Hyperfine Interactions and Electric Dipole Moments in the [16.0]1.5(v

Article pubs.acs.org/JPCA

Hyperfine Interactions and Electric Dipole Moments in the [16.0]1.5(v = 6), [16.0]3.5(v = 7), and X2Δ5/2 States of Iridium Monosilicide, IrSi Anh Le and Timothy C. Steimle* Department of Chemistry and Biochemistry, Arizona State University, Tempe, Arizona 85287-1604, United States

Michael D. Morse and Maria A. Garcia Department of Chemistry, University of Utah, Salt Lake City, Utah 84112, United States

Lan Cheng and John F. Stanton Department of Chemistry and Biochemistry, The University of Texas at Austin, Austin, Texas 78712, United States S Supporting Information *

ABSTRACT: The (6,0)[16.0]1.5−X2Δ5/2 and (7,0)[16.0]3.5−X2Δ5/2 bands of IrSi have been recorded using high-resolution laser-induced fluorescence spectroscopy. The field-free spectra of the 191IrSi and 193 IrSi isotopologues were modeled to generate a set of fine, magnetic hyperfine, and nuclear quadrupole hyperfine parameters for the X2Δ5/2(v = 0), [16.0]1.5(v = 6), and [16.0]3.5 (v = 7) states. The observed optical Stark shifts for the 193IrSi and 191IrSi isotopologues were analyzed to produce the permanent electric dipole moments, μel, of −0.414(6) D and 0.782(6) D for the X2Δ5/2 and [16.0]1.5 (v = 6) states, respectively. Properties of the X2Δ5/2 state computed using relativistic coupled-cluster methods clearly indicate that electron correlation plays an essential role. Specifically, inclusion of correlation changes the sign of the dipole moment and is essential for achieving good accuracy for the nuclear quadrupole coupling parameter eQq0.

I. INTRODUCTION Iridium is one of the rarest transition metal elements in the earth’s crust and yet is of great technological importance. Iridium organometallic complexes are particularly important as catalyst for a wide range of organic synthesis1−4 due, in part, to their thermal and chemical stability. Furthermore, iridium organometallic complexes are being developed for, among other applications, light emitting electrochemical cells,5−8 triplet−triplet annihilation upconversion,9−11 living cell imaging agents,12 and sensitizers for photodriven water splitting.13−15 Much of the photochemical activity of iridium organometallic complexes can be traced to the highly efficient triplet to singlet conversion due to the large spin−orbit coupling (SOC) of the Ir(III) centers. Increasingly, the design of new iridium organometallic complexes is assisted by high-level electronic structure predictions.16−20 Such calculations are challenging since they need to account for electron correlation, which plays an important role in metal-containing systems. Additional considerations are spin−orbit coupling and the scalarrelativistic effects that cause a strong contraction and stabilization of the Ir 6s orbitals with concomitant expansion and destabilization of the 5d orbitals.21−26 Simple gas-phase iridium containing diatomic molecules serve as ideal venues for testing the various computational methodologies being © 2013 American Chemical Society

developed to describe the large relativistic and electron correlation effects because the properties of these molecules can be precisely determined from high-resolution spectroscopic measurements. A comparison of predicted and experimentally determined molecular electric dipole moments, μel, and hyperfine interactions are particularly insightful for assessing predicted electronic wave functions. The electric dipole moment is readily extracted from the analysis of the Stark effect and is primarily dependent on the nature of the chemically relevant valence electrons. Hyperfine interactions probe the nature of the electronic wave function in the region of nuclei having nonzero spin. The interaction of the unpaired electrons with the nuclear magnetic moment, known as the magnetic hyperfine interaction, is primarily sensitive to the valence electrons, whereas the interaction of the nuclear quadrupole moment and the electric field gradient at the nucleus, known as the nuclear quadrupole hyperfine interaction, is sensitive to both core and valence electrons. Special Issue: Terry A. Miller Festschrift Received: May 20, 2013 Revised: June 30, 2013 Published: July 1, 2013 13292

dx.doi.org/10.1021/jp404950p | J. Phys. Chem. A 2013, 117, 13292−13302

The Journal of Physical Chemistry A

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previously.37,38 A laser ablation/supersonic expansion source similar to that used in the recent R2PI study26 was employed. Briefly, a rotating iridium rod was ablated with a pulse of approximately 5 mJ, 532 nm, radiation derived from a Nd:YAG laser. The ablation products were entrained in a pulse supersonic expansion gas mixture composed of 98% argon and 2% silane. A short (approximately 3 mm) interaction distance from the point of ablation to the vacuum chamber was used in order to minimize cluster formation. The LIF signal was detected off-resonance with a 560 ± 10 nm band-pass filter. Photon counting techniques were used to process the signal. The full width at half-maximum (fwhm) of the spectral lines was less than 50 MHz. The absolute wave numbers of the transitions were determined to typical accuracy of ±0.0005 cm −1 by simultaneously recording the sub-Doppler I 2 absorption spectrum. Interpolation between I2 absorption features was achieved by simultaneously recording the transmission of two confocal etalons. One etalon was actively stabilized and calibrated to have a free spectral range of 751.49 MHz, and the other was unstabilized with a free spectral range of 75 MHz. Static electric field strengths of up to 2640 V/cm were generated by application of a voltage across a pair of conducting plates straddling the region of the molecular fluorescence. The Stark plates were two 5 × 5 cm2 neutral density filters that transmitted approximately 90% of the light. A polarization rotator and a polarizing filter were used to orient the static electric field vector of the linearly polarized laser radiation either parallel (ΔMJ =0) or perpendicular (ΔMJ = ± 1) to that of the applied field. Systematic errors in the field strength determination are estimated to be less than 2%.

