Sebastian P.
Sitkiewicz
a,
Daniel
Rivero
b,
Josep M.
Oliva-Enrich
b,
Alfonso
Saiz-Lopez
b and
Daniel
Roca-Sanjuán
*c
aKimika Fakultatea, Euskal Herriko Unibertsitatea UPV/EHU and Donostia International Physics Center (DIPC), P.K. 1072, 20080 Donostia, Euskadi, Spain
bDepartment of Atmospheric Chemistry and Climate, Institute of Physical Chemistry Rocasolano, CSIC, 28006 Madrid, Spain
cInstitut de Ciència Molecular, Universitat de València, P.O. Box 22085, 46071 València, Spain. E-mail: Daniel.Roca@uv.es
First published on 26th November 2018
The electronic-structure properties of the low-lying electronic states and the absorption cross sections (σ(E)) of mercury halides HgCl2, HgBr2, HgI2, HgBrCl, HgClI, and HgBrI have been determined within the UV-vis spectrum range (170 nm ≤ λphoton ≤ 600 nm) by means of the DKH3-MS-CASPT2/SO-RASSI quantum-chemical methodology (with the ANO-RCC basis set) and a semi-classical computational strategy based on nuclear sampling for simulating the band shapes. Computed band energies show a good agreement with the available experimental data for HgX2 with errors around 0.1–0.2 eV; theoretical and σ(E) are within the same order of magnitude. For the mixed HgXY compounds, the present computed data allow us to interpret previously proposed absorption bands estimated from the spectra of the parent molecules HgX2 and HgY2, measured in methanol solution. The analyses performed on the excited-state electronic structure and its changes around the Franck–Condon region provide a rationale on the singlet–triplet mixing of the absorption bands and the heavy-atom effect of the Hg compounds. Furthermore, the present benchmark of HgX2 and HgXY absorption σ values together with the previous benchmark of the electronic-structure properties of HgBr2 [see S. P. Sitkiewicz, et al., J. Chem. Phys., 2016, 145, 244304] has been helpful to set up a methodological and computational protocol which shall be used for predicting the atmospheric absorption and photolysis properties of several Hg compounds present in the atmospheric cycle of Hg.
Among the Hg(II)XY compounds, mercury halides (which from now on we denote as HgX2 and HgXY, with X, Y = Cl, Br, and I) are probably the systems for which more experimental data have been reported to date regarding electronic-structure and spectroscopic properties. Hence, these systems can be used in the benchmarks of computational strategies to establish accurate approaches with a predictive character for more complicated systems.
So far, for the mercury species of interest in this work, the gas-phase absorption spectra have been experimentally measured for HgCl2, HgBr2, and HgI2.9–12 Their similarities in the visible and near UV part of the energy spectrum are the occurrence of three absorption bands: an initial low-intensity and broad band at low energies (band a), a high-intensity and sharp band at higher energies (band b), and an even sharper band in the close vicinity of band b but at slightly higher energies (band c). These bands are red-shifted upon increasing the atomic number of the halogen atoms in HgX2. According to the four available experimental studies, the energy positions of the band maxima (nm) for HgCl2, HgBr2, and HgI2, in this order, are the following: (i) 202,11 22511/22912/221,9 and 2629/27110 for band a, (ii) 182,11 19811/19712/194,9 and 22511/2199/22510 for band b, and (iii) not reported (out of the range of measured energies),11 18311/183,12 and 20811/2019/20810 for band c.
