Ab initio diagnosis of isomerization pathway of diphosphene and diphosphinylidene

Journal Pre-proofs Ab initio diagnosis of isomerization pathway of Diphosphene and Diphosphinylidene Suvonil Sinha Ray PII: DOI: Reference:

S0301-0104(19)30436-7 https://doi.org/10.1016/j.chemphys.2019.110555 CHEMPH 110555

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Chemical Physics

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17 April 2019 5 September 2019 6 October 2019

Please cite this article as: S.S. Ray, Ab initio diagnosis of isomerization pathway of Diphosphene and Diphosphinylidene, Chemical Physics (2019), doi: https://doi.org/10.1016/j.chemphys.2019.110555

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Ab initio diagnosis of isomerization pathway of Diphosphene and Diphosphinylidene Suvonil Sinha Ray1 1

Department of Chemistry, University of Calcutta, Kolkata 700009, India

An appositeness of recently developed multireference perturbation theory coupled with an improved virtual orbitals complete active space configuration interaction reference function (IVOSSMRPT) has been examined here against strongly correlated molecular systems emerging from isomerization of diphosphene and diphosphinylidene. The IVO-SSMRPT is an interesting alternative to the widely used MRPT methods which avoid some of the objections of the conventional MRPTs. IVO-BWMRPT furnish a reliable description of near-degeneracy between occupied and unoccupied orbitals at the twisted geometry where the wave function receives biradical character. Overall, the IVO-SSMRPT results are in good agreement with the more expensive state-of-the-art ab initio calculations discloses the accomplishment of the IVO-SSMRPT method. The IVO-SSMRPT method can be considered as an economical MR ab initio protocol that renders a good compromise between accuracy and computational expense. PACS numbers:

I.

INTRODUCTION

Understanding the properties of molecular systems containing two heavier Group 15 elements (like phosphorus) is a challenging task that becomes increasingly important for various utilities and applications in chemistry and materials science. Chemical reactivity of diphosphenes, an intriguing challenge for both experimentalists and theoreticians, is under the spotlight from the aspect of material synthesis, as they are reactive to a varied range of chemical reagents[1–4]. Diphosphene compounds are more effectively reduced than normal olefins or azo-compounds[3]. Distinctive electrochemical and photochemical properties of diphosphines and diphosphinylidene can be exploited in different applications such as novel electron-rich organometallic ligands.[5]. Moreover, PP bonded systems have been successfully used in chemical hydrogen storage systems[6]. The synthesis as well as isolation of diphosphenes and diphosphinylidenes is a difficult task since they often lean toward oligomerization/polymerization owing to thermodynamic stability[4]. Kinetically stable phosphorus complexes with P=P can be synthesized using bulky substituents[7–9]. In recent past, P=P bonds have been integrated into π-conjugated compounds as building blocks to design molecular electronics. It should be noted that one of the important traits of diphosphenelike systems is the P-P bond distance which lies in the range 2.00-2.034 ˚ A, with the characteristic harmonic vibrational frequencies of about 610 cm−1 indicating the presence of a P-P double bond[10–12]. Various theoretical studies have also been carried out to gain insight into the nature of diphosphene and diphosphinylidene type compounds[3, 6, 13–16]. The purpose of the present work is to study the prototypical P=P doubly bonded phosphorus compounds such as diphosphene (HPPH) and diphosphinylidene (PPH2 ) using recently suggested second-order multireference perturbation theory with a simplified treatment of nondynamical correlation effect. Special attention is given to the investigations of both the

