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Electronic structures and the stabilities of metastable states in [Ru(CN)5NO]2−: A theoretical study
Chemical Physics Letters 412 (2005) 164–170 www.elsevier.com/locate/cplett
Electronic structures and the stabilities of metastable states in [Ru(CN)5NO]2: A theoretical study Takeshi Ishikawa, Kiyoshi Tanaka
*
Division of Chemistry, Graduate School of Science, Hokkaido University, Sapporo 060-0810, Japan Received 27 February 2005; in final form 22 June 2005 Available online 19 July 2005
Abstract The stability of the ground state (GS) and two metastable states (MS1 and MS2) in [Ru(CN)5NO]2 were investigated by ab initio calculations. We obtained the global potential energy surface of the electronic ground state, in which GS, MS1, and MS2 were included as the true minimum and local minima. The barrier heights among them in [Ru(CN)5NO]2 were higher than those of [Fe(CN)5NO]2. We carried out calculations of the six lowest states. Their potential energy surfaces had several crossings in the reaction pathways, and they were in close similarity to the feature of the potential energy surfaces of the lower states in [Fe(CN)5NO]2. Ó 2005 Elsevier B.V. All rights reserved.
1. Introduction Two extremely long-lived photo-induced metastable states (MS1 and MS2) in the sodiumnitorpruside (Na2[Fe(CN)5NO] Æ 2H2O) crystal were discovered by Hauser et al. in 1977 [1]. It turned out that this complex was transferrable from one state to another among the two metastable states and the ground state (GS) by irradiation with light. Since long-lived metastable states are of great interest for technological applications, many experimental [2–12] and theoretical [13–19] studies have since been reported on this material. It has been recognized that Na2[Fe(CN)5NO] Æ 2H2O as well as many related nitrosyl complexes with the general composition of Xn[MLmNO] Æ YH2O have long-lived metastable states [20–22] (M: the central transition metal atom, Lm: the ligands, Xn: cations or anions, and Y: number of water ligands). * Corresponding author. Present address: Advancesoft, Incubation Project (FSIS) CCR, The University of Tokyo, Komaba 4-6-1, Meguro-ku, Tokyo, 153-8904, Japan. Fax: +81 3 5452 6623. E-mail address: [email protected] (K. Tanaka).
0009-2614/$ - see front matter Ó 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2005.06.117
Likewise, the Ru nitrosyl complex, Na2[Ru(CN)5NO] Æ 2H2O, has two photo-induced metastable states, MS1 and MS2. The decay temperatures of the two metastable states, 220 and 230 K [23], respectively, are higher than those of Na2[Fe(CN)5NO] Æ 2H2O, 200 and 150 K [24]. The increases in the decay temperatures are expected to have significant technological importance. Photo-induced transfer processes among GS, MS1, and MS2 are one of typical photoreactions, and information on the global potential energy surfaces of electronic excited states is essential for full understanding of these processes for these complexes. However, only little has yet been reported except for our previous study of [Fe(CN)5NO]2 [19]. In the present Letter, we have focused our attention on the stabilities of the photo-induced metastable states of [Ru(CN)5NO]2. We carried out theoretical calculations of the global potential energy surface of the electronic ground state in multi-reference singly and doubly excited configuration interaction (MRSDCI) with Davidson type quadruple correction [28,29] (MRSDCI + Q). Furthermore, the process of the photo-induced transfer among GS, MS1, and MS2
T. Ishikawa, K. Tanaka / Chemical Physics Letters 412 (2005) 164–170
was investigated by calculations of their potential energy surfaces of five lower excited states using the state-averaged complete active space self-consistent field (SACASSCF) scheme. The results are compared with our previous theoretical study of [Fe(CN)5NO]2 [19].
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(2) among the remaining four degrees of freedom: [the N(2)–O(3) distance, the Ru(1)–G distance, \C(4)– Ru(1)–C(5) (\a), and \N(2)–G–Ru(1) (\b)], N(2)–O(3) and \a were retained at the corresponding values of GS obtained by the X-ray analysis [27], (N(2)– ˚ and \a = 98.3°), where G denotes the O(3) = 1.13 A center of mass of the N(2) and O(3) moiety.
2. Details of calculations We used a set of split valence contracted Gaussian type orbitals (CGTOs) (333331/333/362), and added a p-type CGTO (two terms) and an f-type CGTO (three terms) for Ru. The orbitals describing the core region of this basis set were prepared by Huzinaga et al. [25], and the valence parts and polarization functions were given by Osanai et al. [26]. For carbon, nitrogen, and oxygen atoms, we adopted the basis sets used in our previous study [19]. We did not take the crystal field into account, because its inclusion was found to be insignificant in predicting the vibrational frequencies and electronic excitation energies and in discussing the transfer processes among GS, MS1, and MS2 [13,19]. A geometrical rearrangement among GS, MS1, and MS2 will take place primarily in the nitrosyl group [19], but other geometry parameters are expected to be essentially constant. Similarly to our previous study [19], we used the geometrical parameters of GS obtained by an X-ray analysis [27], although a different treatment was applied to nitrogen (N(2)) and oxygen (O(3)) atoms of the nitrosyl group (see Fig. 1). We set additional constraints on the nitrosyl group as follows:
Consequently, the variables describing the reaction coordinate were Ru(1)–G and \b. This coordinate is a Jacobi-type coordinate for describing intramolecular reaction. The molecular symmetry point group was nearly C4v for GS and MS1, and Cs for MS2 and in the reaction pathway. However, we employed the C1 point group for representing the wavefunctions. The total spin of the wavefunctions was set as a singlet. Firstly, we carried out six state averaged CASSCF calculations, where 12 valence electrons were distributed among 10 orbitals, i.e., r(NO), rðNOÞ , px(NO), py(NO), pxðNOÞ ; pyðNOÞ , dxy(Fe), dyz(Fe), dzx(Fe), and dz2 ðFeÞ . Next, we carried out MRSDCI for the electronic ground state. In this CI, 11 reference configuration state functions (CSFs) were selected from the wavefunctions obtained by CASSCF calculations. The number of CSFs of this CI was about 2 400 000. The Davidson type quadruple correction [28,29] was then carried out (MRSDCI + Q). We calculated the vertical excitation energies of five excited states using MRSDCI + Q for GS, MS1, and MS2, in which 16 CSFs were chosen as reference CFSs, and the dimension of this CI was about 3 600 000.