For the mixed halide compounds – HgBrCl, HgClI, and HgBrI – absorption spectra have been derived from measurements in methanol solutions (not in the gas phase). Griffiths and Anderson calculated the σ(E) data of these systems from the measured spectra of mixed methanol solutions of HgX2 + HgY2, where the HgXY are formed.13,14 We shall use this data for comparisons with the results obtained in our computations. It can be easily seen in the HgXY experimental spectra, reported only in the range 200–340 nm, that low-intensity absorption signals spread over the two a-type bands of the parent molecules HgX2 and HgY2 and a higher-intensity and sharper band appears in between the b-type bands of the parent molecules.13,14
From a theoretical viewpoint, we should emphasize that the study of the excited-state electronic-structure properties of Hg compounds is in general quite complex, especially when spectroscopic accuracy is desired. Firstly, the use of multireference methods is required to correctly describe the multiconfigurational character of the excited states.15,16 Secondly, relativistic effects in molecules with heavy atoms such as Hg and I have to be accounted for – both scalar relativistic effects (through the choice of a proper Hamiltonian and a suitable basis set), and spin–orbit coupling (SOC) (since this type of interaction is also relevant for the excited states and often ground states).16–21 Most of the computational studies on the mercury halides found in the literature were focused on the ground-state electronic structure,19,20,22–25 with some exceptions such as the work of Wadt published in 1980.15 This author determined the electronic-structure of the ground and low-lying excited states of HgCl2 and HgBr2 on the basis of a moderate-size configuration interaction (CI) method, named POL(1) CI, and a double-ζ plus polarization quality basis set with effective core potentials (ECPs). According to his calculations, bands a, b, and c were assigned to the transition from the 11Σ+g ground state to the 11Πu, 11Σ+u, and 21Σ+u singlet states, respectively. However, in his work the SOC effect was not considered and the scalar relativistic effects were accounted for with approximated ECPs. Recently, we carried out an extensive theoretical analysis on the electronic states of IBr and HgBr2 in order to establish a useful and highly accurate theoretical methodology for predicting vertical absorption energies (ΔE) and associated oscillator strengths (f) of the Hg-based systems.16 On the basis of the results, we confirmed some of Wadt's predictions. In addition, we concluded that, for HgBr2, band a has a complex nature, originating from several singlet–singlet and singlet–triplet transitions to low-lying coupled Σ and Π states. Band b corresponds to a pure singlet–singlet transition to the 11Σ+u state. Meanwhile, band c occurs due to the transition to the 13Σ−u0+ state (contrary to Wadt's computations, in which such a transition was spin-symmetry forbidden).15,16
In the present work, we have used the previously established16 high-level multireference multiconfigurational methodology – complete-active-space self-consistent field/multi-state complete-active-space second-order perturbation theory/spin–orbit restricted-active-space state-interaction (CASSCF/MS-CASPT2/SO-RASSI) – for the electronic-structure computations of the HgXY halides with two objectives. Firstly, the study aims to characterize and interpret the red shifts of the transition bands upon changing the X atom to a heavier halogen atom and the spectral modifications arising for the asymmetric structures (with distinct X and Y halogen atoms) as compared to the σ(E) of the symmetric HgX2 molecules. Secondly, we have gone one step further from the conventional determination of theoretical absorption properties, based on ΔE and associated f at one (equilibrium) geometry from the Franck–Condon region, and we have computed the absorption-spectra band shapes of the symmetric and asymmetric HgXY molecules in the UV-vis part of the energy spectrum (up to 170 nm) with relevance to atmospheric chemistry. In order to achieve this goal, we have used a nuclear-ensemble computational approach able to predict, with relatively good accuracy, absorption spectra with physically-meaningful band shapes, as proposed by Barbatti and co-workers.26–28 The same computational methodology has been recently used in other work,29 extending the study to other Hg(II)XY species, which has evaluated the impact that efficient atmospheric photoreduction of Hg(II) has over the global Hg cycle. This study together with the present one allows us to conclude that gaseous Hg(II) photolysis can dominate global atmospheric mercury reduction and lead to substantial changes in atmospheric mercury lifetime, transport, and deposition.
The previous benchmark study16 included also comparisons of the suitability of all-electron basis sets (ANO-RCC-VQZP42 and Sapporo-DKH3-QZP43,44) against basis sets with electron-core potentials (Def2QZVP45 and aug-cc-pVQZ-PP46–49), the number of state-average (SA) roots in the SA-CASSCF wavefunction optimizations, the ionization potential electron affinity (IPEA)50 parameter of the CASPT2 method and the single- and multi-state approaches of this method. Furthermore, the role of SOC in the computed vertical transitions was also analyzed. The basis sets with ECPs (the first two) provided poor descriptions in some cases with strong SOC, and therefore they are not adequate for an accurate determination of the electronic transitions in the systems studied here. The ANO-RCC basis set was shown to be particularly efficient due to its general contraction scheme, which makes it more flexible in the characterization of the excited states. Meanwhile, 8 state-averaged (SA)-CASSCF roots in all the irreducible