transition states (TS) involving two different isomerization pathways. The transition states demand multireference (MR) ab initio based calculations in a more prominent way than the ground states. Note that the description of electronic structure of TSs is generally plagued by quasidegeneracy, displaying itself through the presence of different leading components in the wave function. Thus, the performances of the correlation methods which rely on the single-reference assumption deteriorates in the presence of quasidegeneracy. Coupled cluster T1 diagnostic test[17] has been performed for every molecular system related to the isomerization process discussed in the present work since such diagnostic values can be exploited to assess the MR character of a molecule[17, 18]. Generally a larger value of the T1 diagnostic (≥ 0.02) suggests the importance of the higher-body cluster operators than singles-doubles (i.e. triple as well as quadruple excitations) and thus CCSD approximation is not adequate in such situation. T1 values of cis and trans isomers of diphosphene (HPPH) are found to be 0.0167 and 0.0161, respectively. These suggest a moderate MR character in both cases. The T1 coupled cluster diagnostic value for planar diphosphinylidene (PPH2 ) is 0.0208 suggesting reasonable MR character of PPH2 compared to previous cases. TS connecting trans HPPH and planar PPH2 exhibits a T1 diagnostic value of 0.0256. On the other hand, TS joining trans and cis HPPH minima has a value of 0.0228. Largest value of the T1 diagnostic for the TS uniting trans HPPH and planar PPH2 demonstrates the most prominent MR nature among all of them. Therefore the present isomerization process can be used as a probing ground to calibrate the efficacy of an ab initio method tailored to treat the state plagued by configurational quasi-degeneracy. As one of the widely used MR procedures for treating quasidegeneracy situations nowadays, MR perturbation theory (MRPT) has demonstrated to be at the front line of the recipes of choice. The second-order complete active space (CAS) state specific (SS) MRPT (SSMRPT) method where target-specific parametrisation of the wave

2 function focuses on only one electronic state (the root of principal interest) at a time[19, 20] and many other MRPT methods[21–29] acquire their enormous acclaim from the blend of accuracy and computational efficiency which makes them appealing tools particularly for the description of large molecules in ground as well as excited states. Another useful route to treat the MRsituation is the spin flip (SF)-based protocol pursued for a long time to handle quasidegeneracy by Krylov and coworkers[30]. One should also mention that unlike the case of configuration interaction (CI) scheme, the generalization of perturbation theory for more than one reference configuration is not straightforward. The main difference between the different MRPT methods is in the form of zeroth-order Hamiltonian and definition of the unperturbed wave function. Owing to their structural nature, the implementation of various MRPT methods often exhibits different troubles such as convergence problem associated with intruder states, sizeintensivity, size-consistency, and so on. Some MRPT methods do not allow the upgradation of coefficients in the unperturbed function during the subsequent correlation treatment. It is important to stress that the intruder state problem prompted a search for variations of the MRPT approach which would be free from convergence objection[19, 20, 25, 29]. To overcome the intruder state problem manifestly rather than in an ad hoc manner[31], Mukherjee and coworkers[19, 20] introduced SS version of size-extensive MRPT method with CASSCF reference wave function based on the Jeziorski- Monkhorst (JM) ansatz[32]. The JM ansatz is the starting point of many MRdevelopments[33]. Generally, CASSCF is a widely used method to construct the unperturbed wave function in MR-correlated computations. However, the highly nonlinear nature of the orbital optimisation process in the conventional CASSCF calculation often invite various problems such as multiple solutions of orbitals corresponding to local minima, convergence problems, rootflipping between close-lying states, and symmetry breaking. This makes the CASSCF-based MRPT method less useful when handling chemically challenging systems with large reference space. Therefore, there is appreciable interest in developing an effective replacement of the CASSCF method. One alternative is the improved virtual orbital-complete active space configuration interaction (IVO-CASCI) scheme as originally suggested by Freed and coworkers[34, 35]. The IVO-CASCI protocol is free from iterations beyond those in the initial SCF step because it circumvents the orbital optimization process altogether, introducing a substantial computational advantage . For this reason it is free from multiple solutions and less susceptible to the convergence problems that often infected CASSCF treatments. IVO-CASCI retains the features of CASSCF. An interesting method to treat the MR situation in a target specific way has been suggested by Chattopadhyay and coworkers by fusing SSMRPT with IVO-CASCI method within the frame-

