR spectra. The irradiation of crystalline 12 with blue laser light resulted in the photoisomerisation of, mainly, the bent (1)NO(-) ligand in terms of low-temperature IR spectroscopy.

Structural reinvestigation of the photoluminescent complex [NdCl2(H2O)6]Cl.

The structure of the photoluminescent compound hexaaquadichloridoneodymium(III) chloride has been redetermined from single-crystal X-ray diffraction data at 100 K, with the aim of providing an accurate structural model for the bulk crystalline material. The crystal structure may be described as a network of [NdCl2(H2O)6](+) cations with distorted square-antiprism geometry around the Nd(III) centre. The Nd(III) cation and the nonbonded Cl(-) anion are both located on twofold symmetry axes. The crystal packing consists of three different neodymium pairs linked by a three-dimensional network of O-H···Cl intermolecular interactions. The pair distribution function (PDF) calculated from the experimentally determined structure is used for the discussion of the local structure.

Structural influence on the photochromic response of a series of ruthenium mononitrosyl complexes.

In mononitrosyl complexes of transition metals two long-lived metastable states corresponding to linkage isomers of the nitrosyl ligand can be induced by irradiation with appropriate wavelengths. Upon irradiation, the N-bound nitrosyl ligand (ground state, GS) turns into two different conformations: isonitrosyl O bound for the metastable state 1 (MS1) and a side-on nitrosyl conformation for the metastable state 2 (MS2). Structural and spectroscopic investigations on [RuCl(NO)py(4)](PF(6))(2)·1/2H(2)O (py = pyridine) reveal a nearly 100% conversion from GS to MS1. In order to identify the factors which lead to this outstanding photochromic response we study in this work the influence of counteranions, trans ligands to the NO and equatorial ligands on the conversion efficiency: [RuX(NO)py(4)]Y(2)·nH(2)O (X = Cl and Y = PF(6)(-) (1), BF(4)(-) (2), Br(-)(3), Cl(-) (4); X = Br and Y = PF(6)(-) (5), BF(4)(-) (6), Br(-)(7)) and [RuCl(NO)bpy(2)](PF(6))(2) (8), [RuCl(2)(NO)tpy](PF(6)) (9), and [Ru(H(2)O)(NO)bpy(2)](PF(6))(3) (10) (bpy = 2,2'-bipyridine; tpy = 2,2':6',2"-terpyridine). Structural and infrared spectroscopic investigations show that the shorter the distance between the counterion and the NO ligand the higher the population of the photoinduced metastable linkage isomers. DFT calculations have been performed to confirm the influence of the counterions. Additionally, we found that the lower the donating character of the ligand trans to NO the higher the photoconversion yield.

Properties of metastable linkage NO isomers in Na2[Fe(CN)5NO]·2H2O incorporated in mesopores of silica xerogels.

We study the properties of photoinduced metal-nitrosyl linkage isomers in sodium nitroprusside (SNP) as a function of particle size. By embedding the molecular complex at various concentrations into mesopores of silica xerogels the size of the particles can be adjusted. The ground state is characterized by X-ray diffraction, absorption and infrared spectroscopy. The physical properties of the photoswitched molecules were analysed by steady-state low-temperature absorption, infrared spectroscopy and by nanosecond transient absorption spectroscopy. The electronic structure as well as the activation energies of the metastable linkage isomers are independent of the particle size down to single isolated molecules, indicating that the SNP complexes are quasi-free inside the pores of the gel.

Ultrafast reversible ligand isomerisation in Na2[Fe(CN)5NO] x 2 H2O single crystals.

We present a time-resolved absorption study on the light-induced generation of reversible linkage NO isomers in single crystals of Na(2)[Fe(CN)(5)NO] x 2 H(2)O using laser pulses of 160 fs width. Using the pump wavelength lambda = 500 nm the singlet-singlet (1)A(1)-->(1)E excitation induces the NO rotation by about 90 degrees from the linear Fe-N-O configuration to a side-on configuration [structure: see text]. The formation of the isomer is monoexponential with a characteristic time of tau = 300(20) fs and proceeds along a diabatic potential surface without occupation of further intermediate states. The side-on structure has a lifetime of 270(30) ns at T = 23 degrees C.