(1) N(2) and O(3) atoms in the nitrosyl group were placed in a plane defined by C(4)–Ru(1)–C(5);
3. Results and discussion 3.1. Potential energy surface of the ground state
O(3) G N(2) N
C
Ru(1)
N
C
C(5) N
C(4)
C
N
N Fig. 1. Parameters of two-dimensional potential energy surfaces. G is the center of mass of N(2) and O(3). The shadow indicates the plane created by C(4)–Ru(1)–C(5). N(2) and O(3) remain in this plane throughout the calculations in this Letter.
The potential energy surface, shown in Fig. 2, obtained by MRSDCI + Q has three local minima, ˚ and \b = 5° for GS located at Ru–G = 2.27 A ˚ ˚ and \b = 180° for (Ru–N = 1.75 A), Ru–G = 2.44 A ˚ ˚ and MS1 (Ru–O = 1.88 A), and Ru–G = 1.98 A ˚ \b = 85° for MS2 (Ru–N = 2.03 A and Ru–O = ˚ ). At the deepest minimum (\b = 5°), the Ru– 2.15 A N–O configuration was found to be linear. A minimum located at \b = 180° also showed a linear configuration, which is the inverted bond of the N–O ligand to Ru. A minimum at \b = 85° exhibited the side-on bonding of NO to Ru. An X-ray structure analysis was reported only for GS [27], which showed ˚ and \b = 4.17°. The differences that Ru–G = 2.23 A of the present structure from the X-ray analysis were ˚ and 1.0° for Ru–G and \b, respectively. 0.04 A The global shape of this surface was analogous to that of [Fe(CN)5NO]2 [19].
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T. Ishikawa, K. Tanaka / Chemical Physics Letters 412 (2005) 164–170 MS2 N
MS1
O
N O
Ru
Ru
a.u. -5013.76 -5013.78 -5013.8 -5013.82 -5013.84 -5013.86 -5013.88 -5013.9 GS
O N
3.5
Ru
4 4.5 5 5.5
0
50
100
200
150
3.5
4.0
4.5
5.0
5.5 0
50
100
150
200
Fig. 2. Potential energy surface of the ground state by MRSDCI + Q and its contour map. This surface has three local minima corresponding to the structures of GS, MS1, and MS2.
0.68 eV
0.64 eV 2.36 eV TS
2.34 eV TS 2.34 eV
1.68 eV
1.60 eV 0.66 eV
0.0 eV GS
MS2
MS1
Fig. 3. Energy diagram of the ground state with respect to the energy of GS obtained by MRSDCI + Q. TS represents a near-transition state.
Fig. 3 shows the calculated energies of MS1, MS2, and ˚ and two near-transition states located at Ru–G = 2.38 A ˚ \b = 55°, and Ru–G = 2.54 A and \b = 135° relative to
the energy of GS. The calculated energy barriers were: 0.68 eV (MS1 ! MS2), 0.64 eV (MS2 ! GS), and 0.66 eV (MS2 ! MS1). These values are much higher than those for [Fe(CN)5NO]2, 0.35 eV (MS1 ! MS2), 0.44 eV (MS2 ! GS), and 0.43 eV (MS2 ! MS1) [19]. This difference was further studied by an analysis of the wavefunctions of [Ru(CN)5NO]2 and comparison with those of [Fe(CN)5NO]2. The natural orbitals obtained by MRSDCI (Fig. 4) have significant amplitudes around the Ru–NO area at GS, MS1, and MS2. We summarize their occupation numbers in Table 1, in which those of [Fe(CN)5NO]2 obtained in [19] are included. The natural orbital ðdRu þ pNO Þe of GS shows a bonding character between Ru and NO, whereas ðdRu pNO Þe has an anti-bonding
T. Ishikawa, K. Tanaka / Chemical Physics Letters 412 (2005) 164–170
167
Fig. 4. Natural orbitals obtained by MRSDCI in the vicinity of Ru–NO at GS, MS1, and MS2. Some part of ðpNO Þa0 orbital at MS2 is cut off because of our drawing tool, but it essentially exhibits the character of the orbital. The subscripts designate symmetry groups of the orbitals. Cs symmetry is broken in the two orbitals of ðdRu þ pNO Þi and ðdRu þ pNO Þii .
character. Their occupation numbers are 3.80 and 0.22, respectively, while those of the corresponding orbitals of [Fe(CN)5NO]2 are 3.65 and 0.37, respectively. The occupation number of the bonding orbital in [Ru(CN)5NO]2 is larger than that in [Fe(CN)5NO]2 by 0.15; to the contrary, the value of the anti-bonding orbital in the former is smaller than that in the latter by 0.15. This difference in the occupation numbers of the bonding and anti-bonding orbitals indicates that the bond of Ru–NO is stronger than that of Fe–NO. In spite of the several approximations used in the
present Letter, the differences between the results for [Fe(CN)5NO]2 and [Ru(CN)5NO]2 reflect the fact that the decay temperatures of the metastable states of Na2[Ru(CN)5NO] Æ 2H2O (220 K for MS1 and 230 K for MS2) are higher than 200 K of MS1 and 150 K of MS2 of Na2[Fe(CN)5NO] Æ 2H2O. The tendencies in the occupation numbers of the natural orbitals of the bonding and anti-bonding orbitals for MS1 and MS2 are essentially the same as in the GS case. Higher barrier heights in the Ru complex reflect higher covalency in the Ru complex.