work of a multipartitioning Møller-Plesset (MP) type of partition scheme[36]. The resulting method is termed as IVO-SSMRPT. As that of other genuine MR-correlated methods, the concept of IVO-SSMRPT strategy is simple and consists of three steps: (a) To take into account MR nature, a set of configurations (pertinent to represent the main characteristics of the quasidegenerate wave function) as references is defined to set up the active space by exploiting IVO-CASCI scheme. (b) The expansion space of the MRPT wave function is then generated by orbital excitations from those references (for each component of the reference set separately) using the SSMRPT route[19, 20]. (c) Finally, the coefficients and the energy of the state of interest are obtained by diagonalizing the dressed Hamiltonian. IVO-SSMRPT being a single-root protocol focuses only on one root at a time. All other roots appear just as byproducts of the computations, helping to maintain sufficient separation of the root of interest. The resulting IVO-SSMRPT method inherits all the redeeming features of the parent SSMRPT formalism such as size-extensivity and size-consistency with localized orbitals. It is generally applicable to a various class of chemical problems of closed- and openshell singlet- and nonsinglet ground as well as excited states in a single framework. It is computationally much more handy than MR configuration interaction (MRCI) and MR coupled cluster (MRCC) methodologies. The diagonalization process in the IVO-SSMRPT approach allows the relaxation of the reference space component upon constructing the perturbation corrections which is very crucial to treat mixed states and avoided surface crossings[37]. The IVO-SSMRPT approach has shown wide applicability for treating the complicated electronic states plagued by quasidegeneracies of varying degree during the geometry optimization as well as bond-dissociation processes[37–40] because it has potential for treating mutual interplay of the nondynamical and dynamical correlation effects in the wave functions of closed- and open-shell states in an appropriate manner. The IVO-SSMRPT method shows promising potential concerning limitations of the computational cost as observed in the composite CASSCF-SSMRPT scheme. At this juncture I want to mention that Schaefer et al.[13] have investigated trans- and cis-HPPH diphosphene and planar PPH2 diphosphinylidene using different highly correlated wavefunction based methods including state-specific multireference coupled cluster (SS-MRCC) method suggested by Mukherjee and coworkers (Mk-MRCC)[41–43]. Corresponding MRCI and CCSD(T) values are also available due to their work. It is noted that the IVO-SSMRPT can be viewed as a companion computationally affordable perturbation theory for Mk-MRCC[41–43] computations, extending the range of application of the parent CC method to larger systems.

3 II.

RESULTS AND DISCUSSION

It is fascinating to inspect the results of the IVOSSMRPT[38–40] method in the context of structural properties of both ground and transition states along with barrier heights of isomerization for molecules. IVOSSMRPT computations have been performed using our in house code, which has been interfaced with the GAMESS (US) electronic structure package[44]. The basis sets used here are found from the EMSL database[45]. In this work, correlation consistent quadruple zeta valence (cc-pVQZ) basis[46] due to Dunning and co-workers has been used. CAS(a,b) describes ‘a’ electrons are distributed in ‘b’ orbitals. For all the cases CAS(2,2) has been used for both the MRMP2[21] and IVO-SSMRPT method. Numerical derivative technique is used for both the MRMP2[21] and IVO-SSMRPT procedure. The convergence threshold for the geometry optimizations in this work is 10−4 .

A.

Diphosphene (HPPH) 1.

Trans-HPPH

Figure 1 displays the optimized geometries of trans HPPH molecule. The molecular point group of the optimized structure is found to be C2h having 1 Ag symmetry, which is similar to previous calculation due to Schaefer III et al.[13, 47]. Owing to the existence of bond between heavy elements, its structural parameters, specially the P-P bond character estimation is very interesting[48]. The bond distances found for P-P by various methods considered here demand discussion. We have found that the P-P bond distance increases from 2.024 ˚ Ato 2.031 ˚ Aif one moves from IVO-SSMRPT/cc-pVQZ level of calculation to Mk-MRCCSD/cc-pVQZ[13]. The computed bond length for the same is 2.038 ˚ Adue to CCSD(T) method using aug-cc-pVQZ basis[13]. Depending on the method employed, the computed P-P bond lengths may differ by up to 0.014 ˚ A. The P-H bond length due to IVO-SSMRPT method is more or less matches the predicted length due to Mk-MRCCSD method that uses active space of same dimension with IVO-SSMRPT. The deviation is around 0.007 ˚ Aonly. MRCI results[13] with aug-cc-pVTZ bais are also worth mentioning. MRCI uses sufficiently large zeroth order CASSCF reference function of (12,10). With increasing dimensional space, both the P-P and P-H bond lengths increase. The increment of P-P bond length is maximum compared to the CAS(2,2)IVO-SSMRPT method with a value of 0.03 ˚ A. The elongation of P-H bond length lies within 0.013 ˚ A. The additional antibonding character imported into the wave function at higher CAS space justifies this observation. The ∠HPP prediction due to IVO-SSMRPT method is close to Mk-MRCCSD and CCSD(T) methods with deviations of only 0.77 and 0.43◦ respectively. The correponding deviation between Mk-MRCCSD and MRCI is

