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Hypervalent Bonding in the OF(a#), SF(a#), SF/SF and OSF Species Apostolos Kalemos J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.7b10750 • Publication Date (Web): 12 Feb 2018 Downloaded from http://pubs.acs.org on February 13, 2018
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The Journal of Physical Chemistry
Hypervalent Bonding in the OF( a 4 Σ− ), SF( a 4 Σ− ), SF5/SF6 and OSF4 Species
Apostolos KALEMOS* National and Kapodistrian University of Athens, Department of Chemistry, Laboratory of Physical Chemistry, Panepistimiopolis, Athens 15771, HELLAS
*
[email protected]
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Abstract Hypervalency has struggled the conventional wisdom of too many chemists for so many years. Numerous theories and bonding models have been introduced but the so called “hypervalent” mystery remains. We offer a simple and appealing explanation 4 − 4 − for the bonding mechanism of OF( a Σ ), SF( a Σ ), SF5/SF6 and OSF4 species based
solely on the fact that excited and/or ionic states of the constituent fragments may and actually do occur in the ground states of so many “every day” molecules. In particular and through multireference methods we have found that the bonding in all the studied species is ionic in nature perhaps contrary to the present status of our chemical beliefs. Although the “atoms in molecules” hypothesis is certainly not the only way to explain the formation of the chemical bond we strongly believe that it is the simplest and most economical conceptual principle that should guide our chemical thinking.
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I.
INTRODUCTION
In 1969 Musher1 coined the term “hypervalency” to cater for molecules formed by atoms of Groups V–VIII of the periodic table in their higher valences like e.g. PCl5 and HClO4. These “unfortunate” exceptions to the rule exceed the number of valences allowed by the traditional Lewis–Langmuir theory2,3 tailored upon what we now call the Restricted (Open Shell) Hartree–Fock (R(O)HF) description of the ground atomic configurations of e.g. N, O, F, and He. So, broadly speaking H3,4 the excited states of He2,5 or the ground Be2 state6 are all hypervalent species. He furthermore explicitly stated that the formation of such molecules involves reorganization of the ground atomic configurations so that these atoms use all their valence electrons while he attributed the occurrence of stable hypervalent bonds in pairs to the fact that both the decoupled p2 electrons have to be used in some form of bonding. The first of the above statements is identical to the democracy principle enunciated 25 years later by Cooper et al.,7 stating that “it is the democratic right of every valence electrons to take part in chemical bonding if it wants!” while the decoupled p2 electron pair notion inspired the recoupled pair bonds,8,9 recoupled pair bond dyads,10 and frustrated recoupled pair bond11 model introduced by Dunning and coworkers. There is no doubt anymore that in order to form these “hypervalent” species at least the “central” atom should somehow use all of its valence electrons and that process entails the participation of excited or ionic states. This was already known to the “old” masters of quantum chemistry who investigated it systematically; see e.g. Ref. 12 and references therein. This “promotion” is nowadays acknowledged either implicitly7−11 or explicitly; see e.g. Refs. 13–21.