representations (IrReps) of the D2h point group were found to provide a good description of the electronic states of interest. The IPEA shift of 0.25 a.u. of the CASPT2 method improved the transition energies by 0.2–0.4 eV with respect to the results obtained with the non-modified zeroth-order Hamiltonian of CASPT2. The single- and multi-state approaches of CASPT2 gave rise to basically the same energies, although the latter provided a better description of the relative intensity of the absorption bands in HgBr2. Finally, the benchmark showed that a description based on the spin–orbit (SO) states rather than spin-free (SF) states is mandatory for these halogen/mercury molecular systems since some bands (such as band c) arise as the result of the SOC. All these established parameters have been also employed in the present study for accurately determining ΔE and f in the HgXY molecules. An imaginary shift with a value of 0.2 a.u. was also used to minimize the effect of weakly-interacting intruder states.51 Oscillator strengths (f) were similarly computed as described in the previous work.16 All the electronic-structure computations were carried out using the MOLCAS 8 quantum-chemistry software.52
Hence, the absorption cross sections (σ(E)) were computed for each photon energy E separately, by using the following equation:26
![]() | (1) |
![]() | (2) |
On the energetic scale E, each of the Gaussian functions is centered at the vertical transition energy to a particular l-th exicted state, ΔE0,l(Rk), and δ is the phenomenological broadening. These computations do not take into account the temperature or the refractive index of the medium. Thus, vibrationally cold molecules in the gaseous phase are considered. In the present work, the statistical error of the sampling (δσ(E)) is measured as the standard deviation for the particular sampled photon energy E, in a slightly different manner to the one presented in the study of Crespo-Otero and Barbatti26,27
![]() | (3) |
![]() | (4) |
Sampling of the nuclear coordinates Rk was done according to the Wigner distribution58 for the optimized ground spin-free (SF) states and using the corresponding vibrational harmonic frequencies of the normal modes.26,27,59 The optimization and vibrational analysis were carried out numerically, at the same level of theory used in the electronic-structure calculations of the excited states [DKH3-CASPT2(12,10)/ANO-RCC-VQZP] with the MOLCAS 8 program. The sampled geometries Rk were generated with the 1.4 NEWTON-X program,28,60,61 using the obtained information on the equilibrium structures, whereas the calculation of σ(E) was done with an in-house program. At each of the sampled geometries, the MS-CASPT2 computations of ΔE and f were performed with the Cs symmetry constraint on the wavefunction (all three atoms were placed in the XOY plane). For each of the IrRep belonging to the Cs point group, A′ and A′′, we chose Nfs = 10 for the number of SF states in the CASSCF/CASPT2 computations because it includes all relevant SF transitions up to 170 nm. Finally, Np = 100 geometries were used along with a broadening of the Gaussian shape functions of δ = 0.05 eV, adequate for the triatomic systems studied in this work.
Benchmark computations were also carried out varying the number of sampled geometries and the method used to generate the ground-state minimum geometry and associated frequencies. Thus, nuclear ensembles of 20, 50, 75, and 100 geometries were generated from the CASPT2 equilibrium structure and frequencies and tested. In addition, absorption spectra were also computed, using sampling based on the equilibrium structures and frequencies obtained with the coupled-cluster method including single and double excitations (CCSD) and density functional theory (DFT) with the PBE0 functional, both with the Def2QZVP basis set and using the Gaussian09 (revision C.01) program.62 The atomic masses of the Hg, Cl, Br, and I atoms used in the computations are 201.9706, 34.9688, 78.9183, and 126.9045 Da, which correspond to the most abundant isotopes. For both tests, see a short discussion presented in Section SII of the ESI.†
The CASPT2 results were computed in the present study by using the all-electron ANO-RCC-VQZP basis set which was shown to be more accurate for the determinaton of the geometrical and electronic-structure properties of the HgBr2 molecule as compared to the Def2QZVP and aug-cc-pVQZ-PP basis sets containing ECPs.16 SOC was not considered for the geometry determination due to the negligible effect for the ground-state geometrical parameters. As compared with the best estimations obtained in the literature at the CCSD(T)/CBS(TQ) level and including CV, SO, and SR corrections, the CASPT2 results show in all cases shorter bond lengths with an average difference of 0.014 Å. As compared with the experimental data, CCSD(T) slightly overestimates the bond distances, while CASPT2 underestimates them.
In general, all methodological approaches considered here predict linear structures for the ground-state equilibrium of the HgXY compounds, which is in agreement with the experimental observations.16,19,20,63 The behaviour is different for some low-lying excited states which show bent structures.15,16 This is the case of the low-lying singlet and triplet Σ+u and Πu electronic states, which become A1 and B1/B2 states in C2v symmetry, respectively, with bond angles around 90°.15,16
From the comparison of the different bond distances compiled in Tables SI and SII (ESI†), heavy atom effects can be quantified. The Hg–X bond length in the symmetric compounds (HgX2) increases by 0.13 Å from X = Cl to Br and by 0.17 Å from X = Br to I. For the mixed molecules (HgXY), the change in the Y atom slightly affects the distance of the Hg–X bond and the resulting differences are of order ±0.01 Å.