0.13◦ . With the same active space and equal cc-pVQZ basis, another perturbative method, MRMP2[21] results are worth discussing in this context. The P-P bond length is the second highest with a 0.004 ˚ Adeviation from CCSD(T) level. The corresponding P-H bond length and ∠HPP are almost equal to the IVO-SSMRPT prediction. CAS(2,2) space is composed of the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) having 2au and 2bg symmetries as described in (a) of Figure 2.

2.

Cis-HPPH

Next we focus on the cis isomer of diphosphene. Schaefer III et al.[13] from their CSF analysis, predicted that a multireference character indeed prevails at the cis geometry. Figure 3 assembles the geometrical parameters of 1 A1 cis HPPH having C2v symmetry. The IVOSSMRPT values agree well with the CCSD(T), MRMP2, Mk-MRCCSD and MRCI observations[13]. The P-P length due to IVO-SSMRPT method is 0.009 ˚ Alonger than that of the trans isomer. The same pattern is followed by CCSD(T)/aug-cc-pVQZ, Mk-MRCCSD/ccpVQZ and MRCI/aug-cc-pVTZ level of theories with an increment of 0.01 ˚ Ain each case. On the other hand, P-H bond length is shorter than that of the trans isomer. The P-H bond length deviates from 0.002 ˚ Ato 0.003 ˚ A. As observed previously, here also P-P bond and P-H bond lengths increase when CAS(12,10) is used in MRCI compared to CAS(2,2) in Mk-MRCCSD and IVOSSMRPT methods. The P-P bond elongation is most prominent (0.031 ˚ A) in the case of IVO-SSMRPT. IVOSSMRPT value of the ∠HPP is compatible with MkMRCCSD method with a difference of 0.47◦ only. IVOSSMRPT prediction is also very close to the value of CCSD(T) method. If we follow the MRMP2[21] predictions, the P-P bond length is higher than both IVOSSMRPT and Mk-MRCCSD methods as akin to trans isomer. MRMP2 casts a lower bonding order between two phosphorus atoms like MRCI. The ∠HPP, 98.60◦ is almost comparable to that of IVO-SSMRPT method with a minute difference of 0.06◦ . Overall, a satisfactory agreement of IVO-SSMRPT estimates with different sophisticated level of calculations is perceived according to the Figure 3. Figure 2(b) depicts both the 2b1 HOMO and the 2a2 LUMO. The HOMO and LUMO correspond to π and π ∗ orbitals respectively of the cis isomer.

B.

Diphosphinylidene (Planar PPH2 )

Another molecular system found among these structural isomers is diphosphinylidene [see Figure 4], which has a connectivity of type PPH2 . Akin to the findings of Schaefer III et al.[13, 47], PPH2 is optimized to be of 1 A1 symmetry with planar C2v structure. The P-