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One way of “viewing” the bond formation is based on the Generalized Valence Bond (GVB)22 or Spin Coupled Valence Bond (SCVB)23 wavefunction, the most solid independent particle model theory, just because it monitors the changes in orbitals’ shapes and the weights of the spin functions along the reaction coordinate or in other words it probes the chemical bond upon formation. GVB/SCVB is based on the Wigner24/Kotani et al.25 way of writing the exact electronic wavefunction within the Coulombic approximation, i.e., S
fN r r r r r r r r Ψ S , M ( x1 , x2 ,..., xN ) = ( f NS )−1 ∑ Φ k (r1 , r2 ,..., rN )Θk (σ 1 , σ 2 ,..., σ N ), xi = (ri , σ i ) k =1
with Φk being the exact solutions of the Schrödinger equation, Θk are the spin functions, and f NS is the number of all linearly independent spin functions of N electrons coupled into a spin value S. In the GVB/SCVB approximation all exact Φk spatial functions have been replaced by a single Hartree product of N distinct spatial orbitals and then properly antisymmetrized. This is reminiscent of the Unrestricted Hartree–Fock (UHF) wavefunction but GVB/SCVB considers variationally all f NS spin couplings and respects the spin symmetry properties. It (GVB/SCVB) is also free of the instabilities due to the double occupancy constraint26 as was shown by Coulson and Fischer in the H2 case.27 The GVB/SCVB way of thinking also offers another interesting aspect in the concept of the chemical bond. We no longer view it as two electrons occupying the same molecular orbital just because we have a string of orbitals, unfortunately common to all spin couplings. Moreover and since the atomic GVB/SCVB orbitals are no longer eigenfunctions of L2, the concept of the active space should be “redefined”. For the 4 ACS Paragon Plus Environment
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recovery of the so called static correlation all valence orbitals should be present in the active space. But valence orbitals are defined with respect to the R(O)HF wavefunction that is proven to be unstable.28 Under this perspective it seems plausible to expand the active space by orbitals that contribute to the preservation of the Laplace–Runge–Lenz (LRL) vector instead of L2. This is the origin of the “d orbital participation/hybrization” idea in the chemical theoretical literature. Moreover, and in the case of chemical resonance, states resulting from excited state fragments or ion pair states modify the orbital needs of our active space. So, the latter should be tailored upon the particular state under study and not based solely on the R(O)HF valence orbitals. Practice has shown that the GVB/SCVB molecular orbitals are atom like in shape with delocalization tails on the neighboring atoms. Although such a wavefunction is lucid and highly interpretable it is a single Hartree product approximation and thus it cannot deal with inherently multiconfigurational cases. For example both σ2 and πx2 or πy2 configurations share the same symmetry but only one can be described by a single Hartree product; see also Refs. 29–31 for a real life problem. In exactly these cases the simplicity of the GVB/SCVB wavefunction may lead to not so sound conclusions as for the nature of the chemical bond. We believe 4 − 4 − that this is the case for SF( a Σ ) and OF( a Σ ) hailed as archetypal species that
possess recoupled pair bond9 and frustrated recoupled pair bond,11 respectively. In what follows we shall thoroughly examine the above species with a special 4 − emphasis on the OF( a Σ ) case. A d–aug–cc–pVQZ basis set32 has been used for OF
and an aug–cc–pVQZ basis set for all the S containing species while our calculations have been done with the MOLPRO program.33
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II.
RESULTS AND DISCUSSION
4 − The OF( a Σ ) species acted as the main motivation for the present work since it
appears to be the hallmark of a frustrated recoupled pair bond11 or in other words of an incomplete recoupling at the equilibrium distance based on an unbound GVB/SCVB wavefunction. It was concluded that the rather weak chemical bond of circa 11 kcal/mol was entirely due to dynamical correlation.11 A similar statement was made a few years ago by Schmidt et al.34 for a rather exotic molecule, Be2( X 1 Σ +g ). They explicitly said that “… the attraction between them results entirely from changes in the dynamic electron correlations.” and that “… the binding in Be2 is contingent on the effects of dynamical electron correlation which is uncommon and therefore of considerable interest.” It was concluded that 3d orbitals are responsible for the bond in Be2. As we have recently shown6 two Be atoms excited in their 3P(2s12p1) state form the X state of the dimer and that a suitable description of the 3P(Be) atomic state demands 3d orbitals as nicely explained by Nicolaides.35 So, in our perspective the 3d orbitals, that lie beyond the usual valence space, do not offer dynamical correlation as generally thought of but a correct description of the zeroth order wavefunction; see also Ref. 36 for more details. All of the above are also in congruence with the GVB/SCVB findings since the atomic orbitals are not eigenfunctions of L2 but of the LRL constant of motion and for that to happen we need to go beyond the R(O)HF valence space. Similarly, in ionic cases, i.e., LiF, an active space of purely RHF valence character has been proven to lead to discontinuity problems.37 These additional orbitals needed for the correct description of the problem at hand do not offer portions of the so called dynamical
