A BSSE-Corrected CASSCF/NEVPT2 Procedure. an Application to Weakly Bonded OH..Pi Heterodimer Complexes. Fanis G

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A BSSE-corrected CASSCF/NEVPT2 procedure. An application to weakly bonded OH..pi heterodimer complexes. Fanis G. Kalatzis, Ioannis N Demetropoulos

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Fanis G. Kalatzis, Ioannis N Demetropoulos. A BSSE-corrected CASSCF/NEVPT2 procedure. An application to weakly bonded OH..pi heterodimer complexes.. Molecular Physics, Taylor & Francis, 2008, 105 (17-18), pp.2335-2343. 10.1080/00268970701604689. hal-00513135

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A BSSE-corrected CASSCF/NEVPT2 procedure. An application to weakly bonded OH..pi heterodimer complexes.

Journal: Molecular Physics

Manuscript ID: TMPH20070210

Manuscript Type: Full Paper

Date Submitted by the 06Jul2007 Author:

Complete List of Authors: Kalatzis, Fanis; University of Ioannina, Chemistry Demetropoulos, Ioannis; University of Ioannina, Chemistry

CASSCF, NEVPT2, BSSE, Weakly bonded complexes, OH..ğ Keywords: intermolecular interactions

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1 2 3 4 5 6 7 8 9 10 A BSSE-corrected CASSCF/NEVPT2 procedure. An application to 11 12 weakly bonded OH..π heterodimer complexes. 13 14 15

16 For Peer Review Only 17 [a] [a,b] 18 Fanis G. Kalatzis and Ioannis N. Demetropoulos 19 20 [a]Department of Chemistry, University of Ioannina, GR-45110, Ioannina, Greece. 21 22 [b]Department of Information and Telecommunications Engineering, Section of Applied 23 24 25 Informatics, University of West Macedonia, Park Agiou Dimitriou, Kozani, GR 50100, 26 27 Greece. 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [b]Corresponding Author: 46 47 48 Phone Number: +302651098449 49 50 Fax Number: +302651098798 51 52 53 54 55 e-mail: Fanis G. Kalatzis ([email protected]), Ioannis N. Demetropoulos ([email protected]) 56 57 58 59 60

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1 2 3 4 5 6 Abstract 7 8 9 In this work a stable NEVPT2-based computational procedure was developed, capable to 10 11 study weakly bonded OH..π heterodimer complexes. The procedure was applied to the 12 13 evaluation of the weak OH..π intermolecular interaction energy of the ethene-water C2H4-H2O 14 15 complex, as a model case. The counterpoise method of Boys and Bernardi was used with the 16 For Peer Review Only 17 18 strongly contracted (SC) and partially contracted (PC) variants of the NEVPT2 method and 19 20 the energetic results were benchmarked against CCSD(T) calculations. In particular, for the 21 22 first time a computational methodology is proposed for the appropriate specification of the 23 24 25 active space in order to study weakly bonded OH..π heterodimer complexes, using the super- 26 27 molecular approach. The treatment of weakly bonded OH..π and van der Waals complexes 28 29 using CASSCF wavefunctions with second order perturbation theory seems to render 30 31 32 trustable and accurate results. Also, the present methodology suggests an efficient way for the 33 34 specification of the “ghost” basis functions in the multiconfigurational heterodimer case. The 35 36 Basis Set Superposition Error (BSSE) was eliminated in both CASSCF(2,2) and 37 38 39 CASSCF(10,7) selected case studies of the C2H4-H2O dimer. The behavior of BSSE lowering 40 41 as the basis set increases was verified. The computational procedure which was developed in 42 43 this paper can be easily adapted to the multiconfigurational NEVPT2 treatment of a large 44 45 variety of weakly bonded heterodimers. Finally, the procedure was successfully tested in the 46 47 48 benzene-water heterodimer. 49 50 51 Keywords: CASSCF, NEVPT2, BSSE, weakly bonded complexes, OH..π intermolecular 52 53 interactions. 54 55 56 57 58 59 60