Iridium has two naturally occurring isotopes, 191Ir (37.3%) and 193 Ir (62.7%), that have similar properties: quadrupole moments, Q, of 81.6 fm2 and 75.1 fm2; and magnetic moments of 0.1507 μN and 0.1637 μN, respectively. Here, we report on the high-resolution visible spectrum of IrSi. The (6,0)[16.0]1.5−X2Δ5/2 and (7,0)[16.0]3.5−X2Δ5/2 bands at 18 350 cm−1 and 18 520 cm−1, respectively, were measured field-free and in the presence of a static electric field and analyzed to produce hyperfine parameters and μel values. A Hund’s case (a) labeling scheme for the ground electronic state and a Hund’s case (c) scheme for the excited electronic states are used. The (7,0)[16.0]3.5−X2Δ5/2 designation, for example, indicates that the excited state is the v = 7 vibrational level of an electronic state having |Ω| = 7/2 with an T0 of approximately 16 000 cm−1. High-level ab inito calculations were also carried out for the X2Δ5/2 state. Since the wave function of the IrSi X 2 Δ 5/2 state is dominated by a single configuration (...6σ22π47σ21δ38σ2), coupled-cluster theory24 is an ideal tool to treat electron correlation in this system. Because of the extensive computation time required of the Dirac−Coulomb based fully relativistic coupled-cluster approaches,25 in the present study we employed a composite scheme based on largescale scalar-relativistic coupled-cluster calculations augmented with spin−orbit corrections obtained via an additivity scheme. The current study was prompted in part by the recently reported study of the visible spectrum of IrSi using resonant two-photon ionization (R2PI) spectroscopy.26 In that study, the electronic spectrum in the 17 200 to 26 850 cm−1 range was measured, and 31 of the numerous bands detected were recorded with rotational resolution. The ground state was identified as X2Δ5/2 and proposed to have a dominant ...6σ22π47σ21δ38σ2 electron configuration. Bond lengths and vibrational spacing for the X2Δ5/2 and 12 excited states were experimentally determined. Lifetimes for upper states associated with 33 bands were experimentally measured. In addition, ab initio calculations were also carried out using the CASSCF and multistate complete active space second-order perturbation theory (MS-CASPT2) methods, with scalarrelativistic effects taken into account using the second-order Douglas−Kroll−Hess method and spin−orbit effects included through the restricted active space state interaction with spin− orbit coupling (RASSI-SO) method. No electric dipole moments or hyperfine interaction parameters were predicted or measured. High-resolution spectroscopic investigation of other gas-phase iridium containing molecules are limited to IrC,27,28 IrN,28,29 IrO,30,31 and IrF32−34 with the μel values determined for IrC (X2Δ5/2),28 IrN (X1Σ+)28 and IrF (X3Φ4)33 to be 1.60(7), 1.66(1), and 2.82(6) D, respectively. In addition to the recent combined experimental and computation study,26 there are two other theoretical predictions for IrSi.35,36 Han35 performed density functional theory (DFT) calculations using unrestricted (U) B3LYP exchange-correlation potential and an effective core potential LanL2DZ basis set. A 2Σ ground state with an equilibrium bond length, re, of 2.1447 Å was predicted. More recently, Wu and Su36 performed a similar DFT calculation and predicted ground state re, harmonic vibrational frequency, ωe, and μel values of 2.105 Å, 527 cm−1, and 0.44 D, respectively. A 2Δ ground state with a dominant 8σ23π4δ3 configuration was predicted, in contrast to the results of ref 35.

III. COMPUTATIONAL DETAILS The geometry, dipole moment, and electric-field gradients of the IrSi X2Δ5/2 state were computed at the restricted open-shell Hartree−Fock (ROHF) self-consistent-field (SCF) and coupled-cluster singles and doubles (CCSD)39 augmented with a perturbative inclusion of triple excitations (CCSD(T))40,41 levels of theory in combination with the fully uncontracted ANO-RCC (unc-ANO-RCC)42,43 basis sets. The spin-free version of exact-two-component theory in its one-electron variant (SFX2C-1e)44,45 was used to account for scalar-relativistic effects, hereby exploiting the recent development of the SFX2C-1e analytic-derivative theory46,47 interfaced with well-developed nonrelativistic coupled-cluster machinery.48−51 In these all-electron CC calculations, a frozen-core approximation was employed with a small core consisting of the Ir 1s, 2s, 2p, 3s, 3p, and 3d orbitals and the Si 1s orbital. In addition, the contributions from the full triples excitations to the dipole moment were estimated as the difference between the CCSDT52 and CCSD(T) results using cc-pVTZ basis53,54 in combination with the energy-consistent pseudopotentials54 for Ir. The CFOUR program package55 was used for all the ROHF and CCSD(T) calculations, while the CCSDT calculations were carried out using the MRCC program package56,57 as interfaced to CFOUR. The spin−orbit corrections to the dipole moment and electric-field gradients were obtained as the difference between the results from Dirac−Coulomb (DC) and spin-free Dirac−Coulomb (SFDC)58,59 calculations. The SFDC and DC calculations for the dipole moment were carried out at the CCSD level. In the CC treatments we froze all virtual orbitals higher than 50 au and used a large core consisting of Ir 1s, 2s, 2p, 3s, 3p, 3d, 4s,

II. EXPERIMENTAL SECTION The molecular beam spectrometer and associated laser induced fluorescence (LIF) detection setup has been described 13293



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Figure 1. A 5 cm−1 portion of the high resolution LIF spectra of the (6,0)[16.0]1.5−X2Δ5/2 and the (7,0)[16.0]3.5−X2Δ5/2 band systems. The line widths of unblended spectral features are approximately 35 MHz.