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Table 1 Occupation numbers of natural orbitals in [Ru(CN)5NO]2 and [Fe(CN)5NO]2 a Character
[Ru(CN)5NO]2 b
[Fe(CN)5NO]2 c
GS
ðrNO Þa1 ðdM Þb2 (pNO)e ðdM þ pNO Þe ðdM pNO Þe
Non-bonding Non-bonding Non-bonding Bonding Anti-bonding
1.97 1.98 3.94 3.80 0.22
1.97 1.98 3.92 3.65 0.37
MS1
ðrNO Þa1 ðdM Þb2 (pNO)e ðdM þ pNO Þe ðdM pNO Þe
Non-bonding Non-bonding Non-bonding Bonding Anti-bonding
1.98 1.98 3.93 3.63 0.38
1.97 1.98 3.92 3.52 0.50
MS2
ðrNO Þa0 ðpNO Þa0 ;a00 ðpNO Þa00 ðdM Þa00 ðdM þ pNO Þi ðdM þ pNO Þii ðdM pNO Þa0
Non-bonding Non-bonding Non-bonding Non-bonding Bonding Bonding Anti-bonding
1.98 3.94 0.15 1.86 1.90 1.96 0.10
1.97 3.92 0.15 1.98 1.87 1.77 0.24
For MS1, we obtained five excited states whose vertical excitation energies are 1.50, 1.52, 2.03, 2.06, and 2.08 eV. The main configurations of these states are very similar to those for GS. The two lower states are constructed by ðdRu Þb2 ! ðpNO Þe while the higher three are constructed by ðdRu Þe ! ðpNO Þe . The vertical excitation energies for MS2 are 1.63, 2.09, 2.14, 2.44, and 2.80 eV. In this case, the bond between Ru and NO is nonlinear, and the electronic structures of excited states are complicated, but the primary electronic configurations of calculated excited states are dRu ! pNO , being identical to that for GS and MS1. 3.3. Potential energy surfaces of excited states Fig. 5 shows the cross-sections of two-dimensional potential energy surfaces calculated by the SA-CASSCF scheme, in which Ru–G were set to 2.27, 2.49, and ˚ . The energy minimum at \b = 5° in the cross2.01 A ˚ is close to that for GS, section of Ru–G = 2.27 A ˚ corre\b = 180° in the cross-section of Ru–G = 2.49 A sponds to that for MS1, and \b = 85° in the cross˚ is near that for MS2. section of Ru–G = 2.01 A As is clearly shown in the three figures, there are several crossings of the surfaces. The characters of the wavefunctions change abruptly near the crossings, and for this reason, a non-adiabatic transition takes place with high probability. We can infer that the photo-induced transfers among GS, MS1, and MS2 occur through these non-adiabatic transitions. For example, the value of \b increases in photoinduced transfer (GS ! MS1 or MS2) in accordance with the decrease in the potential energy. The excited state then decays into the local minimum of MS1 or MS2. The lowest excited state at MS1 is much higher in energy than the crossing points between the surface of the ground state and the lowest excited state. Transition from the excited state to the ground state takes place around \b = 150° and 50°. As for the transfer ˚ in from MS2 (see the cross-section of Ru–G = 2.01 A Fig. 5), there are energy barriers on both sides of \b = 85° in excited states. However, the energy decreases with no barrier when Ru–G increases as in the
a M indicates the central transition metal atom, Ru or Fe. The subscript shows the symmetry group of orbitals. b Obtained by MRSDCI (Fig. 4). Present Letter. c Ref. [19].
3.2. Vertical excitation energies for GS, MS1, and MS2 Table 2 shows the vertical excitation energies of the lowest five excited states in GS, MS1, and MS2 calculated by MRSDCI + Q. Olabe et al. [27] observed the electronic spectrum of GS in aqueous solution, and assigned the two peaks around 2.85 and 3.59 eV to ðdRu Þb2 ! ðpNO Þe and ðdRu Þe ! ðpNO Þe . In the present calculation, the vertical excitation energies of the lower two states of GS, with the main configurations of ðdRu Þb2 ! ðpNO Þe , are 2.94 and 3.05 eV. Thus, these values correspond to the peak around 2.85 eV. Higher states have the vertical excitation energies of 4.15, 4.26, and 4.29 eV. Since their primary electronic configurations are ðdRu Þe ! ðpNO Þe , these three states should be attributed to the observed peak around 3.59 eV, although the calculated vertical excitation energies are overestimated by 0.59–0.70 eV.
Table 2 Vertical excitation energies (eV) in GS, MS1, and MS2 obtained by MRSDCI + Q State
GS Main configurations ðpNO Þe
1 2
ðdRu Þb2 !
3 4 5
ðdRu Þe ! ðpNO Þe
a b
MS2a
MS1 Calc.
Exp.b
Main configurations ðpNO Þe
2.94 3.05
2.85
ðdRu Þb2 !
4.15 4.26 4.29
3.59
ðdRu Þe ! ðpNO Þe
The main configurations of the excited states of MS2 are complicated (see text). Ref. [27].
Calc.
Calc.
1.50 1.52
1.63 2.09
2.03 2.06 2.08
2.14 2.44 2.80
T. Ishikawa, K. Tanaka / Chemical Physics Letters 412 (2005) 164–170
169
These features of the potential energy surface of [Ru(CN)5NO]2 are close to those of [Fe(CN)5NO]2 (see Figs. 7–9 in [19]). Namely, we infer that the processes of the photo-induced transfer among GS, MS1, and MS2 are analogous to each other in the two nitrosyl complexes, [Ru(CN)5NO]2 and [Fe(CN)5NO]2.