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1 2 3 4 5 6 Introduction 7 8 9 An accurate exploitation of the weakly bonded intermolecular potential energy surface may 10 11 benefit by the inclusion of electron correlation through multiconfigurational wavefunctions. 12 13 Recalling the classification of Jeffrey[1], weak-bound hydrogen bonded complexes are 14 15 associated with energies below 4 Kcal/mol and the quantitative determination of these relative 16 For Peer Review Only 17 [2] 18 weak forces between molecules is experimentally and theoretically demanding. The 19 20 simplest case of a OH..π type intermolecular interaction is the ethene-water complex, which 21 22 can be sufficiently deployed to develop new computational procedures concerning the study 23 24 [3] 25 of weakly bonded heterodimer complexes. Previous experimental results using the 26 27 molecular beam electric resonance technique[3] and a thorough matrix isolation study[4] 28 29 exhibited a weak OH..π hydrogen bond perpendicular to the ethene plane. In both cases the 30 31 32 hydrogen atom is directed toward the center of the π-orbital of ethene. 33 34 The extension of the single reference self-consistent field wavefunction to the 35 36 multiconfigurational self-consistent field (MCSCF) wavefunction has been proved an 37 38 39 accurate estimate of the non-dynamical electron correlation. A well-applied implementation 40 [5] 41 of the MCSCF method is known as the complete active space (CASSCF) or full-optimized 42 43 reaction space (FORS)[6] method. The non-dynamical correlation energy may be defined as 44 45 the difference between full configuration interaction (CI) within the space of all valence 46 47 48 orbitals and a single determinant of molecular orbitals (Hartree–Fock theory). The exact 49 50 calculation of nondynamical correlation energy, involves computational complexity that 51 52 grows exponentially with molecular size. 53 54 55 An improved description of the multiconfigurational intermolecular potential energy surface 56 57 can be enhanced by the inclusion of dynamical electron correlation. The largest contribution 58 59 60

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1 2 3 4 5 6 of the dynamical electron correlation is recovered by the perturbation theory approach which 7 8 9 essentially preserves the size-consistency of the reference multiconfigurational 10 [7] 11 wavefunction. To the best of our knowledge, several methods have been developed in order 12 13 to extend single-reference perturbation theory to multireference perturbation theory, based on 14 15 a zeroth-order MCSCF wavefunction. The most popular variant is the CASPT2 (second-order 16 For Peer Review Only 17 [8,9] 18 perturbation theory based on a CASSCF reference wavefunction) method. 19 20 Recently, a new variant of multireference perturbation theory, based on a CASSCF zeroth- 21 22 order wave function, called n-electron valence state perturbation theory NEVPT2, has been 23 24 [10,11,12] 25 proposed. The main advantages of this formulation are the strict separability (size- 26 27 consistency) and the absence of intruder states[13], at least in principle. Three different variants 28 29 of this method have been formulated, the strongly contracted (SC), partially contracted (PC), 30 31 32 and uncontracted variants. The SC and PC variants to second order NEVPT2, utilizing 33 [14] [15] 34 Dyall’s Hamiltonian , have been implemented in the Dalton 2.0 program. The two 35 36 variants differ by the number of perturber functions employed in the perturbation summation. 37 38 39 The PC–NEVPT2 uses a richer function space and is in general more accurate than the SC– 40 41 NEVPT2. The results of SC–NEVPT2 and PC–NEVPT2 are anyway usually very close to 42 43 one another. 44 45 In this work, a stable NEVPT2-based computational procedure was developed, capable to 46 47 48 allow the efficient study of weakly bonded OH..π heterodimer complexes. Besides, this 49 50 procedure provides a methodology for the identification of the appropriate active space 51 52 required to evaluate the intermolecular interaction energy of OH..π heterodimers. Considering 53 54 55 the C2H4-H2O heterodimer as a model case, the procedure was applied to the investigation of 56 57 its intermolecular interaction energy using the SC and PC variants of the NEVPT2 method. 58 59 60