IV. OBSERVATIONS A. Field-Free Spectra. The (6,0)[16.0]1.5−X2Δ5/2 and (7,0)[16.0]3.5−X2Δ5/2 bands of IrSi at 18 350 cm−1 and 18 520 cm−1, respectively, were recorded over a range of approximately 10 cm−1. The upper and lower panels of Figure 1 show 5 cm−1 sections of the field-free spectra near the band heads of these bands. The observed relative branch intensities of R > Q > P for the (7,0)[16.0]3.5−X2Δ5/2 band and P > Q > R for the (6,0) [16.0]1.5−X2Δ5/2 band are as expected for a molecule near the Hund’s case (c) coupling scheme limit. The splitting between the band origins of the 191IrSi and 193IrSi isotopologues is large, due to the extensive vibrational isotope shifts in the excited states. Narrow scans of the P(5/2), Q(7/2), and R(5/2) branch features of the (6,0)[16.0]1.5−X2Δ5/2 band for the 193IrSi isotopologue are given in Figure 2 along with the predicted spectra obtained using the optimized parameters (vide infra). Similarly, the observed and predicted spectra for the P(9/2), Q(7/2), and R(5/2) branch features of the (7,0)[16.0]3.5− X2Δ5/2 band of the 193IrSi isotopologue are shown in Figure 3. The small splitting of each branch feature is due to the 193Ir (I = 3/2) hyperfine interaction. A comparison of the various spectral features shows that the hyperfine interaction is substantial in the both the ground X2Δ5/2 state and the [16.0]1.5(v = 6) and [16.0]3.5(v = 7) excited states. Furthermore, a comparison of

4p, and 4d and Si 1s orbitals as means of reducing the computation time. The spin−orbit corrections to the electricfield gradient were obtained at the ROHF level. The ROHF in the DC framework denotes the Kramers restricted open-shell Hartree−Fock method. The implementation of DC-based Hartree−Fock method in the DIRAC program has been described previously.60 Dyall’s triple-ζ basis61,62 was used in the DC calculations. The DC and SFDC calculations described here were carried out using the DIRAC program package63 by means of numerical differentiation of energies obtained at fixed field strengths. In the case of the SFDC and DC CCSD calculations, the dipole moments were obtained by numerical differentiation of the energies at fixed electric field strength. For all other methods employed, the dipole moments and electricfield gradients were obtained as analytic first derivatives of the energy with respect to the dipole and electric-field gradient operators. Finally, the calculated electric-field gradients at the position of the Ir atom were converted to nuclear quadrupolecoupling constants using the value of 81.6 fm2 for the nuclear quadrupole moment of 191Ir and a value of 75.1 fm2 for that of 193 64 Ir. 13294



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Figure 2. Observed slow scan and predicted spectra of the P(5/2), Q(7/2), and R(5/2) lines of the 193IrSi isotopologue in the (6,0)[16.0]1.5− X2Δ5/2 band system. The calculated spectra were obtained using the optimized set of parameters in Table 1.

Figure 3. Observed slow scan and predicted spectra of the P(9/2), Q(7/2), and R(5/2) lines of the 193IrSi isotopologue in the (7,0)[16.0]3.5− X2Δ5/2 band system. The calculated spectra were obtained using the optimized set of parameters in Table 1.

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Figure 4. Observed P(5/2) line of 193IrSi of the (6,0)[16.0]1.5−X2Δ5/2 band system recorded field-free and in the presence of a 1754 V/cm static field with parallel polarization (ΔMF = 0) and the associated energy levels.

applied electric field, the levels are labeled by the projection quantum number MF. The J = 5/2, F = 4,3,2, and 1 field-free levels of the X2Δ5/2(v = 0) state rapidly split into 24 (= (2J + 1)(2I + 1)) MF components due to the degeneracy of the parity components. Similarly, the J = 3/2, F = 3,2,1, and 0 level of the [16.0]1.5(v = 6) state splits into 16 (= (2J + 1)(2I + 1)) MF components. As is evident from the predicted energy level pattern presented in Figure 4, at high-field strengths the energy levels regroup due to the decoupling of I ⃗ and J.⃗ At high fields the levels are characterized by the projection quantum numbers MJ and MI, and the spectral pattern simplifies. Unfortunately, it was not possible to record the spectrum at the applied electric field strengths necessary for the uncoupling of I ⃗ and J ⃗ because the tuned levels overlap other branch features. In the end, a total of 253 Stark shifted features could be identified and were used in the analysis. The assignments, observed Stark shifts, and the differences from the calculated Stark shifts are presented in Supplementary Table 5.