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correlation but the correct static one as also described by the GVB/SCVB wavefunction. 4 − Based on all the above, we wanted to reexamine the OF( a Σ ) molecule since the
whole analysis and conclusions of Ref. 11 are based on a purely repulsive GVB/SCVB wavefunction. 4 − To this end we have constructed the potential energy curve (PEC) of OF( a Σ ) at
the ROHF, CASSCF, and SACASSCF levels of theory in the valence and in an augmented active space; the latter one is suitable for the description of F−(1S). The (SA)CASSCF(val) wavefunction resulted from the distribution of 9 (= 2p4(O) + 2p5(F)) valence electrons to the 6 (2p(O) + 2p(F)) valence orbitals while the (SA)CASSCF(aug) wavefunction resulted from the distribution of the same 9 electrons to the valence active space augmented by 2a1 + 1b1 + 1b2 orbitals. The interaction (~ 0.2 kcal/mol) is practically repulsive at both the ROHF and CASSCF(val) computational levels; see Figure 1. It becomes chemically meaningful only at the CASSCF(aug) level and interestingly enough the PEC presents a hump at around 4 bohr. The situation changes dramatically at the SACASSCF(aug) level predicting also a binding energy of 11.5 kcal/mol. The reason for such an impressive behavior should be clarified if one wants to unmistakably understand the intricacies of the chemical bond in the present case. The morphological change at the CASSCF(aug) level warrants some attention. The presence of a hump is the signature of an avoided crossing and this become even more intense in the SACCASCF(aug) case (see Figure 1). Moreover, the binding energy predicted by this zeroth order wavefunction is practically identical to the much more accurate MRCI+Q value reported in Ref. 11. It is even more puzzling the fact that the “king” of all single 7 ACS Paragon Plus Environment
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reference correlated methods, RCCSD(T), gives a value of 8.53 kcal/mol versus 11.22 kcal/mol at the MRCI+Q level.11 The astute reader may wonder what is really happening in this “simple” diatomic molecule. One may also think that the inability of the RCCSD(T) method to accurately describe the binding energy may be attributed to the repulsiveness of the ROHF wavefunction but this is also the case for the GVB/SCVB and CASSCF(val) ones on which the MRCI expansion is based. Generally speaking the RCCSD(T) and MRCI+Q binding energies are pretty much comparable in most of the cases but not here. And this is indeed strange since OF is such a small molecular system. The reason for such a seemingly paradoxical situation can be gleaned by the inset of Figure 1 where a number (12) of SACASSCF(aug) PECs of 4 Σ − symmetry are displayed. It is more than obvious that the hump and the subsequent deep potential well are due to a severe avoided crossing with a state arising from O+(4S) + F−(1S) that lies experimentally 10.217 eV (= IE(O; 3P) – EA(F; 2
P)) above the ground O(3P) + F(2P) asymptote. Based on that knowledge we can now
perfectly understand why the ROHF, GVB/SCVB, and CASSCF(val) PECs predict an unbound system while the situation starts changing gradually at the CASSCF(aug) and dramatically at the SACASSCF(aug) levels. An ionic diabate moving downwards from 10.217 eV cannot be adequately described by single configuration methods like ROHF or GVB/SCVB. The bonding is ionic in nature and can be visualized by the following valence– bond–Lewis (vbL) diagram (Scheme 1)
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(Scheme 1) The variation of the binding energy at the various computational levels presently used is revealing; De= 8.8 [RCCSD(T)], 7.8(12.9) [MRCI(val)(+Q)], 12.7(14.9) [MRCI(aug)(+Q)], 11.5(15.3)[15.0] {SACASSCF(aug)(MRCI)[+Q]} kcal/mol. The RCCSD(T) and MRCI(val) wavefunctions predict a poor binding energy with only the MRCI(val)+Q
(12.9)
value
being
comparable
to
the
most
accurate
SACASSCF(aug)+1+2 (15.3) and +Q (15.0) values. The rather unfortunate 4 − RCSCD(T) outcome can be rationalized by the fact that OF( a Σ ) is not a single
reference problem. The CASSCF(aug) wavefunction is dominated by a single configuration
with
C0=0.95,
but
the
SACASSCF(aug)
is
inherently
multiconfigurational with four main configurations with C0= 0.83, 0.42, −0.19, and
−0.19. It is not a surprise anymore that single reference methods cannot describe well 4 − this a Σ state.