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1 2 3 4 5 6 Preliminary CI calculations using small basis sets were performed to determine the active 7 8 9 molecular orbitals (MOs) and visualization tools were involved. Actually two different active 10 11 spaces were used in this study with a variety of basis sets. The stable convergence of the 12 13 NEVPT2 method was achieved in all cases. The size-consistency of CASSCF and NEVPT2 14 15 methods efficiently allows such multireference calculations. 16 For Peer Review Only 17 18 Another feature of the developed procedure is related with the elimination of the basis set 19 20 superposition error (BSSE) at the NEVPT2 theory, using the super-molecular approach. The 21 22 most common procedure to remove the BSSE is the counterpoise (CP) method of Boys and 23 24 [16] 25 Bernardi. The CP method calculates each of the monomers’ energy on the basis set of the 26 27 other, using “ghost” atoms. The procedure eliminates the BSSE content of the interaction 28 29 energy according to the following formula: 30 31 BSSE 32 δ = Ε Α (ΑΒ) − Ε Α (Α) + ΕΒ (ΑΒ) − Ε Β (Β) (eq. 1) 33 34 where subscripts denote an individual molecule, while values in brackets refer to the basis set. 35 36 37 The total CP-corrected potential energy of the dimer is defined as: 38 39 CP BSSE Ε = E AB (AB) − δ (eq. 2) 40 41 42 while the CP-corrected interaction energy of the dimer is given by: 43 CP 44 ∆Ε = E AB (AB) − E A (AB) − EB (AB) (eq. 3) 45 46 The NEVPT2 computations of the monomers using “ghost” functions at the basis of the 47 48 49 dimer, proved to be feasible with the appropriate reordering of the MOs. The CP-corrected 50 51 intermolecular interaction energy at the NEVPT2 method was found to exhibit accurate 52 53 quantitative results at various basis sets. 54 55 56 The purpose of the methodology developed in this paper focuses to its applicability in larger 57 [17] 58 heterodimer molecular complexes. In a previous study of the weakly bonded phenol-N2 59 60

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1 2 3 4 5 6 dimer, there was difficulty in achieving convergence, using the CASPT2 method and “ghost” 7 8 [18] 9 functions calculations. Also, in a recent cytosine homodimer study successful 10 11 CASPT2(12,12) CP-corrected intermolecular interaction energies were retrieved. Generally, 12 13 there is difficulty in performing multireference CASSCF CP-corrected computations, 14 15 especially on heterodimers where the MOs cannot be easily distinguished. 16 For Peer Review Only 17 18 The details of the computational procedure, the discussion and the conclusions are presented 19 20 in the following sections respectively. 21 22 23 24 25 Development of the computational procedure 26 27 In this section the computational procedure is displayed and analyzed. The C2H4-H2O 28 29 heterodimer is used as an ideal case to simplify the development and the methodological 30 31 [19] [15] 32 approach. The GAMESS-US and Dalton 2.0 packages were used. All geometric 33 34 optimizations, preliminary CI and CASSCF calculations were performed with the GAMESS- 35 36 US package. The Dalton 2.0 package was used for the NEVPT2 calculations at the specific 37 38 39 points that were determined. 40 41 At a large intermolecular distances R, the C2H4-H2O heterodimer energetic CASSCF 42 43 computations should obey the following formula: 44 45 R 46 EAB [][]CASSCF(n,m) = EA CASSCF(n1 ,m1 ) + EB [CASSCF(n2 ,m 2 )] (eq. 4) where, 47 48 n = n1 + n2 and m = m1 + m2 , 49 50 51 meaning that a strictly separable method such as CASSCF and NEVPT2 should be applied to 52 53 the study. The subscripts A and B denote the C2H4 and H2O monomers respectively. The n, 54 55 n1, n2 and correspond to active electrons while m, m1, m2 correspond to the active orbitals of 56 57 58 59 60

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1 2 3 4 5 6 AB, A and B molecules respectively. The index R represents the relative intermolecular 7 8 9 distance, suggesting size-consistency of the dimer at large separation distances R. 10 11 Considering equation 4, the computational procedure that was developed to study weakly 12 13 bonded OH..π heterodimer complexes should retain the following steps: 14 15 a. Select an experimental or optimized geometry of the heterodimer. 16 For Peer Review Only 17 18 b. Perform preliminary CI/STO-3G (with double excitations) computations to identify 19 20 the π orbitals to be included in the active space. (Also, other orbital identification 21 22 schemes may be used). 23 24 25 c. Perform a single point RHF calculation at the geometry obtained in step a, using an 26 27 arbitrary basis set B. 28 29 d. Decide the core and active spaces using the optimized MOs of steps b and c. 30 31 32 e. Perform a CASSCF/B computation using as initial MOs the optimized from step c. 33 34 The MOs should be reordered in most cases, according to instructions provided in the 35 36 manuals of the ab-initio computational packages. 37 38 39 f. At a large intermolecular separation distance of the experimental or optimized 40 41 geometry perform a CASSCF/B computation using as initial MOs the optimized from 42 43 step c. 44 45 g. Repeat the steps c, d, e twice for each separate monomer in its own active space. 46 47 48 h. Check the size-consistency at the CASSCF level of theory, using results from steps f 49 50 and g. 51 52 i. If the size-consistency fails, the core and active orbitals of the monomers do not 53 54 55 coincide with those used in step e and the process should be repeated from step d. 56 57 58 59 60