Regarding the vibrational normal modes, the documented experimental data correspond to UV, Raman, and IR measurements.65–76 The symmetric stretching (νsym), asymmetric stretching (νasym), and bending (νbend) normal modes frequencies are compiled in Tables SI and SII (ESI†) together with the corresponding theoretical values from the literature (selected DFT19,20 and CC19 methods) and those computed in this study with the CASPT2 method. In general, CASPT2/ANO-RCC-VQZP values of νsym, νasym, and νbend are larger than the best estimations obtained with the CCSD(T) method. Both theoretical findings are slightly larger than the experimental data. However, the differences are not qualitatively significant and therefore the trends are the same in all cases. It can be easily seen that vibrational frequencies decrease upon increasing the atomic number of the halogen atom. The νbend normal mode is much less affected than νsym and νasym. In the HgX2 molecules, substitution of the Hg–Cl bonds with Hg–Br implies a decrease of all frequencies almost twice bigger than that obtained by changing Br for I. This trend is also observed in the case of the mixed HgXY halides for the νbend normal mode, whereas it is not found for νsym and νasym, most probably because the last two frequencies are much more affected by the other halogen atom.
SF state | (D∞h) | Weight [%] | Excitation | ΔE [eV] | f [a.u.] | SO state/Ω state | Weight [%] | SF state | ΔE [eV] | f [a.u.] | |
---|---|---|---|---|---|---|---|---|---|---|---|
11Σ+ | (11Σ+g) | 95 | 0.00 | 11Σ+0+ | (1)0+ | 100 | 11Σ+ | 0.00 | |||
13Π | (13Πg) | 86 | πnb2 → σ+* | 4.86 | 13Π1 | (1)1 | 88 | 13Π | 4.83 | 0.00053 | |
12 | 11Π | ||||||||||
13Π0+ | (2)0+ | 100 | 13Π | 5.01 | 0.00118 | ||||||
11Π | (11Πg) | 84 | πnb2 → σ+* | 5.15 | 0.00318 | 11Π1 | (2)1 | 86 | 11Π | 5.21 | 0.00267 |
11 | 13Π | ||||||||||
2 | 13Σ+ | ||||||||||
23Π | (13Πu) | 83 | πnb1 → σ+* | 5.70 | 23Π1 | (3)1 | 93 | 23Π | 5.70 | 0.00053 | |
4 | 21Π | ||||||||||
23Π0+ | (3)0+ | 100 | 23Π | 5.79 | 0.00073 | ||||||
13Σ+ | (13Σ+u) | 85 | σ+nb → σ+* | 5.84 | 13Σ+1 | (4)1 | 94 | 13Σ+ | 5.88 | 0.00019 | |
2 | 21Π | ||||||||||
2 | 11Π | ||||||||||
21Π | (11Πu) | 83 | πnb1 → σ+* | 6.00 | 0.01676 | 21Π1 | (5)1 | 92 | 21Π | 6.04 | 0.01579 |
5 | 23Π | ||||||||||
2 | 13Σ+ | ||||||||||
21Σ+ | (11Σ+u) | 63 | πnb2 → π | 6.66 | 0.05102 | 21Σ+0+ | (4)0+ | 94 | 21Σ+ | 6.66 | 0.04221 |
23 | σ+nb → σ+* | 5 | 13Σ+ | ||||||||
23Σ+ | (23Σ+u) | 72 | πnb2 → π | 6.66 | 23Σ+1 | (6)1 | 70 | 23Σ+ | 6.44 | 0.00007 | |
11 | πnb1 → π | 29 | 13Σ− | ||||||||
13Δ | (13Δu) | 80 | πnb2 → π | 6.80 | 13Δ1 | (7)1 | 100 | 13Δ | 6.73 | 0.00064 | |
10 | πnb1 → π | ||||||||||
33Σ+ | (13Σ+g) | 38 | πnb1 → π | 6.95 | 33Σ+1 | (8)1 | 88 | 33Σ+ | 6.95 | 0.00003 | |
38 | σ+1 → σ+* | 6 | 13Δ | ||||||||
13 | πnb2 → π | ||||||||||
13Σ− | (13Σ−u) | 80 | πnb2 → π | 6.99 | 13Σ−0+ | (5)0+ | 94 | 13Σ− | 7.02 | 0.01252 | |
10 | πnb1 → π | 6 | 21Σ+ | ||||||||
13Σ−1 | (9)1 | 67 | 13Σ− | 7.25 | 0.00051 | ||||||
28 | 23Σ+ | ||||||||||
3 | 33Σ+ | ||||||||||
31Σ+ | (21Σ+g) | 55 | πnb1 → π | 7.51 | 0.00683 | 31Σ+0+ | (6)0+ | 91 | 31Σ+ | 7.50 | 0.00499 |
28 | σ+1 → σ+* | 9 | 23Σ− | ||||||||
23Δ | (13Δg) | 77 | πnb1 → π | 7.62 | 23Δ1 | (11)1 | 100 | 23Δ | 7.48 | 0.00024 | |
10 | πnb2 → π | ||||||||||
43Σ+ | (23Σ+g) | 49 | σ+1 → σ+* | 7.64 | 43Σ1+ | (10)1 | 64 | 43Σ+ | 7.45 | 1.1 × 10−6 | |