4 − The bonding situation in SF( a Σ ), that is considered to be an archetypal
example of recoupled pair bond,8,9 is similar. But this time the ionic asymptotic channel, S+(4S) + F−(1S), is only 6.959 eV above the ground channel S(3P) + F(2P). Due to this smaller energy gap the GVB/SCVB wavefunction is able to capture the attractive interaction well, although marginally, see Figure 4 in Ref. 9 or Figure 2 in Ref. 11. Now, the character of the GVB/SCVB equilibrium orbitals is completely changed. These do not longer correspond to the neutral S(3P)/F(2P) situation but to the ionic S+(4S)/F−(1S) one; see also Figures 10 and 12 in Ref. 9. The change in the orbitals character is also reflected in the variations of the ω3/ω4 spin coupling coefficients (Figure 11, Ref. 9) and S12/S13/S23 orbital overlaps (Figure 13, Ref. 9); all changes start occurring at ~ ∆r= 0.5 Å precisely at the height of the hump of the 9 ACS Paragon Plus Environment
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GVB/SCVB PEC (Figure 4, Ref. 9) that is a signature of an avoided crossing with an ionic state; see also our Figure 2 for the morphology of all relevant curves. Based on all the above but also on the findings of Ref. 9 we would say that the bonding in SF(
a 4 Σ− ) is also ionic in nature whose vbL diagram should be similar to the one depicted 4 − above for OF( a Σ ).
There are three more electrons coupled in a high spin state that can be used for three covalent bonds to be formed. It is through this state that SF4(1A1) is realized and there is no mystery about it; see also Figure 6 in Ref. 8. Two more valence electrons (
~3sS2 ) are present and certainly they can be used if we invoke the “democracy principle”. This is indeed true as witnessed in the chemical literature.38 We shall briefly examine two representative members from the rich chemistry of sulfur fluorides, SF6 and OSF4. Without any doubt SF6 is a famous, perhaps the most famous hypervalent molecule and the history of its various bonding scenarios are outlined in Ref. 8. Two F(2P) atoms approach the singlet parental species, SF4, and give rise to a singlet final product (SF6). So, based solely on the spin symmetry conservation we absolutely need two more electrons to couple into a singlet spin fashion the two incoming F(2P) 2 doublets. Obviously these two electrons are being provided by the ~3sS shell, but
how? In Ref. 8 the bonding explanation is based on their decoupling, i.e., these two electrons are no more singlet coupled, they polarize along the axis and they finally get singlet coupled with the two incoming F atoms. Our analysis reveals another bonding pattern. In Figure 3 we display SACASSCF PECs of the F + SF4 interaction along an axis perpendicular to the SF4 molecular plane. It is clear that the minimum of the ground 2A1 state is due to a series of avoided crossings with an ionic diabate that 10 ACS Paragon Plus Environment
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confers its character. The Mulliken population analysis is rather apocalyptic. The
~3sS orbital hosts ~1.1 e− and that simply means that the bonding in SF5 is ionic, i.e., F4S+F− (qS= +2.8 and qF= −0.70) with the remaining electron ready to form another bond with an incoming F(2P) atom i.e., SF6. Schematically the bonding in SF5 is nicely depicted by Scheme 2,
(Scheme 2) In SF6 and due to its high point group symmetry the ionic/covalent character is equally spread around all SF bonds. In OSF4 the situation is similar, equally revealing and rather unexpected. A similar argument based on spin conservation reveals that the O atom should be in a singlet spin state if one wants to create a singlet (OSF4) out of a singlet (SF4). And this is nicely revealed in the SACCASCF PECs (see Figure 4) but the bonding is not putative as one might suppose but ionic as well! The interaction is initially repulsive due to the nature of the O(1D) electronic configuration but at ~ 5.0 bohr there is an abrupt change of slope due to the ionic diabate correlating to SF4+(2A1) + O−(2P); see Figure 4. At equilibrium the S atom has a Mulliken charge of +3 with an atomic distribution of ~3s0.84 while the O atom is found with an overall minus charge, i.e., qO= −0.95. We should remind at this point that in SF4 the S bears a charge of +2, so the additional positive charge (+3) is due entirely to O−. Although the wavefunction
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presents a multiconfigurational character its largest component (C0= 0.88) reveals a sigma ionic bond between O−( 2 s 2 2 p x2 2 p y2 2 p1z ) and a (3s3pz)S hybrid; see Scheme 3:
(Scheme 3)
III.