eV 6 5 4 3
4. Summary
2 1 0 GS 0
50
100
150
200
eV 6 5 4 3 2 MS1
1 0 0
50
100
150
200
eV 6 5
The stability of the photo-induced metastable states in [Ru(CN)5NO]2 has been studied using theoretical calculations, based on which the processes of photo-induced transfer among GS, MS1, and MS2 are discussed. The potential energy surfaces of the ground state by MRSDCI + Q have three local minima at the geome˚ and \b = 5°, Ru–G = 2.44 A ˚ tries of Ru–G = 2.27 A ˚ and \b = 85°, and \b = 180°, and Ru–G = 2.01 A which correspond to GS, MS1, and MS2, respectively. The energy diagram of the ground state indicates that the metastable states for [Ru(CN)5NO]2 are much more stable than those for [Fe(CN)5NO]2. The occupation numbers of the natural orbitals in GS, MS1, and MS2 indicate that the bond between Ru and NO is stronger than that between Fe and NO. The vertical excitation energies of the five states in GS, MS1, and MS2 are calculated by MRSDCI + Q, whose main configurations are dRu ! pNO . We have also considered the process of photo-induced transfer among GS, MS1, and MS2 using two-dimensional potential energy surfaces of six states. The decay to lower states takes place in the vicinity of crossing in the potential energy surfaces, which accounts for the photo-induced transfers. Such processes of photo-induced transfer in [Ru(CN)5NO]2 are found to be quite analogous to those in [Fe(CN)5NO]2.
4 3
Acknowledgments
2 MS2
1 0 0
50
100
150
200
Fig. 5. The cross-sections of the two-dimensional potential energy ˚. surfaces of six states, in which Ru–G was set at 2.27, 2.49, and 2.01 A
case of [Fe(CN)5NO]2, as reported in Fig. 10 of [19]. After the increase in Ru–G, a transition to other minima will take place at a large Ru–G distance, and transfer to MS1 and GS will follow even with excitation to the lowest excited state (1.63 eV as stated above).
This work was partially supported by Grant-In-Aid for Scientific Research No. 16550001 of fundamental research from the Ministry of Education, Science, Sports and Culture of Japan. T.I. is grateful for financial support from the Graduate School of Science of Hokkaido University in the form of a research assistantship. All calculations in this Letter were carried out with the Software Package MOLCAS [30].
References [1] U. Hauser, V. Oestreich, H.D. Rohrweck, Z. Phys. A 280 (1977) 125. [2] P. Gu¨tlich, Y. Garcia, Th. Woike, Coord. Chem. Rev. 219–221 (2001) 839.
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[3] P. Coppens, I. Novozhilova, A. Kovalevsky, Chem. Rev. 102 (2002) 861. [4] P.T. Manoharan, H.B. Gray, Inorg. Chem. 5 (1966) 823. [5] Y. Morioka, H. Saitoh, H. Machida, J. Phys. Chem. A 106 (2002) 3517. [6] M.E. Chac´on Villalba, J.A. Gu¨ida, E.L. Varetti, P.J. Aymonino, Inorg. Chem. 42 (2003) 2622. [7] M.E. Chac´on Villalba, J.A. Gu¨ida, E.L. Varetti, P.J. Aymonino, Spectrochim. Acta A 57 (2001) 367. [8] W. Krasser, Th. Woike, P.S. Bechthold, S. Haussu¨hl, J. Mol. Struct. 114 (1984) 57. [9] Y. Morioka, H.-o. Hamaguchi, J. Phys. Chem. Solids 53 (1992) 967. [10] M.D. Carducci, M.R. Pressprich, P. Coppens, J. Am. Chem. Soc. 119 (1997) 2669. [11] P. Coppens, D.V. Fomitchev, M.D. Carducci, K. Culp, J. Chem. Soc., Dalton Trans. (1998) 865. [12] D. Schaniel, J. Schefer, B. Delly, M. Imlau, Th. Woike, Phys. Rev. B 66 (2002) 085103. [13] B. Delley, J. Schefer, T. Woike, J. Chem. Phys. 107 (1997) 10067. [14] S.I. Gorelsky, A.B.P. Lever, Int. J. Quantum Chem. 80 (2000) 636. [15] M. Atanasov, T. Scho¨nherr, J. Mol. Struct. 592 (2002) 79. [16] M.E. Chac´on Villalba, E.L. Varetti, P.J. Aymonino, Spectrochim. Acta A 55 (1999) 1545.
[17] P. Boulet, M. Buchs, H. Chermette, C. Daul, F. Gilardoni, F. Rogemond, C.W. Schla¨pfer, J. Weber, J. Phys. Chem. A 105 (2001) 8991. [18] J.A. Co´mez, D. Guenzburger, Chem. Phys. 253 (2000) 73. [19] T. Ishikawa, K. Tanaka, J. Chem. Phys. 122 (2005) 074314. [20] D.V. Fomitchev, I. Novozhilova, P. Coppens, Tetrahedron 56 (2000) 6813. [21] Y. Morioka, A. Ishikawa, H. Tomizawa, E. Miki, J. Chem. Soc., Dalton Trans. (2000) 781. [22] J.A. Gu¨ida, M.A. Ramos, O.E. Piro, P.J. Aymonino, J. Mol. Struct. 609 (2002) 39. [23] J.A. Gu¨ida, O.E. Piro, P.S. Schaiquevich, P.J. Aymonino, Solid State Commun. 101 (1997) 471. [24] H. Zo¨llner, W. Krasser, Th. Woike, S. Hau¨ssuhl, Z. Krist. 188 (1989) 139. [25] S. Huzinaga, J. Andzelm, M. Klovukouwski, E. Radzio-Andelm, Y. Sakai, H. Tatewaki, Gaussian Basis Set for Molecular Calculations, Elsevier, New York, 1984. [26] Y. Osanai, M. Sekiya, T. Noro, T. Koga, Mol. Phys. 101 (1–2) (2003) 65. [27] J.A. Olabe, L.A. Gentil, G. Rigotti, A. Navaza, Inorg. Chem. 23 (1984) 4297. [28] S.R. Langhoff, E.R. Davidson, Int. J. Quantum Chem. 8 (1974) 61. [29] E.R. Davidson, D.W. Silver, Chem. Phys. Lett. 52 (1977) 403. [30] K. Andersson et al., MOLCAS, Lund University, Sweden, 2002.