4 P bond length in the planar structure is much shorter than both the isomers of diphosphene. A greater double bond character between the two P atoms is anticipated. IVO-SSMRPT predicts a shorter P-P bond length than both the trans and cis isomers of HPPH with differences of 0.094 ˚ Aand 0.103 ˚ Arespectively. CCSD(T) with aug-cc-pVQZ basis forecasts a similar pattern with 0.107 ˚ Aand 0.117 ˚ Adeviations. It is important to note that P-P bond lengths predicted via IVO-SSMRPT and CCSD(T) methods are in good accordance here with a very small disagreement of 0.001 ˚ A[13]. Mk-MRCCSD(2,2)/ccpVQZ due to our calculation shows a very small difference of 0.009 ˚ Ain P-P distance with respect to the IVOSSMRPT value. All the P-H bond lengths presented here via various methods are in good harmony. IVOSSMRPT also reproduces the P-H bond length result of CCSD(T) within 0.001 ˚ A. IVO-SSMRPT predicted P-H bond length is exactly same as the Mk-MRCCSD prediction. The IVO-SSMRPT ∠HPP value agrees well with other methods having a maximum deviation of 0.77◦ . This isomer reveals a larger dipole moment than the cis HPPH[13]. The planar PPH2 isomer is more elongated along the C2 axis, which is modeled by the P-P bond. In these molecular sytems, the direction of the C2 axes contributes to dipole moments. These dipole moments are parallel to the P-P bond in planar PPH2 instead of perpendicular in cis-HPPH. MRMP2[21] optimizes the P-P bond length at 1.930 ˚ A. It is the shortest P-P bond legth among all the methods discussed, unlike in the cases of cis and trans isomers. P-P double bond character is best expressed via MRMP2 method in the planar PPH2 isomer. The P-H bond length corrsponding to the MRMP2 method, 1.401 ˚ Ais very close to 1.400 ˚ Adue to our IVO-SSMRPT. Figure 2(c) illustrates the frontier MOs (FMO) of vinylidene type planar PPH2 system. The HOMO has a Mulliken symbol, b2 in the C2v point group, whereas LUMO is b1 .

C. 1.

Transition states (TS)

TS linking trans HPPH and planar PPH2

Figure 5 assembles different geometrical parameters, calculated using different levels of theory, of the transition state for the transformation of the trans HPPH to the planar PPH2 . The optimized transition state is of C1 symmetry singlet state (1 A). Molecular systems like SCH2 and NPH2 show 1,2 hydrogen shift[49]. According to Nguyen et al., the shifting hydrogen atom acts as a proton in the TS[49]. The ∠P2 P1 H1 values correspond to IVO-SSMRPT, CCSD(T)/aug-cc-pVQZ and CISD/aug-cc-pVQZ are 103.81, 103.52 and 104.12◦ respectively. The IVO-SSMRPT value of 103.81◦ is greater than 93.55◦ of trans HPPH and 128.82◦ of planar PPH2 . The ∠P1 P2 H2 is about 47.45◦ projected by IVO-SSMRPT, which is approximately half of 93.55◦ of the trans isomer. This confirms that the proton (H2 )

migrates above the P-P bond through formation of a 3centered bond as argued by Schaefer III et al [13]. The H1 P1 P2 H2 dihedral angle (around 100◦ ) confirms that the P1 H1 bonding is also responsible. With increasing electron correlation the structure of the TS tends towards that of planar PPH2 as indicated by the variation in the P2 -H2 bond length[13]. Table 4, in the work of Schaefer III and co-workers[13], tabulates that later transition states are related to greater endothermic reactions as predicted from the Hammond postulate[50]. Figure 6(a) deliniates the HOMO and LUMO in the C1 point group.

2.

TS linking trans and cis HPPH

Figure 7 depicts the transition state linking trans and cis HPPH minima in the isomerization path. Transcis isomerization of HPPH can be achieved via two different pathways. The first one is the torsional motion about P-P bond and the second one is the inversion process through a linear P-P-H bond. It is worth mentioning that the second process is eliminated due to large barrier height[47]. In between trans and cis isomer, the transition state is detected to be a singlet state (1 A) of C2 symmetry. The trans HPPH (C2h ) and cis HPPH (C2v ) structures have non-identical orbital occupation in the C2 subgroup related to the transition state. So, single reference methods are not adequate to satisfactorily recount the TS. Our CAS(2,2)IVO-SSMRPT/cc-pVQZ results are presented and compared with CAS(2,2) based Mk-MRCCSD/cc-pVQZ and CASPT2/aug-cc-pVQZ data and also CAS(12,10) based MRCI/aug-cc-pVTZ results[13]. Analyzing CSF values, it can be concluded that a CAS(2,2) space with added dynamical correlation effect via PT or CC is ample to characterize the transition state[13]. From the geometrical parameters it can be easily shown that P-P bond is longer than both trans and cis isomers. The increments of P-P bond length at IVO-SSMRPT level from the global minimum trans HPPH and cis HPPH are 0.147 ˚ Aand 0.138 ˚ Arespectively. A similar trend is observed for MkMRCCSD level with deviations of 0.148 ˚ Aand 0.137 ˚ A. The elongation of P-P bond can be justified by the orientation of p-orbitals without forming a π bond. The dihedral angle (around 90◦ ) confirms the position of TS in the midway between trans(180◦ ) and cis(0◦ ) minima. Figure 6(b) depicts the HOMO and LUMO with a and b symmetry at C2 point group.