38 | πnb1 → π | 34 | 23Σ− | ||||||||
23Σ− | (13Σ−g) | 76 | πnb1 → π | 7.81 | 23Σ−1 | (7)0+ | 88 | 23Σ− | 7.85 | 0.00259 | |
11 | πnb2 → π | ||||||||||
41Σ+ | (31Σ+g) | 50 | σ+1 → σ+* | 8.14 | 1.54965 | 41Σ+0+ | (9)0+ | 98 | 41Σ+ | 8.16 | 1.58677 |
26 | πnb1 → π | ||||||||||
33Π | (23Πu) | 63 | σ+1 → π | 8.19 | 33Π1 | (12)1 | 49 | 33Π | 8.03 | 0.00601 | |
29 | σ+nb → π | 31 | 31Π | ||||||||
14 | 23Σ− | ||||||||||
5 | 43Σ+ | ||||||||||
33Π0+ | (8)0+ | 99 | 33Π | 8.00 | 0.00001 |
In terms of SO electronic states, it can be seen in Table 1 and Tables SIII, SIV (ESI†) that 11Πu, 11Σ+u, and 21Σ+u contribute predominantly to (2)1u, (2)0+u, and (4)0+u, respectively. While (2)0+u and (4)0+u arise mainly from the respective singlet SF states, (2)1u presents a large participation of triplet states, in particular 13Σ+u and 13Πu. In addition, new probable transitions (with non-negligible f values) appear mainly arising from triplet states (which are forbidden without SOC). This is the case of (1)1u, (1)0+u, (3)1u, and (3)0+u, with f values of 0.004–0.007. The comparison of the SO data for the distinct halogen compounds allows us to analyze the heavy-atom effect, which contributes by increasing the SOC or singlet–triplet mixing. This can be easily seen by analyzing the contributions of singlet and triplet SF states to the SO states. Thus, greater mixing appears in HgI2 as compared to HgBr2 and HgCl2, which in some cases makes transitions more probable and in other cases less probable depending on the relative contribution of singlet and triplet SF states. Significant changes of several orders of magnitude in the f values can be seen, for example, in the transition to the (1)0+u state, with f = 0.00001, 0.00645, and 0.04102 for HgCl2, HgBr2, and HgI2, respectively. The (3)1u SO state also has higher f values for HgI2 and HgBr2 than for HgCl2. Meanwhile, the transition to the (5)1u SO state with a pure triplet character is also more probable for the HgI2 compound than for HgBr2 and is very small in HgCl2.
In general, there are five relevant vertical electronic transitions in the SF description of the mixed halides, ascribed to the energetically ordered 11Π, 21Π, 21Σ+, 31Σ+, and 41Σ+ states. The most intense is the last one, whereas distinct relative intensities appear when the other transitions are compared in the three compounds. In particular, while 31Σ+ is more intense than 21Σ+ in HgClI, their relative intensity decreases in HgBrI, and the opposite trend is found for HgBrCl.
Regarding the energy splitting between related singlet and triplet states, the gaps are higher than those obtained for the non-mixed halides. Singlet–triplet energy splittings are around 0.1 eV for the Δ and Σ− states and 0.3 eV for the Π states. As can be seen in Table 2 and Tables SV, SVI (see ESI†), Σ+ states show a strong mixture of the πnb1/2 → π and σ+1/σ+nb → σ+ configuration state functions, producing, in general, larger gaps. Similarly to the parent HgX2 compounds, inclusion of a less electronegative halogen atom gives rise to a decrease in ΔE, with an average difference of 0.3 eV between HgBrCl and HgClI, of 0.3 eV between HgClI and HgBrI, and of 0.6 eV between HgBrCl and HgBrI. A proportional shift of 0.3 eV is then obtained when changing one halogen atom in the HgXY (X, Y = Cl, Br, and I) halides.