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1 2 3 4 5 6 j. If the size-consistency verified, continue with the NEVPT2 computations. Also, the 7 8 9 optimized CASSCF/B MOs from step e can be used without reordering. 10 11 The active molecular orbitals, which was included in the active space of the C2H4-H2O case, 12 13 were determined by a preliminary CI calculation using the STO-3G basis set. The doubly- 14 15 excited determinants, using all the valence electrons of the dimer, were included at the CI 16 For Peer Review Only 17 18 expansion. The small STO-3G basis set offers the capability to construct a CI wavefunction 19 20 using all possible doubly-excited determinants of the 20 valence electrons of the dimer to the 21 22 18 active MOs. 23 24 25 The natural orbital occupation numbers (NOONs) of the preliminary CI calculation clearly 26 27 indicated two partially occupied molecular orbitals to be included in the active space. These 28 29 orbitals were characterized as the π and π* of the ethene monomer (figure 1b, 1c) according to 30 31 32 their shape. The active space of the heterodimer should be composed of these two active 33 34 MOs, denoting a CASSCF(2,2) computation. The examination of the NOONs suggested 35 36 another MO to be included in the active space. This MO belongs to water molecule (figure 37 38 39 1d). The selection of this MO led to a more extended CASSCF(10,7) computation of the 40 41 C2H4-H2O dimer. The choice of MOs for both active spaces was also validated by performing 42 43 CI calculations using the small 3-21G and 6-31+G* basis sets. 44 45 Once the active spaces were determined, the CASSCF computations were carried out with the 46 47 48 GAMESS-US package. The strict separability of equation 4 implies that the total CASSCF 49 50 electronic energy of the C2H4-H2O dimer should confirm the following equations: 51 52 R 53 EC2H4-H2O [CASSCF(2,2)] = EC2H4 [CASSCF(2,2)]+ EH2O [RHF] (eq. 5), 54 55 E R []CASSCF(10,7) = E [CASSCF(2,2)]+ E [CASSCF(8,5)] (eq. 6) 56 C2H4-H2O C2H4 H2O 57 58 59 60

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1 2 3 4 5 6 The CASSCF(2,2)/6-31+G* and CASSCF(10,7)/6-31+G* calculations of the dimer were 7 8 9 carried out at the MP2/6-31+G* optimized geometry (figure 1a), using the MOs from a 10 11 preliminary RHF/6-31+G* calculation. The identification of the core and active MOs was 12 13 verified by visual inspection of their shapes using the MacMolPlt program.[20] 14 15 The CASSCF(2,2)/6-31+G* computation was carried out using 12 core orbitals and the two π, 16 For Peer Review Only 17 18 π* active orbitals of ethene (figure 2). Actually, the ordering of the initial 69 RHF/6-31+G* 19 20 MOs requires the accommodation of the 16th π* ΜΟ inside the active space, by swapping the 21 22 14th and 16th MOs. The reordering procedure was necessitated by the requirement to 23 24 25 preserve the active orbitals’ shapes. In figure 2 the active space of the CASSCF(2,2)/6-31+G* 26 27 and the appropriate MO reordering is depicted. 28 29 The total electronic energy of the CASSCF(2,2)/6-31+G* calculation at the MP2/6-31+G* 30 31 0 32 optimized geometry (R=0Å) was found to be EC2H4-H2O [CASSCF(2,2)] = -154.08124466 a.u 33 34 To test the size-consistency using equation 2 the CASSCF(2,2)/6-31+G* calculation was 35 36 37 performed at the relative large (R=200Å) intermolecular distance, resulting 38 39 200 EC2H4-H2O []CASSCF (2,2) = -154.0796675 a.u. The subsequent CASSCF(2,2)/6-31+G* and 40 41 42 RHF/6-31+G* energetic calculations of the C2H4 and H2O monomers were found to be 43 44 EC2H4 []CASSCF(2,2) = -78.06313015 a.u. and EH2O [RHF] = -76.01653735 a.u. respectively. 45 46 47 These results successfully validate the size-consistency of the equation 5 by mixing the 48 49 multiconfigurational CASSCF and the single reference RHF method. 50 51 The 7 active MOs of the CASSCF(10,7) calculation were selected by inspecting and 52 53 54 reordering the initial RHF/6-31+G* MOs as depicted in figure 3. 55 56 The CASSCF(10,7) computation demands the reordering of 8 MOs to construct the 57 58 appropriate core and active spaces. According to equation 6 the core space of the dimer 59 60