D.

Vibrational frequencies

The harmonic vibrational (IR) frequencies for all the ground states and TSs are calculated and assmebled in the supporting information [see Table (S.1-S.5)]. Results due to IVO-SSMRPT method have been compared primarily with CCSD(T) values of Schaefer III et al.[13].

5 MRCI, CASPT2 and Mk-MRCCSD values are also compared where avialable. The harmonic vibrational frequencies of trans HPPH [see Table (S.1)] clearly establishes that for ω3 the frequency due to CCSD(T) is very close (within 5 cm−1 ) to the IVO-SSMRPT value. Unlike the trans isomer, the frequencies of cis HPPH are almost basis set independent as predicted from CCSD(T) values [see Table (S.2)]. For planar PPH2 isomer [see Table (S.3)] IVO-SSMRPT shows deviations from CCSD(T) in between 9 to 80 cm−1 . Only one imaginary frequency for each of Table (S.4) and Table (S.5) confirms the successful prediction of the transition state. IVO-SSMRPT estimates are in acceptable proximity with already published reference values.

E.

Relative energies and Barrier height

Figure 8 represents the isomerization potential energy surface between cis and trans isomers of HPPH through a TS of C2 symmetry and also between the trans HPPH and planar PPH2 through another TS of C1 symmetry. From the geometrical optimization at different levels of theory, it can be concluded that trans HPPH is the global minimum of the total isomerization path. In Table (I) we consider the energy of the trans molecule to be zero and calculate the relative energies of other two minima structures. The CCSD(T) method using two different basis sets predicts isomerization energy to be 3.38 kcal/mol[13]. Change in basis set has no effect in that case. For all the methods tabulated here estimated energy of isomerization lies in the range 3.323.85 kcal/mol. Similarly for structural isomerization path from trans HPPH to planar PPH2 , the isomerization energy is found in between 24.89 and 30.03 kcal/mol. MRMP2[21], being a competitive method with our IVOSSMRPT, finds a much higher structural isomerization energy compared to other higher order ab initio calculations. MRMP2 method is unable to consider the two different electronic correlation effects on an equal footing. Our IVO-SSMRPT prediction of 24.89 kcal/mol is very close to the zero-point vibrational energy corrected CCSD(T)/aug-cc-pVQZ value of 25.21 kcal/mol due to Schaefer III et al [13]. The energy barriers of two different isomerization pathway furnished by the IVO-SSMRPT along with other database values[13] are presented in Table (II). This helps us envisage that IVO-SSMRPT values are in good accordance with those of the MRCI method with large dimensional CAS space and higher order CCSD(T) method. Even our perturbative calculation anticipates the trans-cis barrier height in satisfactory agreement with computationally more expensive Mk-MRCCSD with same CAS space. Isomerization of trans HPPH to planar PPH2 has a barrier height of around 50 kcal/mol. The different predictions lie within the range from 50.31 kcal/mol to 51.00 kcal/mol. Structural isomerization barrier values from the most stable HPPH to planar

PPH2 is suggested between 34.87 and 39.97 kcal/mol. It is noted that trans HPPH → planar PPH2 process is non-spontaneous with 51.00 kcal/mol isomerization barrier. The geometrical isomerization is undoubtedly more feasible with a lower activation barrier. It is worth mentioning that the central issue in the numerical implementation of the MR-correlated method is to use a minimum model space to attain the correct result. The modest motto of this work is to use a model space that is the minimal for the qualitatively correct description of the isomerization pathways. However, to study the effect of the size of the CAS, IVOSSMRPT with IVO-CASCI(4,4) single point energy calculations using the optimized structures obtained by IVO-SSMRPT(2,2) have also been performed. The energy gaps and barrier heights are found to vary only within 1 kcal/mol indicating that the changing the model space alters the results negligibly. CAS(2,2) can be considered to be sufficient for proper description of the present isomerization process.