Figures 2 and 3 reveals that the hyperfine interaction in the [16.0]1.5(v = 6) and [16.0]3.5(v = 7) states is markedly different. Finally, the irregular spectral patterns of Figures 2 and 3 indicate that the electric nuclear quadrupole interaction is large. The spectra for the 191IrSi isotopologue are strikingly similar to those of Figures 2 and 3, but less intense due to the lower relative abundance. A total of 91 and 111 low-J, field-free, spectral features for the 191IrSi and 193IrSi isotopologues, respectively, of the (6,0)[16.0]1.5−X2Δ5/2 band were precisely measured. Similarly, a total of 74 low-J, field-free, spectral features for both the 191IrSi and 193IrSi of the (7,0)[16.0]3.5− X2Δ5/2 band were precisely measured. The measured transition wavenumbers, assignment, and difference between the observed and predicted transition wavenumber can be found in Supplementary Tables 1−4. B. Stark Spectra. It was only possible to analyze the Stark spectrum of the (6,0)[16.0]1.5−X2Δ5/2 band due to spectral congestion in the (7,0)[16.0]3.5−X2Δ5/2 band. The P(5/2) line of the 193IrSi isotopologue and the Q(5/2) of the 191IrSi isotopologue were selected for optical Stark studies because these features are in relatively uncongested portions of the spectrum and involve low-J rotational levels. The observed P(5/2) line of the 193IrSi isotopologue recorded field-free and in the presence of a 1754 V/cm static field with parallel (ΔMJ = 0) polarization is presented in Figure 4. Also shown in Figure 4 is the predicted Stark tuning of the energy levels associated with the P(5/2) spectral feature obtained using the optimized μel values (vide infra). The Stark spectrum is complicated and overlapped at the field strength employed. The J = 5/2 and J = 3/2 rotational levels of the X2Δ5/2 (v = 0) and [16.0]1.5 (v = 6) states split into four (= 2I + 1) closely spaced levels, which are labeled by the total angular momentum quantum number, F, due to the nuclear hyperfine interaction. In the presence of the

V. ANALYSIS A. Field-Free Spectra. The energies for the X2Δ5/2(v = 0), [16.0]1.5(v = 6), and [16.0]3.5(v = 7) states were modeled using a Hund’s case (aβJ) basis set (ψ = |ηΛ⟩|SΣ⟩|JΩ(JI1)F⟩) and the effective Hamiltonian operator eff 2 4 Ĥ = AL̂ ZSẐ + BR̂ − DR̂ + hΩ(191,193Ir)IF̂ ̂ 2

+ eQq0(191,193Ir)

2

3IẐ − I ̂ 4I(2I − 1)

(1)

where R̂ , I,̂ and F̂ are the rotational, nuclear spin, and total angular momenta operators, respectively. There was no evidence of Ω-doubling in the spectra recorded in this study. The centrifugal distortion corrections, D, for the X2Δ5/2(v = 0), 13296



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Table 1. Spectroscopic Parameters in Wavenumber (cm−1) of the (6,0) [16.0]1.5−X2Δ5/2 and (7,0) [16.0]3.5−X2Δ5/2 Bands for 193 IrSi and 191IrSi states

193

parameters

X Δ5/2(v = 0) 2

B h5/2(Ir) eQq0(Ir) μel T0(−18300) B h3/2(Ir) eQq0(Ir) μel T0(−18500) B h7/2(Ir) eQq0(Ir)

[16.0]1.5(v = 6)

[16.0]3.5(v = 7)

0.157939(5) 0.00553(13) −0.00403(64) −0.4139(64) D 47.816747(75) 0.138469(5) 0.00622(21) −0.00672(67) 0.7821(63) D 19.059713(90) 0.133375(5) 0.00282(14) −0.00389(67)

191

IrSi

0.158158(6) 0.00501(13) −0.00334(63) 49.229956 0.138656(5) 0.00533(22) −0.00518(79) 20.614422(92) 0.133556(5) 0.00261(14) −0.00444(69)

Boltzmann factor, and superimposing a Lorentzian line shape for each spectral feature. The predicted spectra, for example, those presented in Figures 2, 3, and 4, were then obtained by coadding the Lorentzian line shapes. A width of 30 MHz was used, which is slightly less than the observed width of approximately 50 MHz. The transition moment for each spectral feature was obtained by cross-multiplication of the Hund’s case (aβJ) electric-dipole transition moment matrix with the Hund’s case (aβJ) eigenvectors for the X2Δ5/2(v = 0) and either the [16.0]1.5(v = 6) or [16.0]3.5(v = 7) state.

[16.0]1.5(v = 6), and [16.0]3.5(v = 7) states were constrained to zero. The eigenvalues and eigenvectors were obtained by diagonalization of matrix representations with dimension of 16 (=2 × (2S+1) × [2I(191,193Ir) + 1]) constructed in the Hund’s case (aβJ) basis set above. Similar to the IrC analysis,28 the spin−orbit parameter, A, for the X2Δ5/2(v = 0), [16.0]1.5 (v = 6), and [16.0]3.5(v = 7) states was constrained to 1500 cm−1. The analysis is insensitive to any values of the spin−orbit parameters greater than approximately 500 cm−1 for these states. Fits using various combinations of ground and excited state parameters were performed. Both band systems were fit simultaneously because of the common ground state. In the end, a total of 11 parameters including the rotational, B, magnetic hyperfine, hΩ (191,193Ir), nuclear electric quadrupole, eQq0(191,193Ir), and the origins for the X2Δ5/2(v = 0), [16.0]1.5(v = 6), and [16.0]3.5(v = 7) states were used. The optimized parameters and associated errors are given in Table 1. The standard deviation of the 191IrSi and 193IrSi fits were 0.00053 and 0.00052 cm−1, respectively, which are consistent with the measurement uncertainty. B. Stark Spectra. The interaction between the static electric field, E⃗ , and the molecular electric dipole moment, μ⃗ el, is represented by the Stark Hamiltonian Stark Ĥ = −μel⃗ ·E ⃗