CONCLUSIONS
For the formation of the so called hypervalent species all valence electrons should be used. The only way this can happen is through the excited or ionic configurations of the constituent fragments. In order to properly describe this electronic reorganization we should ensure that both the basis set and active space of our CASSCF wavefunction is able to describe all ingredients necessary for the transformation to happen. 4 − 4 − In particular we have found that the bonding in OF( a Σ ) and SF( a Σ ) is due to
an avoided crossing with an ionic state lying 10.217 eV and 6.959 eV above the 4 − ground neutral asymptotic fragments, respectively. The ionic SF( a Σ ) state acts as
the natural precursor of the SF4(1A1) species. Then, the addition of two F(2P) or one O(1D) atoms to SF4(1A1) results into the well known SF6 and OSF4 systems. The equilibrium of the latter molecules is also ionic in nature due to severe avoided crossings with the respective ionic channels.
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Under the point of view presented herein, the hypervalent story should not be covered by a mystery haze but as a normal situation where the constituent fragments are not in their ground states. At the very end, we can ask ourselves, what is all the buzz about hypervalency?
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References 1. Musher, J.I. The Chemistry of Hypervalent Molecules. Angew. Chem. Internat. Edit. 1969, 8, 54–68. 2. Lewis, G.N. The Atom and the Molecule. J. Amer. Chem. Soc. 1916, 38, 762–785. 3. Langmuir, I. The Arrangement of Electrons in Atoms and Molecules. J. Amer. Chem. Soc. 1919, 41, 868–934. 4. Jacox, M.E. Electronic Energy Levels of Small Polyatomic Transient Molecules. J. Phys. Chem. Ref. Data 1988, 17, 269–511. 5. Huber, K.P.; Herzberg, G. Constants of Diatomic Molecules (data prepared by J.W. Gallagher and R.D. Johnson, III) in NIST Chemistry WebBook, NIST Standard Reference Database Number 69, Eds. P.J. Linstrom and W.G. Mallard, National Institute of Standards and Technology, Gaithersburg MD, 20899, doi:10.18434/T4D303. 6. Kalemos, A. The Nature of the Chemical Bond in Be2+, Be2, Be2−, and Be3. J. Chem. Phys. 2016, 145, 214302(1–13) . 7. Cooper, D.L.; Cunningham, T.P.; Gerratt, J.; Karadakov, P.B.; Raimondi, M. Chemical Bonding to Hypercoordinate Second–Row Atoms: d Orbital Participation versus Democracy. J. Amer. Chem. Soc. 1994, 116, 4414– 4426. 8. Woon, D.E.; Dunning, T.H., Jr. Theory of Hypervalency: Recoupled Pair Bonding in SFn (n= 1−6). J. Phys. Chem. A 2009, 113, 7915–7926. 9. Dunning, T.H., Jr.; Xu, L.T.; Takeshita, T.Y. Fundamental Aspects of Recoupled Pair Bonds. I. Recoupled Pair Bonds in Carbon and Sulfur Monofluoride. J. Chem. Phys. 2015, 142, 034113(1–13). 14 ACS Paragon Plus Environment