Reversible photoswitching between nitrito-N and nitrito-O isomers in trans-[Ru(py)(4)(NO(2))(2)].

Nitro-nitrito photoisomerisation is investigated in solid samples and solutions of trans-[Ru(py)(4)(NO(2))(2)]. Using light of wavelength 325 nm 50% of the N-bound Ru-NO(2) ligands can be switched to the O-bound Ru-ONO configuration (nitrito-N to nitrito-O isomerisation) at temperatures below T = 250 K in solids. The population of the isomeric configurations is determined with infrared spectroscopy from the decrease of the area of the nu(NO) stretching and delta(NO) deformation modes. In a frozen methanol-ethanol solution nearly 100% can be converted to the nitrito-O configuration. Upon heating above T = 250 K the Ru-NO(2) configuration is restored. The nitrito-O Ru-ONO configuration can be partially transferred back to the nitrito-N configuration by irradiation with light in the spectral range 405-442 nm. Using absorption spectroscopy on a frozen methanol-ethanol solution, two new bands at 447 and 380 nm are observed in the nitrito-O configuration compared to one at 334 nm of the nitrito-N ground state configuration. The photoconversion is initiated by the metal-to ligand charge transfer transition Ru(d) -->pi*(NO(2),py) as shown by the calculated partial density of states using Density Functional Theory. The calculations yield also the structure of the nitrito-N and nitrito-O isomer as well as the corresponding vibrational densities. The experimental structure of the ground state is determined using powder diffraction.

Phototriggered NO and CN release from [Fe(CN)5NO]2- molecules electrostatically attached to TiO2 surfaces.

Phototriggered NO and CN release from [Fe(CN)(5)NO](2-) (NP) molecular monolayers is studied by a combination of electrochemistry, infrared spectroscopy, and mass spectrometry under light irradiation at temperatures of 80 K and 294 K. The NP molecular monolayers were electrostatically attached to thin films of mesoporous TiO(2) deposited on silicon. Irradiation of the surfaces results in NO and CN release, which is verified using mass spectrometry. The kinetic trace of the light driven NO release of the [Fe(CN)(5)NO](2-) is determined by inspection of the nu(NO) stretching mode as a function of exposure to light in the violet/green spectral range. The decrease of the nu(NO)-amplitude can be modeled considering the NO release as a two-step process with an intermediate state between the attached and the released state. According to literature, the intermediate state may be related to the light-induced linkage NO isomerization of the NP.

Photogeneration of nitrosyl linkage isomers in octahedrally coordinated platinum complexes in the red spectral range.

Octahedrally coordinated platinum nitrosyl complexes [Pt(NH(3))(4)(NO(3))(NO)](NO(3))(2) (1) and [Pt(NH(3))(4)(SO(4))(NO)](HSO(4))(CH(3)CN) (2) undergo linkage isomerization at temperatures below 130 K when excited with red light. Irradiation in the spectral range of 570-800 nm results in an inversion of the NO ligand from a Pt-NO to a Pt-ON configuration. The metastable state Pt-ON can be reverted back to the ground state (GS) Pt-NO by irradiation with blue-green or infrared light or by heating above 130 K. The characteristic shift of the nu(NO) stretching vibration from 1744 to 1815 cm(-1) in 1 and from 1714 to 1814 cm(-1) in 2 allowed the unambiguous identification of the respective nitrosyl isomers. Up to 26% of the complexes of 1 and 20% of 2 may be photochemically excited toward the metastable state (MS). Using X-ray crystallography and DFT calculations, it is shown that the Pt-NO in these {MNO}(8) complexes exhibits a bent arrangement with a Pt-N-O angle in the range of 117-120 degrees. As a consequence and in contrast to the known {MNO}(6) complexes only one metastable linkage isomer Pt-ON with a correspondingly bent Pt-O-N arrangement is formed, as evidenced by spectroscopy and DFT calculations. The calculated partial density of states shows that the charge transfer transition Pt(5d) --> pi(star)(NO) is responsible for the formation of the metastable state.