IrSi

VI. DISCUSSION The low-J branch features exhibit a complicated pattern due to a large nuclear electric quadrupole interaction relative to the magnetic hyperfine interaction. The calculated X2Δ5/2(v = 0) hyperfine energy level splitting as function of rotation for the 193 IrSi isotopologue is illustrated in Figure 5, where the

(2)

̂ Stark

The matrix representation of H is block diagonal in MF but of infinite order, which is truncated at a finite size to be commensurate with the experimental measurement uncertainty. The predicted Stark shifts in the X2Δ5/2(v = 0) and [16.0]1.5(v = 6) states were obtained by diagonalization of a 96 × 96 matrix representation constructed using the Hund’s case aβJ basis set for F″ = 1−6 and F′ = 0−5. The observed Stark shifts for P(5/2) line of the 193IrSi and the Q(5/2) line of the 191IrSi isotopologues were simultaneously optimized using a nonlinear least-squares fitting procedure. The resulting μel values are −0.414(6) D and 0.782 (6) D for X2Δ5/2(v = 0) and [16.0]1.5(v = 6) states, respectively. The error limits represent a 90% statistical confidence level, which is smaller than the estimated maximum systematic error of 2%. The correlation coefficient was 0.66 and the standard deviation of the fit was 21 MHz, which is commensurate with the measurement uncertainty. Modeling the spectra was essential for the Stark analysis. The intensities were calculated by generating the electric dipole transition moment which was then squared, multiplied by a

Figure 5. Calculated 193IrSi hyperfine and quadrupole energy pattern as the function of rotational quantum number, J, in the X2Δ5/2 state.

rotational energy [≈ B × J(J + 1)] has been subtracted from the total energy. The asymmetric splitting, which increases with rotation, is due to the quadrupole interaction. At approximately J = 27/2, the order of the energy levels having F = J − 3/2 and F = J − 1/2 reverses, with F = J − 1/2 lying lowest in energy for higher J-values. The ratios of effective magnetic hyperfine parameters for the X2Δ5/2(v = 0), [16.0]1.5(v = 6), and [16.0]3.5(v = 7) states, hΩ(191IrSi)/hΩ(193IrSi), are 0.91 ± 0.03, 0.85 ± 0.05, and 0.92 ± 0.07, respectively, which are in excellent agreement with the 13297



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Figure 6. Molecular orbital correlation diagrams for IrSi and IrC. Orbital occupation for the ground state configurations of IrSi and IrC are shown.

⎛ 2μ g μ μ × 10−6 ⎞ l̂ 0 N B N ⎟ 1 × ⟨ΛΣ| ∑ zi |ΛΣ⟩ a /MHz = ⎜⎜ ⎟Λ 4πh ri 3 ⎝ ⎠ i

ratio of the nuclear gI-factors (= 0.92). Similarly, the ratios of the less well determined nuclear electric quadrupole parameters, eQq0(191Ir)/eQq0(193Ir), for the X2Δ5/2(v = 0), [16.0]1.5(v = 6), and [16.0]3.5(v = 7) states are 0.83 ± 0.20, 0.77 ± 0.14, and 1.14 ± 0.26, which are in reasonably good agreement with the ratio of the quadrupole moments, 191Ir(Q)/193Ir(Q) of 1.086. These agreements suggest that the magnetic hyperfine and nuclear electric quadrupole terms in the effective Hamiltonian used to model the spectra are not strongly contaminated by higher order terms. The molecular orbital correlation diagram presented in Figure 6 is useful for a qualitative interpretation of the determined ground state properties of IrSi and for rationalizing the relative values of these properties for IrSi and isovalent IrC.28 The ionization energies of Si(8.15 eV), Ir(8.96 eV), and C(11.26), and the predicted 6s and 5d orbital energy splitting26 were used in constructing the molecular orbital correlation diagram. The previously determined 28 values for the h5/2(191IrC) and h5/2(193IrC) of 0.0036(10) and 0.0051(10) cm−1, respectively, are very similar, albeit less precisely determined, to the h5/2(191IrSi) and h5/2(193IrSi) values of 0.00553(13) and 0.00501(13) cm−1 determined in the present study. The similarity of h5/2 for IrSi and IrC is due to the fact that the sole unpaired electron in both molecules is in the nonbonding, highly unpolarizable, Ir-centered 1δ(5d±2) orbital. Atomic information can be used to estimate h5/2 for IrSi and IrC. Specifically, the effective magnetic hyperfine fitting parameter, hΩ, can be expressed in terms of the Frosch and Foley parameters65 as hΩ = {aΛ + (bF + (2/3)c)Σ}. The simple molecular orbital diagram (Figure 6) suggests that bF = 0 because there is no open shell s-orbital character. Therefore, h5/2 = 2a + c/3 where a and c are