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10. Dunning, T.H., Jr.; Takeshita, T.Y.; Xu, L.T. Fundamental Aspects of Recoupled Pair Bonds. II. Recoupled Pair Bond Dyads in Carbon and Sulfur Difluoride. J. Chem. Phys. 2015, 142, 034114(1–10). 11. Takeshita, T.Y.; Dunning, T.H., Jr. Fundamental Aspects of Recoupled Pair Bonds. III. The Frustarted Recoupled Pair Bond in Oxygen Monofluoride. J. Phys. Chem. A 2016, 120, 9607–9611. 12. Heitler, W. Quantum Chemistry: The Early Period. Int. J. Quantum Chem. 1967, I, 13–36. 13. Moffitt, W. Atoms in Molecules and Crystals. Proc. Roy. Soc. (London) A 1951, 210, 245–268. 14. Ruedenberg, K. The Physical Nature of the Chemical Bond. Rev. Mod. Phys. 1962, 34, 326–376. 15. Langhoff, P.W. Spectral Theory of Physical and Chemical Binding. J. Phys. Chem. 1996, 100, 2974–2984. 16. Nicolaides, C.A.; Komninos, Y. Geometrically Active Atomic States and the Formation of Molecules in their Normal Shapes. Int. J. Quantum Chem. 1998, 67, 321–328. 17. Komninos, Y.; Nicolaides, C.A. Molecular Shape, Shape of the Geometrically Active Atomic States, and Hybridization. Int. J. Quantum Chem. 1999, 71, 25–34. 18. Langhoff, P.W.; Boatz, J.A.; Hinde, R.J.; Sheehy, J.A. Atomic Spectral Methods for Moelcular Electronic Structure Calculations. J. Chem. Phys. 2004, 121, 9323–9342.
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19. Kalemos, A.; Mavridis, A. Bonding Elucidation of the Three Common Acids, H2SO4, HNO3, and HClO4. J. Phys. Chem. A 2009, 113, 13972– 13975. 20. Kalemos, A.; Mavridis, A. Myths and Reality of Hypervalent Molecules. The Electronic Structure of FClOx, x= 1−3, Cl3PO, Cl3PCH2, Cl3CClO, and C(ClO)4. J. Phys. Chem. A 2011, 115, 2378–2384. 21. Shaik, S.; Danovich, D.; Hiberty, P.C. To Hybridize or Not to Hybridize? This is the Dilemma. Comp. Theor. Chem. 2017, 1116, 242–249. 22. Ladner, R.C.; Goddard, W.A., III Improved Quantum Theory of Many– Electron Systems. V. The Spin–Coupling Optimized GI Method. J. Chem. Phys. 1969, 51, 1073–1087. 23. Gerratt, J. General Theory of Spin–Coupled Wave Functions for Atoms and Molecules. Adv. At. Mol. Phys. 1971, 7, 141–221. 24. Wigner, E.P. Group Theory and its Applications to the Quantum Mechanics of Atomic Spectra. Academic Press, 1959, p. 259, formula 22.20b and the paragraph that follows it. The German edition of the book appeared in 1931. 25. Kotani, M.; Amemiya, A.; Ishiguro, E.; Kimura, T. Table of Molecular Integrals. Maruzin Co., Ltd. 1955. 26. Karadakov, P.; Castano , O. Stability Properties of Closed−Shell Restricted Hartree−Fock Solutions for Electronic Systems in the Framework of the Projected Hartree−Fock Method and Their Utilization. Int. J. Quantum Chem. 1983, XXIV, 453−477. 27. Coulson, C.A.; Fischer, I. Notes on the Molecular Orbital Treatment of the Hydrogen Molecule. Phil. Mag. S7 1949, 40, 386–393. 16 ACS Paragon Plus Environment
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28. Adams, W.H. Stability of Hartree–Fock States. Phys. Rev. 1962, 127, 1650–1658. 29. Takeshita, T.Y.; Lindquist, B.A.; Dunning, T.H., Jr. Insights into the Electronic Structure of Ozone and Sulfur Dioxide from Generalized Valence Bond Theory: Bonding in O3 and SO2. J. Phys. Chem. A 2015, 119, 7683–7694. 30. Kalemos, A. Comment on “Insights into the Electronic Structure of Ozone and Sulfur Dioxide from Generalized Valence Bond Theory: Bonding in O3 and SO2.” J. Phys. Chem. A 2016, 120, 169–170. 