III.

CONCLUSION

The IVO-SSMRPT formulation allows strongly correlated molecules to be treated adequately with incorporation of both the dynamical and nondynamcial correlation energies. IVO-SSMRPT has been used here to resolve the two different isomerization pathways of molecules contatining two phosphorus atoms. To judge the accuracy of our method, barrier height and isomerization energy have been calculated and compared with various sophisticated ab initio methods. From the data, it is quite clear that addition of dynamical correlation (via PT) and non-dynamical correlation (via IVO-CASCI) not only predicts good absoulte energies but, also relative energies. Our method is also flexible to determine the vibrational frequencies as predicted from the comparison. The present work boosts our confidence that the IVOSSMRPT protocol with a low computational cost could be a promising boon for theoretical modelling of many isomerization pathways, associated with different level of electron correlation effects.

IV.

ACKNOWLEDGMENT

Author acknowledges Professors Sudip Chattopadhyay (IIEST, Shibpur) and Pinaki Chaudhuri (University of Calcutta) for their valuable suggestions. Author also acknowledges University Grant Commission of India for DSKPDF fellowship (Grant No- F.4-2/2006 (BSR)/CH/18-19/0076).

6 TABLE I: Relative Energies (kcal/mol) of cis-HPPH and planar PPH2 with respect to the trans-HPPH isomer obtained by different methods and basis set. Theory IVO-SSMRPT/cc-pVQZ MRMP2/cc-pVQZ CCSD(T)/cc-pVQZ CCSD(T)/aug-cc-pVQZ Mk-MRCCSD/cc-pVQZ MRCI/aug-cc-pVTZ

∆Ecis ∆Eplanar 3.85 24.89 3.63 30.03 3.38 25.28 3.38 25.28 3.32 – 3.34 –

7 TABLE II: Energy barriers(kcal/mol) of trans-cis isomerization and trans HPPH- planar PPH2 isomerization obtained via different level of theories. Theory TS linking TS linking trans HPPH and Planar PPH2 trans and cis HPPH IVO-SSMRPT/cc-pVQZ 51.00 39.96 CCSD(T)/cc-pVQZ 50.50 35.19 CCSD(T)/aug-cc-pVQZ 50.31 34.87 Mk-MRCCSD/cc-pVQZ – 35.19 MRCI/aug-cc-pVTZ – 35.05

8 Figure Captions: Figure 1: Optimized geometrical parameters of the ground 1 Ag state of trans HPPH. Here bond lengths are in angstroms (˚ A) and the angles are in degrees (◦ ). Figure 2: HOMO and LUMO of (a) Trans HPPH, (b) Cis HPPH and (c) Planar PPH2 . Figure 3: Optimized geometrical parameters of the ground 1 A1 state of cis HPPH. Here bond lengths are in angstroms (˚ A) and the angles are in degrees (◦ ). Figure 4: Optimized geometrical parameters of the planar 1 A1 state of PPH2 . Here bond lengths are in angstroms (˚ A) and the angles are in degrees (◦ ). Figure 5: Optimized geometrical parameters of the 1 A transition state between the trans HPPH and planar PPH2 isomers. Here bond lengths are in angstroms (˚ A) and the angles are in degrees (◦ ). Figure 6: HOMO and LUMO of (a) TS linking trans HPPH and planar PPH2 , (b) TS linking trans and cis HPPH. Figure 7: Optimized geometrical parameters of the 1 A transition state between the trans and cis HPPH isomers. Here bond lengths are in angstroms (˚ A) and the angles are in degrees (◦ ). Figure 8: Schematic pathway showing both geometrical and structural isomerism of HPPH and PPH2 molecules.

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