Electronic structures and the stabilities of metastable states in [Ru(CN)5NO]2: A theoretical study Takeshi Ishikawa, Kiyoshi Tanaka
*
Division of Chemistry, Graduate School of Science, Hokkaido University, Sapporo 060-0810, Japan Received 27 February 2005; in final form 22 June 2005 Available online 19 July 2005
Abstract The stability of the ground state (GS) and two metastable states (MS1 and MS2) in [Ru(CN)5NO]2 were investigated by ab initio calculations. We obtained the global potential energy surface of the electronic ground state, in which GS, MS1, and MS2 were included as the true minimum and local minima. The barrier heights among them in [Ru(CN)5NO]2 were higher than those of [Fe(CN)5NO]2. We carried out calculations of the six lowest states. Their potential energy surfaces had several crossings in the reaction pathways, and they were in close similarity to the feature of the potential energy surfaces of the lower states in [Fe(CN)5NO]2. Ó 2005 Elsevier B.V. All rights reserved.
1. Introduction Two extremely long-lived photo-induced metastable states (MS1 and MS2) in the sodiumnitorpruside (Na2[Fe(CN)5NO] Æ 2H2O) crystal were discovered by Hauser et al. in 1977 [1]. It turned out that this complex was transferrable from one state to another among the two metastable states and the ground state (GS) by irradiation with light. Since long-lived metastable states are of great interest for technological applications, many experimental [2–12] and theoretical [13–19] studies have since been reported on this material. It has been recognized that Na2[Fe(CN)5NO] Æ 2H2O as well as many related nitrosyl complexes with the general composition of Xn[MLmNO] Æ YH2O have long-lived metastable states [20–22] (M: the central transition metal atom, Lm: the ligands, Xn: cations or anions, and Y: number of water ligands). * Corresponding author. Present address: Advancesoft, Incubation Project (FSIS) CCR, The University of Tokyo, Komaba 4-6-1, Meguro-ku, Tokyo, 153-8904, Japan. Fax: +81 3 5452 6623. E-mail address: [email protected] (K. Tanaka).
0009-2614/$ - see front matter Ó 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2005.06.117
Likewise, the Ru nitrosyl complex, Na2[Ru(CN)5NO] Æ 2H2O, has two photo-induced metastable states, MS1 and MS2. The decay temperatures of the two metastable states, 220 and 230 K [23], respectively, are higher than those of Na2[Fe(CN)5NO] Æ 2H2O, 200 and 150 K [24]. The increases in the decay temperatures are expected to have significant technological importance. Photo-induced transfer processes among GS, MS1, and MS2 are one of typical photoreactions, and information on the global potential energy surfaces of electronic excited states is essential for full understanding of these processes for these complexes. However, only little has yet been reported except for our previous study of [Fe(CN)5NO]2 [19]. In the present Letter, we have focused our attention on the stabilities of the photo-induced metastable states of [Ru(CN)5NO]2. We carried out theoretical calculations of the global potential energy surface of the electronic ground state in multi-reference singly and doubly excited configuration interaction (MRSDCI) with Davidson type quadruple correction [28,29] (MRSDCI + Q). Furthermore, the process of the photo-induced transfer among GS, MS1, and MS2
T. Ishikawa, K. Tanaka / Chemical Physics Letters 412 (2005) 164–170
was investigated by calculations of their potential energy surfaces of five lower excited states using the state-averaged complete active space self-consistent field (SACASSCF) scheme. The results are compared with our previous theoretical study of [Fe(CN)5NO]2 [19].
165
(2) among the remaining four degrees of freedom: [the N(2)–O(3) distance, the Ru(1)–G distance, \C(4)– Ru(1)–C(5) (\a), and \N(2)–G–Ru(1) (\b)], N(2)–O(3) and \a were retained at the corresponding values of GS obtained by the X-ray analysis [27], (N(2)– ˚ and \a = 98.3°), where G denotes the O(3) = 1.13 A center of mass of the N(2) and O(3) moiety.
2. Details of calculations We used a set of split valence contracted Gaussian type orbitals (CGTOs) (333331/333/362), and added a p-type CGTO (two terms) and an f-type CGTO (three terms) for Ru. The orbitals describing the core region of this basis set were prepared by Huzinaga et al. [25], and the valence parts and polarization functions were given by Osanai et al. [26]. For carbon, nitrogen, and oxygen atoms, we adopted the basis sets used in our previous study [19]. We did not take the crystal field into account, because its inclusion was found to be insignificant in predicting the vibrational frequencies and electronic excitation energies and in discussing the transfer processes among GS, MS1, and MS2 [13,19]. A geometrical rearrangement among GS, MS1, and MS2 will take place primarily in the nitrosyl group [19], but other geometry parameters are expected to be essentially constant. Similarly to our previous study [19], we used the geometrical parameters of GS obtained by an X-ray analysis [27], although a different treatment was applied to nitrogen (N(2)) and oxygen (O(3)) atoms of the nitrosyl group (see Fig. 1). We set additional constraints on the nitrosyl group as follows:
Consequently, the variables describing the reaction coordinate were Ru(1)–G and \b. This coordinate is a Jacobi-type coordinate for describing intramolecular reaction. The molecular symmetry point group was nearly C4v for GS and MS1, and Cs for MS2 and in the reaction pathway. However, we employed the C1 point group for representing the wavefunctions. The total spin of the wavefunctions was set as a singlet. Firstly, we carried out six state averaged CASSCF calculations, where 12 valence electrons were distributed among 10 orbitals, i.e., r(NO), rðNOÞ , px(NO), py(NO), pxðNOÞ ; pyðNOÞ , dxy(Fe), dyz(Fe), dzx(Fe), and dz2 ðFeÞ . Next, we carried out MRSDCI for the electronic ground state. In this CI, 11 reference configuration state functions (CSFs) were selected from the wavefunctions obtained by CASSCF calculations. The number of CSFs of this CI was about 2 400 000. The Davidson type quadruple correction [28,29] was then carried out (MRSDCI + Q). We calculated the vertical excitation energies of five excited states using MRSDCI + Q for GS, MS1, and MS2, in which 16 CSFs were chosen as reference CFSs, and the dimension of this CI was about 3 600 000.
