Comment pubs.acs.org/JPCA
Reply to the “Comment on ‘An ab initio Study of the E 3Πg State of the Iodine Molecule’” Apostolos Kalemos,*,† Á lvaro Valdés,‡ and Rita Prosmiti‡ †
Laboratory of Physical Chemistry, Department of Chemistry, National and Kapodistrian University of Athens, Panepistimiopolis, Athens 15771, Greece ‡ Instituto de Física Fundamental, CSIC, Serrano 123, 28006 Madrid, Spain
J. Phys. Chem. A 2012, 116 (9), 2366−2370. DOI: 10.1021/jp3000202 J. Phys. Chem. A 2013, 117. DOI: 10.1021/jp308740j interference with our work on He−I2(E3Πg)10 because the diatomic I2 was fixed at its equilibrium distance. Lawley et al.11 treated the coupled system D′2g/X[2Π3/2]c;5d 2g and β1g/X[2Π3/2]c;7s 1g nonadiabatically but insufficiently optimized the parameters used. They failed to adapt the vibrational overlaps to the relaxed curves resulting in significant errors of 33% (2g case) and 12% (1g case) for the interaction matrix element H12.12 It was finally suggested that our E curve should be viewed as a possible candidate for the D′2g/ X[2Π3/2]c;6s 2g coupled states whose Rydberg minimum is believed to lie at ∼48 400 cm−1 and be of 3Πg symmetry. Our Rydberg minimum is at 49 557 cm−1 and certainly a complete SO and non-BO treatment would modify that energy region; although in light of any direct experimental evidence, we should view such issues with extreme caution. At this energy region the main problem is the presence of nonadiabatic effects, requiring both SO corrections and nuclear nonadiabatic dynamics calculations. Such an extended and computationally expensive treatment could be of particular interest when experimental data are available. Both theorists and experimentalists recourse to approximations due to technical difficulties. Making approximations is a difficult art in physical sciences. Knowing the way to apply them correctly leads to meaningful results.
e have recently reported on the E 3Πg state of I2 on the basis of MRCI expansions coupled with effective core potential (ECP28MDF) for the [Ar+3d10] electrons and an aug-cc-pV5Z-PP Gaussian basis set for the remaining 4s24p64d105s25p5 electrons.1 The calculated curve presents two well-defined minima of ion-pair (re = 3.593 Å, Te = 41 457 cm−1) and Rydberg (re = 2.589 Å, Te = 49 557 cm−1) nature at the MRCI+Q level of theory.2 An excellent agreement with the existing experimental results (cf. Table 1 of ref 1) refrained us from a more sophisticated treatment that would result in cumbersome calculations considering the size of the molecular system and the highly excited nature of the titled state. The Comment by Ridley3 addresses the interesting issue of comparison between experiment and theory that seems somewhat problematic in several cases when a theorist compares with experimental data based on approximations and vice versa, although an exact treatment is always desirable but unfortunately not plausible. The author challenges the validity of the approach adopted and correctly points out that some approximations are not the most appropriate for a comparison over the whole energy range. However, we should note that given the complexity of the system, such highly excited states have not been studied theoretically, so approximations are in essence mandatory.4,5 In his contribution Ridley argues that in the literature6 two Rydberg states [X2Π3/2g]c;6s 2g and 1g have minima at ∼48 300 cm−1. However, in their study Lehmann et al.6 reported only one state at 48 426 cm−1 that was attributed to a 2g (2Π3/2g) σg symmetry on the basis of a number of assumptions and postulates. Furthermore, a state at 53 006 cm−1 is reported7 that was tentatively assigned to a 0g (2Π1/2g) σg symmetry. There was no report at all for a 3Σg− component conjectured by Wilson et al.8 We started by comparing our MRCI+Q curve of the E3Πg state with the RKR curve by Wilson et al.8 that serves as a monitor of the computational scheme employed. The RKR curve hosts 422 vibrational levels extending up to 62 000 cm−1 , although they explicitly stated the onset of perturbations at ∼56 000 cm−1 mainly due to interactions with Rydberg states.9 We showed that our MRCI+Q curve could reproduce the experimental values for levels up to v′ ∼ 200, with a deviation of ∼5% at energy of ∼55 000 cm−1. This agreement indicates that the chosen computational scheme recovers the physics of the E state for that energy range. Consequently, there is no
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© 2013 American Chemical Society
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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REFERENCES
(1) Kalemos, A.; Valdés, Á .; Prosmiti, R. J. Phys. Chem. A 2012, 116, 2366. (2) It is incorrectly reported in the Comment that our ion-pair and Rydberg minima lie at ∼ 41 300 and 48 300 cm−1, respectively. (3) Ridley, T. J. Phys. Chem. A 2013, DOI: 10.1021/jp308740j. (4) The author of the Comment says that “States are either linear combinations of equal weights of singlet and triplet spin, sometimes abbreviated to ‘singlet’, states or pure triplet states.” This is not correct. Received: October 5, 2012 Revised: January 8, 2013 Published: January 8, 2013 790
dx.doi.org/10.1021/jp309853g | J. Phys. Chem. A 2013, 117, 790−791
The Journal of Physical Chemistry A
Comment
Only an inspection of the eigenvectors of the SO matrix can inform us on the composition of the Ω states. (5) The author of the Comment says that “In their calculations the authors included eleven 3Πg states but none of any other spin multiplicity.” In the Results and Discussion section of ref 1, we describe the method employed for the generation of the molecular orbitals. The author of the Comment has misunderstood the computational strategy of our CASSCF procedure with SO calculations. (6) Lehmann, K. K.; Smolarek, J.; Goodman, L. J. Chem. Phys. 1978, 69, 1569. (7) Miller, J. C. J. Phys. Chem. 1987, 91, 2589. (8) Wilson, P. J.; Ridley, T.; Lawley, K. P.; Donovan, R. J. Chem. Phys. 1994, 18, 325. (9) The authors of ref 8 approximated the outer branch of their RKR curve by a truncated Rittner function, they have smoothed curves resulting from different set of data, disregarded several avoided crossings with other states, used a constant value for the transition dipole moment, conjectured the presence of a 3Σg− perturber state below 56 000 cm−1, and most importantly fitted experimental results of nonadiabatic nature to a single curve. (10) Kalemos, A.; Valdés, Á .; Prosmiti, R. J. Chem. Phys. 2012, 137, 034303. (11) Lawley, K. P.; Ridley, T.; Min, Z.; Wilson, P. J.; Al-Kahali, M. S. N.; Donovan, R. J. Chem. Phys. 1995, 197, 37. (12) A proper least-squares fitting should follow the lines of the following article: Lefebvre-Brion, H. Can. J. Phys. 1969, 47, 541.
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dx.doi.org/10.1021/jp309853g | J. Phys. Chem. A 2013, 117, 790−791