In the SO description of the absorption spectra, many transitions become probable, which arise not only from dominant singlet SF states but also from singlet–triplet mixture and even dominant triplet SF states. As can be seen by comparing Table 2 and Tables SV, SVI (ESI†), this mixing is more pronounced in HgBrI due to the heavy-atom effect. The brightest transition computed corresponds to the (9)0+ SO state which is mainly generated by the singlet 41Σ+ SF state. The other singlet SF states 11Π, 21Π, 21Σ+, and 31Σ+ give rise mainly to the (2)1, (5)1, (4)0+, and (6)0+ SO states, respectively. In general, mixing with other triplet SF states is largely increased in the cases of HgBrI and HgClI. At low energies, below that of the important “singlet” (4)0+ state, the relevant transitions to SO states with dominant triplet character are (2)0+ for HgBrCl, (2)0+, (3)0+, and (6)1 for HgClI and (2)0+, (3)1, (3)0+, and (4)1 for HgBrI. The SO states (2)0+ and (3)0+ are basically pure triplet 13Π and 23Π SF states, respectively. Meanwhile, at higher energies, significant transitions characterized by strong triplet components are (7)0+ and (8)0+ for HgClI and HgBrI. They are mainly formed from the 33Π or 23Σ− SF states.
Fig. 2 displays the σ(E) of all the HgXY halide compounds, computed in the present study with the DKH3-SOC-MS-CASPT2(12,10)/ANO-RCC-VQZP level of theory and the semi-classical approximation for the nuclear sampling. Spectra of the HgBr2 and HgBrCl representatives are displayed in Fig. 3 and 4, respectively, along with the experimental absorption spectra reported in the literature.9,11–13 The analogous figures for the remaining compounds were moved to the ESI† (see Fig. S3–S6) for the sake of a more appropriate organization of the work. Note that for the symmetric HgX2 molecules, experimental spectra correspond to gas-phase data,9–12 whereas for the mixed halides they are obtained from measurements in methanol solution.13 Therefore, for HgXY, the simulated spectra in vacuo are not strictly comparable to the experimental spectra. Dipole moments, which are helpful for a rough qualitative analysis on the possible effects of polar solvents on the band shifts, are compiled in Table SXVI of the ESI.† In general, excited states of HgXY are characterized by larger dipole moments than that of the ground state. This is in part related to the asymmetric AO contributions to the excitations from the halogen atoms to Hg (see Fig. 1). Consequently, general solvatochromic shifts to the red might be expected especially in highly polar solvents. Finally, we shall focus in this section on the UV-vis absorption spectra of interest up to around 170 nm, which includes electronic transitions with energies up to those of the 13Σ−u0+ and 13Σ−0+ states for HgX2 and HgXY, respectively. This corresponds to the bands a, b, and c of HgX2 discussed in Section 1. At higher energies, Rydberg states are present according to the experimental observations.77 Those states might interact with the valence states and affect the computed electronic-transition properties of the latter. Computation of Rydberg states requires basis sets with extra diffuse functions and inclusion of the Rydberg orbitals in the active space, which is out of the scope of our work focused on an accurate determination at lower energies.