(1) N(2) and O(3) atoms in the nitrosyl group were placed in a plane defined by C(4)–Ru(1)–C(5);
3. Results and discussion 3.1. Potential energy surface of the ground state
O(3) G N(2) N
C
Ru(1)
N
C
C(5) N
C(4)
C
N
N Fig. 1. Parameters of two-dimensional potential energy surfaces. G is the center of mass of N(2) and O(3). The shadow indicates the plane created by C(4)–Ru(1)–C(5). N(2) and O(3) remain in this plane throughout the calculations in this Letter.
The potential energy surface, shown in Fig. 2, obtained by MRSDCI + Q has three local minima, ˚ and \b = 5° for GS located at Ru–G = 2.27 A ˚ ˚ and \b = 180° for (Ru–N = 1.75 A), Ru–G = 2.44 A ˚ ˚ and MS1 (Ru–O = 1.88 A), and Ru–G = 1.98 A ˚ \b = 85° for MS2 (Ru–N = 2.03 A and Ru–O = ˚ ). At the deepest minimum (\b = 5°), the Ru– 2.15 A N–O configuration was found to be linear. A minimum located at \b = 180° also showed a linear configuration, which is the inverted bond of the N–O ligand to Ru. A minimum at \b = 85° exhibited the side-on bonding of NO to Ru. An X-ray structure analysis was reported only for GS [27], which showed ˚ and \b = 4.17°. The differences that Ru–G = 2.23 A of the present structure from the X-ray analysis were ˚ and 1.0° for Ru–G and \b, respectively. 0.04 A The global shape of this surface was analogous to that of [Fe(CN)5NO]2 [19].
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T. Ishikawa, K. Tanaka / Chemical Physics Letters 412 (2005) 164–170 MS2 N
MS1
O
N O
Ru
Ru
a.u. -5013.76 -5013.78 -5013.8 -5013.82 -5013.84 -5013.86 -5013.88 -5013.9 GS
O N
3.5
Ru
4 4.5 5 5.5
0
50
100
200
150
3.5
4.0
4.5
5.0
5.5 0
50
100
150
200
Fig. 2. Potential energy surface of the ground state by MRSDCI + Q and its contour map. This surface has three local minima corresponding to the structures of GS, MS1, and MS2.
0.68 eV
0.64 eV 2.36 eV TS
2.34 eV TS 2.34 eV
1.68 eV
1.60 eV 0.66 eV
0.0 eV GS
MS2
MS1
Fig. 3. Energy diagram of the ground state with respect to the energy of GS obtained by MRSDCI + Q. TS represents a near-transition state.
Fig. 3 shows the calculated energies of MS1, MS2, and ˚ and two near-transition states located at Ru–G = 2.38 A ˚ \b = 55°, and Ru–G = 2.54 A and \b = 135° relative to
the energy of GS. The calculated energy barriers were: 0.68 eV (MS1 ! MS2), 0.64 eV (MS2 ! GS), and 0.66 eV (MS2 ! MS1). These values are much higher than those for [Fe(CN)5NO]2, 0.35 eV (MS1 ! MS2), 0.44 eV (MS2 ! GS), and 0.43 eV (MS2 ! MS1) [19]. This difference was further studied by an analysis of the wavefunctions of [Ru(CN)5NO]2 and comparison with those of [Fe(CN)5NO]2. The natural orbitals obtained by MRSDCI (Fig. 4) have significant amplitudes around the Ru–NO area at GS, MS1, and MS2. We summarize their occupation numbers in Table 1, in which those of [Fe(CN)5NO]2 obtained in [19] are included. The natural orbital ðdRu þ pNO Þe of GS shows a bonding character between Ru and NO, whereas ðdRu pNO Þe has an anti-bonding
T. Ishikawa, K. Tanaka / Chemical Physics Letters 412 (2005) 164–170
167
Fig. 4. Natural orbitals obtained by MRSDCI in the vicinity of Ru–NO at GS, MS1, and MS2. Some part of ðpNO Þa0 orbital at MS2 is cut off because of our drawing tool, but it essentially exhibits the character of the orbital. The subscripts designate symmetry groups of the orbitals. Cs symmetry is broken in the two orbitals of ðdRu þ pNO Þi and ðdRu þ pNO Þii .
character. Their occupation numbers are 3.80 and 0.22, respectively, while those of the corresponding orbitals of [Fe(CN)5NO]2 are 3.65 and 0.37, respectively. The occupation number of the bonding orbital in [Ru(CN)5NO]2 is larger than that in [Fe(CN)5NO]2 by 0.15; to the contrary, the value of the anti-bonding orbital in the former is smaller than that in the latter by 0.15. This difference in the occupation numbers of the bonding and anti-bonding orbitals indicates that the bond of Ru–NO is stronger than that of Fe–NO. In spite of the several approximations used in the
present Letter, the differences between the results for [Fe(CN)5NO]2 and [Ru(CN)5NO]2 reflect the fact that the decay temperatures of the metastable states of Na2[Ru(CN)5NO] Æ 2H2O (220 K for MS1 and 230 K for MS2) are higher than 200 K of MS1 and 150 K of MS2 of Na2[Fe(CN)5NO] Æ 2H2O. The tendencies in the occupation numbers of the natural orbitals of the bonding and anti-bonding orbitals for MS1 and MS2 are essentially the same as in the GS case. Higher barrier heights in the Ru complex reflect higher covalency in the Ru complex.