(3)

and ⎛ 3μ g μ μ × 10−6 ⎞ 0 N N B ⎟ 1 × ⟨ΛΣ| c /MHz = ⎜⎜ ⎟Σ 4 h π ⎝ ⎠

∑ i

(3 cos2 θi − 1) ri 3

szî |ΛΣ⟩

(4)

In eqs 3 and 4, lzî and ŝzi are the z-components of the orbital and spin angular momentum operators for the unpaired electrons and θi and ri are the polar coordinates for those electrons. Assuming the configuration of Figure 6 (i.e., one unpaired electron in the nonbonding, Ir-centered, δ orbital), then h5/2(IrSi) = h5/2(IrC) = 95.412(MHz/au −3)gI(Ir) ⎡ −3 01 3 2 −3 12 ⎤ ⎢⎣2⟨r ⟩5d + × ⟨r ⟩5d ⎥⎦ 2 7

(5)

The 2/7 factor is the angular expectation value of (3 cos2 θi − 1) for a 1δ(5d±2) orbital. The effective radial integrals that appear in eq 5 can be approximated as those derived from the analysis of the atomic 191Ir and 193Ir hyperfine interactions in the low-lying states arising from the 5d76s2 configuration.66 The −3 12 −3 values determined for 191Ir are ⟨r−3⟩01 5d = 9.75 a0 and ⟨r ⟩5d = 193 −3 01 −3 −3 12 12.31 a−3 , and for Ir, ⟨r ⟩ = 9.76 a and ⟨r ⟩ = 12.33 0 5d 0 5d a−3 . Substitution of these values for the radial integrals along 0 with the nuclear g-factors of 0.9746 and 0.10613 for 191Ir and 193 Ir, respectively, into eq 5 results in predicted h5/2 values for 191 IrSi and 193IrSi of 0.00659 and 0.00719 cm−1. These compare 13298



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well with the 0.00553(13) and 0.00501(13) cm−1 values determined in the present study. The experimentally determined eQq0 parameters for IrSi (Table 1) contrast with the situation for IrC. Specifically, the eQq0 determined for IrSi are moderately large, well determined, and negative, whereas these parameters were not determinable for IrC.28 The inability to determine eQq0 for IrC could be attributed to either the insensitivity and poorer quality of the data set for IrC28 or a reflection of intrinsically small values. The electric quadrupole coupling parameter, eQq0, expressed in spherical polar coordinates is

electronegativities (Pauling scale) of Si (= 1.90), C (= 2.55), N (= 3.04), and F (= 3.98). The computational results for the X2Δ5/2 state of IrSi are listed in Table 3. The equilibrium bond distance re = 2.083 Å Table 3. Spectroscopic Parameters Computed for the X2Δ5/2 State of IrSi μel (D)a ROHFb CCSD(T)b +ΔTc +ΔSOd exptl

⎡ e × 10−6 ⎤ (3 cos θi − 1) |Λ⟩ eQq0(MHz) = Q ⎢ ⎥⟨Λ| ∑ r −3 ⎣ 4πε0h ⎦ i = 234.96 × Q ⟨Λ| ∑

(3 cos θi − 1)

i

r

−3

state μ⃗el (D) r0 (Å) μ⃗el/r0 (D/Å) electroneg. diff.d

−0.0154 −0.0062

−0.0042e −0.00403(64)

−0.0039 −0.00334(63)

obtained with the SFX2C-1e/CCSD(T)/unc-ANO-RCC model is in good agreement with the experimental r0 value of 2.0899(1) Å reported in ref 26, as the vibrational effects on the geometry are arguably small for IrSi. It can be seen that electron correlation reverses the sign of the calculated dipole moment, which is found to be 0.658 D at the ROHF level and −0.619 D at the CCSD(T) level. Therefore, it is necessary to use highly correlated methods to obtain even a qualitatively correct prediction. An essentially quantitative description for the dipole moment was obtained with further inclusion of the full triples (about 0.08 D) and spin−orbit (about 0.13 D) contributions. Concerning the nuclear quadrupole-coupling constants, electron correlation also plays an essential role, e.g., the ROHF value for the 193Ir eQq0 value is very inaccurate (−0.0167 cm−1) in comparison to the CCSD(T) value (−0.0067 cm−1). As expected, the first-order spin−orbit effects (≅ 0.0025 cm−1) are indispensible for an accurate calculation of this open-shell system. The final results are in reasonably good agreement with the experimental data. We should mention that a quantitative computation for the nuclear quadrupole-coupling constants requires further inclusion of the full triples corrections that are currently beyond our computational resources due to the need to use extensive basis functions in the core region for this property.67,68

Table 2. Permanent Electric Dipole Moments, μ⃗el, Bond Distance, r0, and Reduced Dipole Moments, μe/r0, of Ground State IrSi, IrC, IrN, and IrF IrSia