31. Penotti, F.B.; Cooper, D.L. Combining Rival π−Space Descriptions of O3 and SO2. Int. J. Quantum Chem. 2016, 116, 718–730. 32. Dunning, T.H., Jr. Gaussian Basis Sets for Use in Correlated Molecular Calculations. I. The Atoms Boron through Neon and Hydrogen. J. Chem. Phys. 1989, 90, 1007–1023. 33. MOLPRO is a package of ab initio programs written by H.−J. Werner, P. J. Knowles, G. Knizia, F. R. Manby, M. Schütz, P. Celani, W. Györffy, D. Kats, T. Korona, R. Lindh, A. Mitrushenkov, G. Rauhut, K. R. Shamasundar, T. B. Adler, R. D. Amos, A. Bernhardsson, A. Berning, D. L. Cooper, M. J. O. Deegan, A. J. Dobbyn, F. Eckert, E. Goll, C. Hampel, A. Hesselmann, G. Hetzer, T. Hrenar, G. Jansen, C. Köppl, Y. Liu, A. W. Lloyd, R. A. Mata, A. J. May, S. J. McNicholas, W. Meyer, M. E. Mura, A. Nicklaß, D. P. O'Neill, P. Palmieri, D. Peng, K. Pflüger, R. Pitzer, M. Reiher, T. Shiozaki, H. Stoll, A. J. Stone, R. Tarroni, T. Thorsteinsson and M. Wang. MOLPRO, version 2012.1, a package of ab initio programs; University College Cardiff Consultants Limited: Cardiff, U.K., 2008.
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34. Schmidt, M.W.; Ivanic, J. Ruedenberg, K. Electronic Structure Analysis of the Ground State Potential Energy Curve of Be2. J. Phys. Chem. A 2010, 114, 8687–8696. 35. Nicolaides, C.A. State– and Property–Specific Quantum Chemistry: Basic Characteristics and Sample Applications to Atomic, Molecular, and Metallic Ground and Excited States of Beryllium. Int. J. Quantum Chem. 2011, 111, 3347–3361. 36. Nicolaides, C.A. State– and Property–Specific Quantum Chemistry. Adv. Quantum Chem. 2011, 62, 35–103. 37. Meras, A.S. de; Lepetit, M.B.; Malrieu, J.−P. Discontinuity of Valence CASSCF Wavefunctions Around Weakly Avoided Crossing Between Valence Configurations. Chem. Phys. Lett. 1990, 172, 163–168. 38. Greenwood, N.N.; Earnshaw, A. Chemistry of the Elements, Butterworth− Heinemann, Oxford, 1997.
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4 − Figure 1: PECs of the OF( a Σ ) state at various levels of theory. The inset displays
PECs at the SACASSCF(aug) level for a number (12) of different states of the same 4
Σ − symmetry (in black circles).
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Figure 2: PECs of SF( 4 Σ − ) at the SACASSCF(aug)/AVQZ computational level. The wavefunction, state averaging 12 states, resulted from the distribution of 9 valence electrons to the valence active space (3p(S) + 2p(F)) augmented by 2a1 + 1b1 + 1b2 orbitals.
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Figure
3:
PECs
describing
the
F
+
SF4
interaction
at
the
SA(12
states)CASSCF/AVQZ computational level. The wavefunction resulted from the distribution of 3 valence electrons to 5 orbitals.
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Figure
4:
PECs
describing
the
O
+
SF4
interaction
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at
the
SA(12
states)CASSCF/AVQZ computational level. The wavefunction resulted from the distribution of 6 valence electrons to 7 orbitals. The active space thus chosen assures the correct dissociation to the molecular states shown in the figure.
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