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Table 1 Occupation numbers of natural orbitals in [Ru(CN)5NO]2 and [Fe(CN)5NO]2 a Character
[Ru(CN)5NO]2 b
[Fe(CN)5NO]2 c
GS
ðrNO Þa1 ðdM Þb2 (pNO)e ðdM þ pNO Þe ðdM pNO Þe
Non-bonding Non-bonding Non-bonding Bonding Anti-bonding
1.97 1.98 3.94 3.80 0.22
1.97 1.98 3.92 3.65 0.37
MS1
ðrNO Þa1 ðdM Þb2 (pNO)e ðdM þ pNO Þe ðdM pNO Þe
Non-bonding Non-bonding Non-bonding Bonding Anti-bonding
1.98 1.98 3.93 3.63 0.38
1.97 1.98 3.92 3.52 0.50
MS2
ðrNO Þa0 ðpNO Þa0 ;a00 ðpNO Þa00 ðdM Þa00 ðdM þ pNO Þi ðdM þ pNO Þii ðdM pNO Þa0
Non-bonding Non-bonding Non-bonding Non-bonding Bonding Bonding Anti-bonding
1.98 3.94 0.15 1.86 1.90 1.96 0.10
1.97 3.92 0.15 1.98 1.87 1.77 0.24
For MS1, we obtained five excited states whose vertical excitation energies are 1.50, 1.52, 2.03, 2.06, and 2.08 eV. The main configurations of these states are very similar to those for GS. The two lower states are constructed by ðdRu Þb2 ! ðpNO Þe while the higher three are constructed by ðdRu Þe ! ðpNO Þe . The vertical excitation energies for MS2 are 1.63, 2.09, 2.14, 2.44, and 2.80 eV. In this case, the bond between Ru and NO is nonlinear, and the electronic structures of excited states are complicated, but the primary electronic configurations of calculated excited states are dRu ! pNO , being identical to that for GS and MS1. 3.3. Potential energy surfaces of excited states Fig. 5 shows the cross-sections of two-dimensional potential energy surfaces calculated by the SA-CASSCF scheme, in which Ru–G were set to 2.27, 2.49, and ˚ . The energy minimum at \b = 5° in the cross2.01 A ˚ is close to that for GS, section of Ru–G = 2.27 A ˚ corre\b = 180° in the cross-section of Ru–G = 2.49 A sponds to that for MS1, and \b = 85° in the cross˚ is near that for MS2. section of Ru–G = 2.01 A As is clearly shown in the three figures, there are several crossings of the surfaces. The characters of the wavefunctions change abruptly near the crossings, and for this reason, a non-adiabatic transition takes place with high probability. We can infer that the photo-induced transfers among GS, MS1, and MS2 occur through these non-adiabatic transitions. For example, the value of \b increases in photoinduced transfer (GS ! MS1 or MS2) in accordance with the decrease in the potential energy. The excited state then decays into the local minimum of MS1 or MS2. The lowest excited state at MS1 is much higher in energy than the crossing points between the surface of the ground state and the lowest excited state. Transition from the excited state to the ground state takes place around \b = 150° and 50°. As for the transfer ˚ in from MS2 (see the cross-section of Ru–G = 2.01 A Fig. 5), there are energy barriers on both sides of \b = 85° in excited states. However, the energy decreases with no barrier when Ru–G increases as in the
a M indicates the central transition metal atom, Ru or Fe. The subscript shows the symmetry group of orbitals. b Obtained by MRSDCI (Fig. 4). Present Letter. c Ref. [19].
3.2. Vertical excitation energies for GS, MS1, and MS2 Table 2 shows the vertical excitation energies of the lowest five excited states in GS, MS1, and MS2 calculated by MRSDCI + Q. Olabe et al. [27] observed the electronic spectrum of GS in aqueous solution, and assigned the two peaks around 2.85 and 3.59 eV to ðdRu Þb2 ! ðpNO Þe and ðdRu Þe ! ðpNO Þe . In the present calculation, the vertical excitation energies of the lower two states of GS, with the main configurations of ðdRu Þb2 ! ðpNO Þe , are 2.94 and 3.05 eV. Thus, these values correspond to the peak around 2.85 eV. Higher states have the vertical excitation energies of 4.15, 4.26, and 4.29 eV. Since their primary electronic configurations are ðdRu Þe ! ðpNO Þe , these three states should be attributed to the observed peak around 3.59 eV, although the calculated vertical excitation energies are overestimated by 0.59–0.70 eV.
Table 2 Vertical excitation energies (eV) in GS, MS1, and MS2 obtained by MRSDCI + Q State
GS Main configurations ðpNO Þe
1 2
ðdRu Þb2 !
3 4 5
ðdRu Þe ! ðpNO Þe
a b
MS2a
MS1 Calc.
Exp.b
Main configurations ðpNO Þe
2.94 3.05
2.85
ðdRu Þb2 !
4.15 4.26 4.29
3.59
ðdRu Þe ! ðpNO Þe
The main configurations of the excited states of MS2 are complicated (see text). Ref. [27].
Calc.
Calc.
1.50 1.52
1.63 2.09
2.03 2.06 2.08
2.14 2.44 2.80
T. Ishikawa, K. Tanaka / Chemical Physics Letters 412 (2005) 164–170
169
These features of the potential energy surface of [Ru(CN)5NO]2 are close to those of [Fe(CN)5NO]2 (see Figs. 7–9 in [19]). Namely, we infer that the processes of the photo-induced transfer among GS, MS1, and MS2 are analogous to each other in the two nitrosyl complexes, [Ru(CN)5NO]2 and [Fe(CN)5NO]2.