![]() | ||
Fig. 3 Simulated UV-vis absorption cross sections (σ(E)) of HgBr2 both without (SF, orange) and with (SOC, violet) taking into account the spin–orbit coupling between states. Shaded areas represent the statistical error for the sampled photon energies (δσ(E)). Experimental spectra9,11,12 are included for comparison (for a better comparison, the σ(E) values of the spectrum of Frantom et al.12 are shown on the same axis as theoretical ones). Additionally, vertical excitation energies in eV (ΔE) and associated f values between SO states for the optimized ground-state structure of HgBr2 are graphically represented with red sticks (see the discussion in Section 2). |
![]() | ||
Fig. 4 Simulated UV-vis absorption cross sections (σ(E)) of HgBrCl both without (SF, orange) and with (SOC, violet) taking into account the spin–orbit coupling between states. Shaded areas represent the statistical error for the sampled photon energies (δσ(E)). Experimental spectra13 are included for comparison. Additionally, vertical excitation energies in eV (ΔE) and associated f values between SO states for the optimized ground-state structure of HgBrCl are graphically represented with red sticks (see the discussion in Section 2). |
As described in the Introduction, three main bands characterize the UV absorption spectra of the three halogen–mercury compounds (bands a, b, and c). The lowest-energy one (band a) is broad with low intensity. Our computations predict band maxima at approximately 6.20 eV (200 nm), 5.55 eV (223 nm), and 4.95 eV (250 nm) for HgCl2, HgBr2, and HgI2, respectively, which are mainly produced by transitions to 13Πu1, 11Πu1, 13Πu0+, and 13Σ+u1 SO states (see Table 1 and Tables SIII, SIV, ESI†). Therefore, band a involves a certain degree of SOC. For HgCl2, the most intense transition is related to the 11Πu1 state with dominant singlet character (11Πu). The second most intense transition corresponds to 13Πu1 which has mainly triplet character (13Πu). In HgBr2, the transition to the “singlet” 11Πu1 state is still the most intense but now three SO states with triplet dominance have similar σ values: 13Πu1, 13Πu0+, and 13Σ+u1. Finally, in HgI2, the “triplet” 13Πu0+ becomes the most probable transition, and the “singlet” 11Πu1 has a similar f to 13Πu1 and 13Σ+u1. Such intense triplet absorptions are the consequence of SOC and heavy-atom effects which are evident by comparing the spectra generated by SF and SO states (see differences in Fig. 3 and Fig. S3, S4, ESI†). Whereas the SF and SO descriptions are similar in HgCl2 and no significant SOC role can be interpreted from the spectra, band a is clearly more prominent in the SO spectra than in the SF spectra for HgI2.
Band b is much sharper and more intense than band a and, according to our simulations, it has band maxima at 6.85 eV (181 nm), 6.34 eV (196 nm), and 5.88 eV (211 nm) for HgCl2, HgBr2, and HgI2, respectively. This band mainly originates from the electronic transition to the 11Σ+u0+ SO state. As can be seen in Table 1 and Tables SIII, SIV (ESI†), this state is mainly formed by the singlet 11Σ+u SF state with small contributions from states of triplet character (13Σ−u for HgCl2 and HgBr2 and this state plus 13Πu for HgI2). The “singlet” nature of band b and the increasing “triplet” nature of band a in the series Cl, Br, and I allows us to interpret the distinct relative intensity of the two analyzed bands observed experimentally (a large relative intensity difference in HgCl2 and small in HgI2). This is another clear manifestation of the higher SOC for the heavy atom.
In the high-energy part of the spectra, an even sharper band arises (band c), with band maxima at 7.34 eV (169 nm), 6.75 eV (184 nm), and 6.16 eV (201 nm) for HgCl2, HgBr2, and HgI2, respectively. The σ values of this band are the largest in the spectrum of HgCl2, largely decrease for HgBr2, and become very low in HgI2. Band c can be related to the 13Σ−u0+ SO state, which is mainly formed by the triplet 13Σ−u.16 However, subtle contributions seem to affect the band intensity. Firstly, in HgCl2, there is an 8% contribution of the 11Σ+u state which according to the SF properties has very large f value (see Table SIII, ESI†). In HgBr2, the small contribution of the singlet 11Σ+u state in the ground-state optimized geometry (only 1%; see Table 1) seems to underestimate the intensity of the band in the corresponding spectrum in Fig. 3. For HgI2, even though the contribution of the 11Σ+u SF state to the 13Σ−u0+ SO state is higher (2%; see Table SIV, ESI†), this band almost disappears in the absorption spectrum (see Fig. S4, ESI†). Such findings point to greater mixing of the singlet 11Σ+u state in HgBr2 due to the nuclear sampling and a shorter interaction in HgI2. The triplet nature of band c becomes evident when comparing the spectra with and without the SOC effect. It fully disappears in the SF simulated spectra. This confirms our predictions on the nature of this band (which are contrary to Wadt's first predictions).15,16 Finally, it is also worth noticing that in HgI2 a close-lying band at 6.06 eV (205 nm) is present related to the transition to the (5)1u SO state (which is a pure triplet 13Δu). The peak corresponding to this transition cannot be identified in the spectra of the other symmetrical halide compounds.