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1 2 3 4 5 6 should contain one MO of water and seven MOs of ethene. The 4th and 7th MOs of the dimer 7 8 9 belong to water (figure 3) and should be swapped with the 9th and 11th MOs which belong to 10

11 ethene, respectively. The 30th MO of the water monomer (figure 1d) should be inserted in the 12 13 active space along with the 16th π* MO of ethene. The total energies of the CASSCF(10,7)/6- 14

15 0 16 31+G* calculationFor Peerare: E C2H4Review-H2O [CASSCF(10,7 )Only] = -154.10386090 a.u and 17 18 E 200 CASSCF(10,7) = -154.1022176 a.u.. The monomers’ computations concerning the 19 C2H4-H2O [] 20 21 right part of equation 6 are: EC2H4 [CASSCF(2,2)] = -78.0631301 a.u. and 22 23 24 EH2O []CASSCF(8,5) = -76.0390875 a.u. resulting the size-consistency of the (10,7) active 25 26 space. 27 28 29 As long as the size-consistency of both active spaces was verified, the CP-corrected 30 31 heterodimer intermolecular interaction energy was obtained by carrying out computations 32 33 with “ghost” functions. The calculations of the monomers at the dimer’s basis with “ghost” 34 35 36 functions require reordering of the core and active MOs of the dimer. Specifically, the core 37 38 and active space of the dimer should be reduced to that of each monomer. Adopting the 39 40 notation of equation 4, the core and active space of each monomer A and B can be denoted as: 41

42 1 2 k1 1 2 m1 1 2 k 2 1 2 m2 43 C AC A ⋅⋅⋅C A AA AA ⋅⋅⋅ AA and CBCB ⋅⋅⋅CB AB AB ⋅⋅⋅ AB . The subscripts denote each one of 44 45 the A and B monomers which are composed of k1, m1 and k2, m2 core and active orbitals 46 47 48 respectively. The CASSCF heterodimer computation should contain k=k1+k2 core and 49 1 2 k 1 2 m 50 m=m1+m2 active orbitals, expanded as: C ABC AB ⋅⋅⋅C AB AAB AAB ⋅⋅⋅ AAB . It is possible to map 51

52 k m 53 the CAB and AAB orbitals of the heterodimer back to each monomer by inspecting orbital 54 55 energies and shapes. This reverse mapping leads to the reduction of the dimer’s core and 56 57 active space to that of each monomer. The CASSCF computations with “ghost” functions 58 59 60

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1 2 3 4 5 6 were achieved by reordering the core and active MOs of the heterodimer, so as to construct 7 8 9 the reduced monomers’ orbital spaces in the whole basis of the complex. 10 11 The CASSCF(2,2)/6-31+G* calculation of the ethene monomer with “ghost” functions leads 12 13 to the swapping of MOs as depicted in figure 4. The core and active spaces were reordered so 14 15 as to contain only the MOs of ethene. 16 For Peer Review Only 17 18 The calculation of water monomer with “ghost” functions was performed at the RHF level of 19 20 theory. The results are: E GHOST [CASSCF(2,2)] = -78.06321495 a.u. and 21 C2H4 22 GHOST 23 EH2O []RHF = -76.01694641 a.u. 24 25 26 The computation of ethene with “ghost” functions at the CASSCF(10,7)/6-31+G* case was 27 28 obtained using the same reordering as shown in figure 4. The CASSCF(8,5)/6-31+G* 29 30 evaluation of the water monomer with “ghost” functions requires the reordering of MOs as 31 32 depicted in figure 5. Eight pairs of the dimer’s MOs were swapped in order to construct an 33 34 35 active space which is composed only of the water’s MOs. 36 37 The result of the water computation using “ghost” functions is: 38 39 GHOST 40 EH2O []CASSCF (8,5) = -76.03959923 a.u. 41 42 The computational treatment of the heterodimer was accomplished by the addition of electron 43 44 correlation using the NEVPT2 method. All the aforementioned CASSCF calculations on 45 46 47 GAMES-US were also validated using the Dalton 2.0 package. The CASSCF optimized MOs 48 49 from the GAMESS-US calculations were modeled as initial MOs to the Dalton package. By 50 51 applying the CASSCF optimized MOs as input to Dalton, the reordering was avoided except 52 53 54 for the calculations with ghost atoms. 55 56 The CASSCF and NEVPT2 results of both active spaces at the MP2/6-31+G* optimized 57 58 geometry are presented in table 1. The NEVPT2 and the MP2 methods was found to coincide 59 60