IrCb

IrNb

IrFc

X Δ5/2 −0.414(6) 2.0899 −0.20 −0.30

X Δ5/2 1.60(7) 1.6086 0.99 0.35

XΣ 1.66(1) 1.6094 1.03 0.84

X Φ4 2.82(6) 1.8507 1.52 1.78

1 +

−0.0167 −0.0067

Evaluated at r = 2.083 Å obtained at the SFX2C-1e/CCSD(T)/uncANO-RCC level of theory. bObtained using the SFX2C-1e scheme and the unc-ANO-RCC basis. cTriples corrections (ΔT) calculated as the difference between CCSDT and CCSD(T) values using effective core potentials for Ir and the cc-pVTZ basis obtained using the SFX2C-1e scheme and the unc-ANO-RCC basis. dSpin−orbit corrections (ΔSO) obtained as the difference between Dirac−Coulomb and spin-free Dirac−Coulomb results using Dyall’s triple-ζ basis for Ir and uncontracted cc-pVTZ basis for Si. eAn analytic scheme for the evaluation of electric-field gradient is not available for DC-based CC methods. A numerical scheme shows a substantial instability with the presence of steep functions in the basis sets. Thus, an estimate of SO corrections was taken as the difference between DC and SFDC ROHF values.

where the summation runs over all electrons and the conversion factor assumes that Q is in barns and ⟨r−3⟩ is in a−3 0 . The prediction of eQq0 is more difficult than h5/2 because this parameter depends upon the field gradient generated by the valence 6σ, 7σ, 8σ, 2π, and 1δ orbitals and the gradient associated with the polarization of the core. It is reasonable to assume that the 6σ and 8σ orbitals are primarily Si-centered and makes only a small contribution to eQq0. If it assumed that 7σ, 2π, and 1δ orbitals are pure 5d0, 5d±1, and 5d±2 Ir orbitals and by ignoring the core polarization, then eQq0 is predicted to be approximately −10 GHz for 191IrSi, which is much larger than the observed value. Evidently the core electrons make a significant contribution. The molecular orbital correlation diagram also provides a qualitative understanding of the observed small and negative value for μel (i.e., a Ir−δSi+δ charge distribution). The ground state μel for IrC was determined to be 1.60(7) D and assumed to have a Ir+δC−δ charge distribution. As seen in Figure 6, the energy of the Ir 6s orbital is similar to the Si 3p0 and 3s orbitals but greatly different from the C 2p0 and 2s orbitals. Therefore, it is expected that the highly polarizable 8σ of IrSi is more polarized toward the Si-center than the equivalent 6σ orbital in IrC. The dipole moments, μel, bond lengths, re, reduced dipole moment, μel/re, and electronegativities (Pauling scale) for the ground states of IrX (X = Si, C, N, and F) are compared in Table 2. A comparison of reduced dipole moment (≡ μ⃗ el/re) is more insightful than a comparison of μ⃗ el because it emphasizes the change in electronic character. The ordering of the ground state μ⃗ el/re values for IrSi (−0.198 D/Å), IrC (0.99/Å), IrN (1.03 D/Å), and IrF (1.78 D/Å) is consistent with the difference of the electronegativity of Ir (2.20) and the

2

eQq0(191Ir) (cm−1)a

a

|Λ⟩, (6)

2

0.658 −0.619 −0.535 −0.408 −0.4139(64)

eQq0(193Ir) (cm−1)a

VII. CONCLUSIONS The most insightful experimentally derived information for the nature of a chemical bond comes from the analysis of the permanent electric dipole moment and hyperfine interactions. The dipole moment is sensitive to the charge distribution of the valence electrons, and the magnetic hyperfine interactions are sensitive to the nature of the molecular orbitals of the unpaired electrons. The magnetic hyperfine interactions in the X2Δ5/2 state can be fairly accurately predicted by assuming a single

3

a

This work. bReference 25. cReference 30. dThe difference between the electronegativity of Si, C, N, or F and Ir on the Pauling scale. 13299



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dominant ...6σ22π47σ21δ38σ2 configuration and using atomic information. Such an approach fails for prediction of the nuclear quadruple coupling parameter, eQq0. The ab initio calculations performed here clearly reveal that the failure of the simple orbital model is due to the neglect of electroncorrelation effects. The most fundamental electrostatic property, μ⃗ el, for IrSi, IrC, IrN, and IrF, has now been accurately determined. The ordering of μ⃗ el can be rationalized using the simple qualitative arguments presented here. As relativistic coupled-cluster methods are shown here to yield accurate results for the dipole moment of IrSi, it might be of interest to study their performance for this entire series. Ab initio predictions of μ⃗el for the low-lying excited states, which have been experimentally determined for this series, are relatively less well explored and remain a major challenge for the development of quantumchemical methodologies. Furthermore, although the relativistic coupled-cluster methods employed here have been shown to accurately predict the nuclear quadrupole hyperfine interaction for the ground state of IrSi, equivalent methodology for predicting the magnetic hyperfine interaction needs to be developed.