[Ru(py)4Cl(NO)](PF6)2.0.5H2O: a model system for structural determination and ab initio calculations of photo-induced linkage NO isomers.

Structure analysis of ground state (GS) and two light-induced (SI and SII) metastable linkage NO isomers of [Ru(py)4Cl(NO)](PF6)2.0.5H2O is presented. Illumination of the crystal by a laser with lambda = 473 nm at T = 80 K transfers around 92% of the NO ligands from Ru-N-O into the isomeric configuration Ru-O-N (SI). A subsequent irradiation with lambda = 980 nm generates about 48% of the side-on configuration Ru<(N)(O) (SII). Heating to temperatures above 200 K or irradiation with light in the red spectral range transfers both metastable isomers reversibly back to the GS. Photodifference maps clearly show the N-O configurations for both isomers and they could be used to find a proper starting model for subsequent refinements. Both metastable isomers have slightly but significantly different cell parameters with respect to GS. The main structural changes besides the Ru-O-N and RU<(N)(O) linkage are shortenings of the trans Ru-Cl bonds and the equatorial Ru-N bonds. The experimental results are compared with solid-state calculations based on density functional theory (DFT), which reproduce the observed structures with high accuracy concerning bond lengths and angles. The problem of how the different occupancies of SI and GS could affect refinement results was solved by a simulation procedure using the DFT data as starting values.

Pronounced photosensitivity of molecular [Ru(bpy)2(OSO)]+ solutions based on two photoinduced linkage isomers.

Photosensitive properties of [Ru(bpy)(2)(OSO)] PF(6) dissolved in propylene carbonate originating from photoinduced linkage isomerism have been studied by temperature and exposure dependent transmission and UV/Vis absorption spectroscopy. An exceeding photochromic photosensitivity of S = (63 +/- 10) x 10(3) cm l J(-1) mol(-1) is determined. It is attributed to a maximum population of 100% molecules in the photoinduced isomers, a unique absorption cross section per molecule and a very low light exposure of Q(0) = (0.25 +/- 0.03) Ws cm(-2) for isomerism. Relaxation studies of O-bonded to S-bonded isomers at different temperatures verify the existence of two distinct structures of linkage isomers determined by the activation energies of E(A,1) = (0.76 +/- 0.08) eV and E(A,2) = (1.00 +/- 0.14) eV.

Necessary conditions for the photogeneration of nitrosyl linkage isomers.

We investigate the fundamental necessary conditions for optical generation of nitrosyl linkage isomers in ML(5)NO compounds (M = transition metal, L arbitrary ligand) on the examples of K(3)[Mn(CN)(5)NO].2H(2)O and Na(2)[Fe(CN)(5)NO].2H(2)O. We show that the NO linkage isomers of the side-on bonded type (SII, 90 degrees rotation of NO) and of the isonitrosyl type M-ON, where NO is O-bound to the metal M (SI, 180 degrees rotation of NO), can be generated if two conditions are fullfilled. First the optical excitation must lead to a change in the bond between the NO group and the central metal atom M, either by a metal-to-ligand charge transfer of type d -->pi*(NO) or by a d-->d(z(2)) transition, which changes the sigma bonding of the NO group to the metal, such that the vibrational deformation mode delta(M-N-O) can drive the system into the SII configuration. Second the excited state potential must posses a minimum close to the saddle point of the ground state surface between GS and SII, SI, or cross that surface, such that the relaxation from the excited state into the metastable minima can occur. The same is true for transfers between the two metastable states SII and SI. As a further constraint with respect to the amount of population, i.e. the number of complexes which can be transferred into SII or SI, the cross sections sigma(GS,SII,SI) of the states GS, SII, and SI must be considered. If sigma(GS) > sigma(SII) and sigma(SI) > sigma(SII) SII can be occupied while SI can be significantly occupied if sigma(GS) > sigma(SI) and sigma(SII) > sigma(SI). More simply speaking the depletion rate of the metastable state should be smaller than its population rate for a given wavelength.