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1 2 3 4 5 6 at the computations of the water monomer with and without “ghost” functions using the 7 8 9 NEVPT2(2,2)/6-31+G* active space. The SC and PC variants of the NEVPT2 method 10 11 confirm the size consistency at both active spaces. The BSSE and the CP-corrected 12 13 intermolecular interaction energy of the C2H4-H2O heterodimer were evaluated using the 14 15 equations 1-3. The CP-corrected NEVPT2(2,2)/6-31+G* evaluation proposes a stable 16 For Peer Review Only 17 18 computational scheme of combining the multireference second-order NEVPT2 perturbation 19 20 theory with the single reference MP2 theory. 21 22 The study of the C H -H O dimer was expanded with NEVPT2 computations using larger 23 2 4 2 24 25 basis sets at their corresponding MP2 optimized geometries. The C2H4-H2O dimer was 26 27 optimized at the MP2/6-311++G**, MP2/aug-cc-pVDZ, MP2/ANO-1 and the 28 29 MRMP2(10,7)/6-311++G** levels of theory; the optimized geometries are notated as G1, G2, 30 31 [21,22] [23,24] 32 G3 and G4 respectively. The MRMP2 method of Hirao and Nakano was 33 34 implemented in the GAMESS-US package with numerical derivatives. The ANO-1 basis set 35 36 of Roos and coworkers[25] was applied using the contraction [3s2p] for the H atom and 37 38 39 [4s3p2d] for the C and O atoms. The 6-311++G** basis set is of triple-zeta quality for the 40 41 valence electrons and energetically performs better than the double-zeta quality aug-cc-pVDZ 42 43 basis set.[26] 44 45 46 47 48 Discussion 49 50 In former theoretical and experimental studies the binding energy of C2H4-H2O complex has 51 52 been determined between 1.50–2.0 kcal/mol.[4,27] According to table 1, the NEVPT2/6-31+G* 53 54 55 CP-corrected intermolecular interaction energies ∆ΕCP provide good agreement with the 56 57 literature. The richer space of the PC-NEVPT2 approach performs slightly better in the 58 59 60

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1 2 3 4 5 6 relative small 6-31+G* basis set. Both unperturbed CASSCF(2,2)/6-31+G* and 7 8 9 CASSCF(10,7)/6-31+G* computations failed to predict a good estimate of the CP-corrected 10 11 intermolecular interaction energy. The NEVPT2 results that were determined at the G1, G2, 12 13 G3 and G4 optimized geometries are presented in table 2. Single point NEVPT2 calculation 14 15 were carried out at the optimized G1, G2, G3 and G4 geometries using their corresponded 16 For Peer Review Only 17 18 basis set. At the larger basis sets, the initial MOs were accommodated using reordering 19 20 instructions to preserve the required orbital shapes for both (2,2) and (10,7) active spaces. The 21 22 procedure of MOs’ swapping was achieved as described in the previous section. 23 24 25 In all cases, the PC-NEVPT2 method performs more accurately and efficiently than the SC 26 27 approach. The evaluations that were accomplished at the (2,2) active space exhibit identical 28 29 accuracy of the SC and PC variants. Also, all the NEVPT2 ∆ΕCP results at the (2,2) active 30 31 [4,27] 32 space exhibit very good agreement with the former theoretical and experimental studies. 33 34 The behavior of BSSE lowering as the basis set increases was verified by comparing the SC 35 36 and PC variants of the NEVPT2/6-31+G* and NEVPT/6-311++G** results. Besides, all the 37 38 39 PC-NEVPT2 evaluations provide larger BSSE values than the SC approach. The equivalent 40 41 results of the aug-cc-pVDZ and ANO-1 basis sets arise from their matching double-zeta 42 43 quality. The much different G1 and G4 optimized geometries provided similar quantitative 44 45 values using the NEVPT2/6-311++G** method; this fact illustrates the very flat potential 46 47 [4] 48 around the equilibrium geometry. Moreover, the experimental notion of the very weak 49 50 C2H4-H2O intermolecular interaction was also validated by the NEVPT2/6-311++G** 51 52 calculations. 53 54 55 In order to verify the accuracy of the energetic results, CCSD(T) calculations were carried 56 57 out, accordingly to the optimized geometries and basis sets of table 2. In table 3 are illustrated 58 59 60