Regarding the low-energy part of the spectra, signals have in general lower intensity and are spread over the range of the low-energy band of the parent non-mixed halides. A lack of differences between the SF and SO simulated spectra clearly indicates that this part of the spectra is not very affected by triplet states in HgBrCl (see Fig. 4) while for the other two compounds, HgClI and HgBrI, there are significant triplet contributions (see Fig. S5 and S6, ESI†). Thus, in HgBrCl, two mainly singlet states, 11Π1 and 21Π1, contribute to the low-energy part of the spectrum, and one “triplet” state, 13Π0+, appears although with low σ values. For HgClI, two “triplet” SO states, 13Π0+ and 23Π0+, have similar intensities to 21Π1. In the case of HgBrI, four “triplet” states, 13Π0+, 23Π1, 23Π0+, and 13Σ1+, and one “singlet” state, 21Π1, are responsible for the low-energy signals.
Finally, as in the case of HgCl2 and HgBr2, the spectra of HgBrCl and HgClI are also characterized by almost pure triplet bands (sharp bands at around 6.7–7.0 eV in the last two compounds). The corresponding electronic transitions are already described in detail in Section 3.2.2 and their nature is once more clearly understood by comparing the SF and SO spectra of Fig. 4 and Fig. S5 (ESI†).
In the first part of the work, in the same manner as in the HgBr2 study, we have assigned the main electronic bands on the basis of ΔE and f computed at the Franck–Condon geometry. We have adapted the previously benchmarked CASSCF/MS-CASPT2/SO-RASSI methodology using the DKH3 Hamiltonian for treating the scalar relativistic effects of the inner electrons and the relativistic-correlation-consistent ANO-RCC-VQZP basis set.16 The main results of this part confirm the experimental trends observed in the HgX2 and HgXY UV-vis spectra9–11,13 and provide new information on the nature of the electronic transitions:
(1) Electronic excitations (up to 170 nm) are almost of the same nature, and upon increasing the atomic number of the halogen atoms (X or Y) in the series Cl, Br, and I, ΔE systematically decreases by 0.3 and 0.6 eV for the HgXY and HgX2 halides, respectively.
(2) The low-energy part of the absorption spectra with low-intensity signals (band a) has some mixing of singlet and triplet states. The sharp band b, which follows at higher energy, corresponds mainly to singlet states, and band c is basically the electronic transition to a pure triplet state (appearing only with SOC corrections).
(3) Stronger singlet–triplet mixing (due to SOC) affects the energetics of the excited states of HgXY halides containing I atoms.
In the second part of this work, we have presented theoretically simulated σ(E) of the studied mercury compounds, which were generated with the semi-classical approach based on computations of ΔE and f for the probed set of geometries (sampled according to the Wigner distribution).26–28 This approach has allowed the determination of the general shapes of the electronic bands (and intensities), while keeping a high-level methodology for the electronic-structure computations of the excited states, namely DKH3-SOC-MS-CASPT2/ANO-RCC-VZQP. For HgX2, where experimental gas-phase electronic spectra are available, despite the differences in σ(E) (within the same order of magnitude), the position and shape of the electronic bands are reproduced properly. This is especially meaningful for the mixed HgXY halides, since no experimental spectra up to 170 nm have been reported (only part of the HgXY spectra is available which is estimated from the spectra of the parent molecules HgX2 and HgY2, measured in methanol solution).13,14
The results of the benchmarking on the simulations related to the choice of geometrical ensembles have shown the correct applicability of the semi-classical approach. It seems to be invariant to the method employed in the geometry optimizations (and computed vibrational frequencies) for generating the Wigner ensemble. This has been useful in simulations of UV-vis spectra of larger mercury-based compounds, for which computationally cheaper methods (for example DFT) could be chosen for producing the geometrical ensembles.29
Overall, the methodological and computational approaches presented in this paper and applied to the HgX2 and HgXY compounds have allowed us to clearly establish the nature of the UV absorption bands of these molecules (orbital excitations, singlet–triplet mixing, and heavy-atom effects) and systematically relate the bands of the HgXY to those of the parent HgX2 and HgY2 compounds. Furthermore, this work has been proved worthy in recent σ(E) predictions in mercury compounds with no available experimental spectra.29
Footnote |
† Electronic supplementary information (ESI) available: Tables compiling information on the experimental and theoretical bond lengths for the studied compounds; tables compiling information on computed vertical transitions of HgCl2, HgI2, HgClI and HgBrI and the nature of the important electronic states; figures displaying simulated absorption spectra of HgCl2, HgI2, HgClI, and HgBrI; and a section on the benchmark of the computational procedure of simulation of UV-vis spectra of the studied compounds. See DOI: 10.1039/c8cp06160b |
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