eV 6 5 4 3
4. Summary
2 1 0 GS 0
50
100
150
200
eV 6 5 4 3 2 MS1
1 0 0
50
100
150
200
eV 6 5
The stability of the photo-induced metastable states in [Ru(CN)5NO]2 has been studied using theoretical calculations, based on which the processes of photo-induced transfer among GS, MS1, and MS2 are discussed. The potential energy surfaces of the ground state by MRSDCI + Q have three local minima at the geome˚ and \b = 5°, Ru–G = 2.44 A ˚ tries of Ru–G = 2.27 A ˚ and \b = 85°, and \b = 180°, and Ru–G = 2.01 A which correspond to GS, MS1, and MS2, respectively. The energy diagram of the ground state indicates that the metastable states for [Ru(CN)5NO]2 are much more stable than those for [Fe(CN)5NO]2. The occupation numbers of the natural orbitals in GS, MS1, and MS2 indicate that the bond between Ru and NO is stronger than that between Fe and NO. The vertical excitation energies of the five states in GS, MS1, and MS2 are calculated by MRSDCI + Q, whose main configurations are dRu ! pNO . We have also considered the process of photo-induced transfer among GS, MS1, and MS2 using two-dimensional potential energy surfaces of six states. The decay to lower states takes place in the vicinity of crossing in the potential energy surfaces, which accounts for the photo-induced transfers. Such processes of photo-induced transfer in [Ru(CN)5NO]2 are found to be quite analogous to those in [Fe(CN)5NO]2.
4 3
Acknowledgments
2 MS2
1 0 0
50
100
150
200
Fig. 5. The cross-sections of the two-dimensional potential energy ˚. surfaces of six states, in which Ru–G was set at 2.27, 2.49, and 2.01 A
case of [Fe(CN)5NO]2, as reported in Fig. 10 of [19]. After the increase in Ru–G, a transition to other minima will take place at a large Ru–G distance, and transfer to MS1 and GS will follow even with excitation to the lowest excited state (1.63 eV as stated above).
This work was partially supported by Grant-In-Aid for Scientific Research No. 16550001 of fundamental research from the Ministry of Education, Science, Sports and Culture of Japan. T.I. is grateful for financial support from the Graduate School of Science of Hokkaido University in the form of a research assistantship. All calculations in this Letter were carried out with the Software Package MOLCAS [30].
References [1] U. Hauser, V. Oestreich, H.D. Rohrweck, Z. Phys. A 280 (1977) 125. [2] P. Gu¨tlich, Y. Garcia, Th. Woike, Coord. Chem. Rev. 219–221 (2001) 839.
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[3] P. Coppens, I. Novozhilova, A. Kovalevsky, Chem. Rev. 102 (2002) 861. [4] P.T. Manoharan, H.B. Gray, Inorg. Chem. 5 (1966) 823. [5] Y. Morioka, H. Saitoh, H. Machida, J. Phys. Chem. A 106 (2002) 3517. [6] M.E. Chac´on Villalba, J.A. Gu¨ida, E.L. Varetti, P.J. Aymonino, Inorg. Chem. 42 (2003) 2622. [7] M.E. Chac´on Villalba, J.A. Gu¨ida, E.L. Varetti, P.J. Aymonino, Spectrochim. Acta A 57 (2001) 367. [8] W. Krasser, Th. Woike, P.S. Bechthold, S. Haussu¨hl, J. Mol. Struct. 114 (1984) 57. [9] Y. Morioka, H.-o. Hamaguchi, J. Phys. Chem. Solids 53 (1992) 967. [10] M.D. Carducci, M.R. Pressprich, P. Coppens, J. Am. Chem. Soc. 119 (1997) 2669. [11] P. Coppens, D.V. Fomitchev, M.D. Carducci, K. Culp, J. Chem. Soc., Dalton Trans. (1998) 865. [12] D. Schaniel, J. Schefer, B. Delly, M. Imlau, Th. Woike, Phys. Rev. B 66 (2002) 085103. [13] B. Delley, J. Schefer, T. Woike, J. Chem. Phys. 107 (1997) 10067. [14] S.I. Gorelsky, A.B.P. Lever, Int. J. Quantum Chem. 80 (2000) 636. [15] M. Atanasov, T. Scho¨nherr, J. Mol. Struct. 592 (2002) 79. [16] M.E. Chac´on Villalba, E.L. Varetti, P.J. Aymonino, Spectrochim. Acta A 55 (1999) 1545.
[17] P. Boulet, M. Buchs, H. Chermette, C. Daul, F. Gilardoni, F. Rogemond, C.W. Schla¨pfer, J. Weber, J. Phys. Chem. A 105 (2001) 8991. [18] J.A. Co´mez, D. Guenzburger, Chem. Phys. 253 (2000) 73. [19] T. Ishikawa, K. Tanaka, J. Chem. Phys. 122 (2005) 074314. [20] D.V. Fomitchev, I. Novozhilova, P. Coppens, Tetrahedron 56 (2000) 6813. [21] Y. Morioka, A. Ishikawa, H. Tomizawa, E. Miki, J. Chem. Soc., Dalton Trans. (2000) 781. [22] J.A. Gu¨ida, M.A. Ramos, O.E. Piro, P.J. Aymonino, J. Mol. Struct. 609 (2002) 39. [23] J.A. Gu¨ida, O.E. Piro, P.S. Schaiquevich, P.J. Aymonino, Solid State Commun. 101 (1997) 471. [24] H. Zo¨llner, W. Krasser, Th. Woike, S. Hau¨ssuhl, Z. Krist. 188 (1989) 139. [25] S. Huzinaga, J. Andzelm, M. Klovukouwski, E. Radzio-Andelm, Y. Sakai, H. Tatewaki, Gaussian Basis Set for Molecular Calculations, Elsevier, New York, 1984. [26] Y. Osanai, M. Sekiya, T. Noro, T. Koga, Mol. Phys. 101 (1–2) (2003) 65. [27] J.A. Olabe, L.A. Gentil, G. Rigotti, A. Navaza, Inorg. Chem. 23 (1984) 4297. [28] S.R. Langhoff, E.R. Davidson, Int. J. Quantum Chem. 8 (1974) 61. [29] E.R. Davidson, D.W. Silver, Chem. Phys. Lett. 52 (1977) 403. [30] K. Andersson et al., MOLCAS, Lund University, Sweden, 2002.