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1 2 3 4 5 6 the CCSD(T) results as a benchmark against the NEVPT2 calculations. The CP-corrected 7 8 9 intermolecular interaction energy exhibits actually the same CP-corrected values compared 10 11 with the corresponded values obtained by the NEVPT2 computations at the (2,2) active space. 12 13 [27] In a previous theoretical single-reference MP2 study of the C2H4-H2O complex somewhat 14 15 higher ∆Ε values were obtained, while the multi-reference NEVPT2 method used in this 16 CP For Peer Review Only 17 18 work, followed by CCSD(T) calculations, seems to register more accurately the weakly 19 20 bonded character of the dimer. 21 22 The computational procedure that was developed in this study was also tested by 23 24 [28] 25 computations performed to the benzene-water complex. In our previous work an 26 27 exploration of the benzene-water intermolecular potential energy surface was carried out. The 28 29 [29] equilibrium geometry demands the oxygen of the water monomer to be located on the C6 30 31 32 axis of the benzene while both hydrogens point toward the benzene plane. The NEVPT2 33 34 method was applied to the benzene-water dimer using an active space composed of 6 35 36 electrons, the 6 π and π* orbitals of benzene and 23 core orbitals. The initial MOs that were 37 38 39 employed for the NEVPT2(6,6)/6-31G** computation, were generated at the RHF/6-31G** 40 41 level. The results of the benzene-water computation are presented in table 4 and lie well 42 43 within the experimental values of 1.4–2.8 kcal/mol.[29,30,31] Between the ethene-water and 44 45 benzene-water cases, the only difference concerns the active orbital selection and active 46 47 48 orbital reordering. 49 50 51 52 Conclusions 53 54 55 This work proposes a stable CASSCF/NEVPT2 procedure which can be applied to study the 56 57 CP-corrected OH..π intermolecular interaction of heterodimer molecular complexes. All 58 59 60

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1 2 3 4 5 6 computations were performed using the GAMESS-US and Dalton 2.0 packages. The 7 8 9 calculated CASSCF results were validated between the two packages. It was found that the 10 11 transfer of the CASSCF optimized MOs from GAMESS-US to Dalton efficiently ensures the 12 13 convergence of the NEVPT2 method. 14 15 The well-established strict-separability of the NEVPT2 method, make it a suitable target to 16 For Peer Review Only 17 18 apply the Boys and Bernardi counterpoise scheme. The SC and PC variants of the NEVPT2 19 20 method were successfully applied to study the CP-corrected intermolecular interaction energy 21 22 of the weakly hydrogen bonded ethene-water complex. The calculations concerning the 23 24 25 ethene-water heterodimer were carried out using the small CASSCF(2,2) and the medium 26 27 CASSCF(10,7) wavefunctions with a variety of basis sets. The reliability of the NEVPT2 28 29 method was confirmed by all calculations and was also validated by benchmark computations 30 31 32 at the CCSD(T) level of theory. The two different active spaces that were used in this study, 33 34 exhibit the more accurate performance of the PC-NEVPT2 approach, as expected. The CP- 35 36 corrected ethene-water intermolecular interaction energy was remarkably improved by the 37 38 39 NEVPT2 method against the unperturbed CASSCF results. A very good agreement between 40 41 NEVPT2 calculated and experimental results was observed in this extremely weak 42 43 heterodimer intermolecular interaction case. Furthermore, the developed NEVPT2 44 45 computational procedure was successfully testified to the benzene-water complex ensuring 46 47 48 stability and convergence using the (6,6) active space. 49 50 The strict-separability of the NEVPT2 method seems to offer an efficient multireference 51 52 second order perturbation theory capable to treat heterodimer molecular complexes more 53 54 55 easily. Finally, it seems that the multiconfiguration character of the CP-corrected OH..π 56 57 intermolecular interactions can be attractively enhanced by the employment of the NEVPT2 58 59 60