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(4) Church, T. L.; Andersson, P. G. Iridium Catalysts for the Asymmetric Hydrogenation of Olefins with Nontraditional Functional Substituents. Coord. Chem. Rev. 2008, 252, 513−531. (5) Hu, T.; He, L.; Duan, L.; Qui, Y. Solid State Light-Emitting Electrochemical Cells Based on Ionic Iridium (III) Complexes. J. Mater. Chem. 2012, 22, 4206−4215. (6) Yang, C.-H.; Mauro, M.; Polo, F.; Watanabe, S.; Muenster, I.; Frölich, R.; De Cola, L. Deep- Blue-Emitting Heteroleptic Iridium (III) Complexes Suited for Highly Efficient Phosphorescent OLEDs. Chem. Mater. 2012, 24, 3684−3695. (7) Tordera, D.; Pertegas, A.; Shavaleev, N. M.; Scopelliti, R.; Orti, E.; Bolink, H. J.; Baranoff, E.; Gratzel, M.; Nazeeruddin, M. K. Efficient Orange Light-Emitting Electrochemical Cells. J. Mater. Chem. 2012, 22, 19264−19268. (8) You, Y.; Park, S. Y. Phosphorescent Iridium (III) Complexes: Toward High Phosphorescence Quantum Efficiency Through Ligand Control. Dalton Trans. 2009, 1267−1282. (9) Sun, J.; Wu, W.; Guo, H.; Zhao, J. Visible-Light Harvesting with Cyclometalated Iridium (III) Complexes Having Long-Lived 3IL Excited States and Their Application in Triplet-Triplet-Annihilation Based Upconversion. Eur. J. Inorg. Chem. 2011, 21, 3165−3173. (10) You, Y.; Nam, W. Photofunctional Triplet Excited States of Cyclometalated Ir (III) Complexes: Beyond Electroluminescence. Chem. Soc. Rev. 2012, 41, 7061−7080. (11) Sun, J.; Zhong, F.; Yi, X.; Zhao, J. Efficient Enhancement of the Visible-Light Absorption of Cyclometalated Ir(III) Complexes Triplet Photosensitizers With Bodipy and Applications in Photooixidation and Triplet−Triplet Annihilation Upconversion. Inorg. Chem. 2013, 52, 6299−6310. (12) Zhou, Y.; Jia, J.; Li, W.; Fei, H.; Zhou, M. Luminescent Biscarbene Iridium (III) Complexes as Living Cell Imaging Reagents. Chem. Commun. 2013, 49, 3260−3262. (13) Yuan, Y.-J.; Yu, Z.-T.; Chen, X.-Y.; Zhang, J.-Y.; Zou, Z.-G. Visible-Light-Driven H2 Generation from Water and CO2 Conversion by Using a Zwitterionic Cyclometalated Iridium (III) Complex. Chem.Eur. J. 2011, 17, 12891−12895. (14) Eckenhoff, W. T.; Eisenberg, R. Molecular Systems for Light Driven Hydrogen Production. Dalton Trans. 2012, 41, 13004−13021. (15) Gärtner, F.; Cozzula, D.; Losse, S.; Boddien, A.; Anilkumar, G.; Junge, H.; Schulz, T.; Marquet, N.; Spannenberg, A.; Gladiali, S.; Beller, M. Synthesis, Characterization and Application of Iridium (III) Photosensitisers for Catalytic Water Reduction. Chem.Eur. J. 2011, 17, 6998−7006. (16) Fantacci, S.; De Angelis, F. A Computational Approach to the Electronic and Optical Properties of Ru (II) and Ir (III) Polypyridyl Complexes: Applications to DSC, OLED and NLO. Coord. Chem. Rev. 2011, 255, 2704−2726. (17) Kadari, A.; Monocomble, A.; Ciofini, I.; Brahimi, M.; Adamo, C. Theoretical Study of Absorption and Emission Properties of Green and Yellow Emitting Iridium (III) Complexes. J. Phys. Chem. A 2011, 115, 11861−11865. (18) Ladouceur, S.; Fortin, D.; Zysman-Colman, E. Role of Substitution on the Photophysical Properties of 5,5′-Diaryl-2,2′bipyridine (bpy) in [Ir (ppy)2 (bpy)]PF6 Complexes: A Combined Experimental and Theoretical Study. Inorg. Chem. 2010, 49, 5625. (19) De Angelis, F.; Santoro, F.; Nazeruddin, M. K.; Barone, V. Ab Initio Prediction of the Emission Color in Phosphorescent Iridium (III) Complexes for OLEDs. J. Am. Chem. Soc. 2008, 212, 13181− 13183. (20) Bischof, S. M.; Ess, D. H.; Meier, S. K.; Oxgaard, J.; Nielsen, R. J.; Bhalla, G.; Goddard, W. A., III; Periana, R. A. Benzene C−H Bond Activation in Carboxylic Acids Catalyzed by O-Donor Iridium (III) Complexes: An Experimental and Density Functional Study. Organometallics 2010, 29, 742−756. (21) Pyykkö, P. Relativistic Effects in Chemistry: More Common Than You Thought. Annu. Rev. Phys. Chem. 2012, 63, 45−64. (22) Autschbach, J. Perspective: Relativistic Effects. J. Chem. Phys. 2012, 136, 150902.

ASSOCIATED CONTENT

S Supporting Information *

Five tables of related spectroscopic data are provided. In Tables 1 and 3 are the observed and calculated line positions of the (7,0)[16.0]3.5−X2Δ5/2 band system of 191IrSi and 191IrSi, respectively. In Tables 2 and 4 are the observed and calculated line positions in wavenumber (cm−1) of the (6,0)[16.0]1.5− X2Δ5/2 band system of 191IrSi and 193IrSi, respectively. The assignments, observed Stark shifts, and the differences from the calculated Stark shifts are presented in Table 5. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*(T.C.S.) Phone: 480-965-3265. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The research at Arizona State University has been supported by a grant from the Fundamental Interactions Branch, Division of Chemical Sciences, Office of Basic Energy Sciences, Department of Energy (DE-FG02-01ER15153-A003). Work from the University of Utah was supported by the National Science Foundation under grant No. CHE-0808984. The research at U. of Texas was supported by the Robert A. Welch Foundation (GrantF-1283) and the National Science Foundation (Grant No. CHE1012743).

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