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1 2 3 4 5 6 method; this claim may advance future developments on heterodimers’ studies which exhibit 7 8 9 degenerate states and the multiconfigurational treatment is necessitated. 10 11 12 13 Acknowledgements 14 15 The authors would like to acknowledge Prof. Kenneth Ruud for his insightful comments and 16 For Peer Review Only 17 18 suggestions concerning this work. Also, it is gratefully acknowledged the computer time 19 20 provided by the Computer Center and the Computational Materials Science Laboratory of the 21 22 University of Ioannina in Greece. 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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1 2 3 4 5 6 References 7 [1] G. A. Jeffrey, An Introduction to Hydrogen Bonding, Oxford University Press, Oxford, 8 9 10 (1997). 11 12 [2] A. J. Stone, The Theory of Intermolecular Forces, Clarendon, Oxford, (1996). 13 14 [3] K. I. Peterson, W. Klemperer. J Chem. Phys., 85, 725, (1986). 15 16 For Peer Review Only 17 [4] A. Engdahl and B. Nelander Chem. Phys. Lett., 113, 49, (1985). 18 19 [5] B.O. Roos, P.R. Taylor, P.E.M. Siegbahn, Chem. Phys., 48, 157, (1980). 20 21 [6] K. Ruedenberg, M.W. Schmidt, M.M. Gilbert, S.T. Elbert, Chem. Phys., 71, 41, (1982). 22 23 24 [7] A. Szabados, Z. Rolik, G. Toth, P. R. Surjan, J. Chem. Phys., 122, 114104, (2005). 25 26 [8] K. Andersson, P.-A. Malmqvist, B. O. Roos. J. Chem. Phys. 96, 1218, (1992). 27 28 [9] K. Andersson, P.-A . Malmqvist, B. O. Roos, A. J. Sadlej, K. Wolinski, J. Phys. Chem., 29 30 94, 5483, (1990). 31 32 33 [10] C. Angeli, R. Cimiraglia, S. Evangelisti, T. Leininger, J. P. Malrieu. J. Chem. Phys., 114, 34 35 10252, (2001). 36 37 [11] C. Angeli, R. Cimiraglia, J. P. Malrieu. Chem. Phys. Lett., 350, 297, (2001). 38 39 40 [12] C. Angeli, R. Cimiraglia, J. P. Malrieu. J. Chem. Phys., 117, 9138, (2002). 41 42 [13] H. A. Witek, Y.-K. Choe, J. P. Finley, K. Hirao J. Comp. Chem., 23, 957, (2002). 43 44 [14] K. G. Dyall. J. Chem. Phys., 102, 4909, (1995). 45 46 47 [15] Dalton, a molecular electronic structure program, Release 2.0 (2005), see 48 49 http://www.kjemi.uio.no/software/Dalton/Dalton.html. 50 51 [16] S. F. Boys, F. Bernardi, Mol. Phys., 19, 553, (1970). 52 53 [17] M. J. Watkins, K. Muller-Dethlefs, M. C. R. Cockett, Phys. Chem. Chem. Phys., , 5528, 54 2 55 56 (2000). 57 58 59 60

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1 2 3 4 5 6 [18] G. Olaso-González, D. Roca-Sanjuán, L. Serrano-Andrés, M. Merchán, J. Chem. Phys., 7 8 9 125, 231102, (2006). 10 11 [19] M.W. Schmidt, K.K. Baldridge, J.A. Boatz, S.T. Elbert, M.S. Gordon, J.H. Jensen, S. 12 13 Koseki, N. Matsunaga, K.A. Nguyen, S. Su, T.L. Windus, M. Dupuis, J.A. Montgomery, J. 14 15 Comput. Chem., 14, 1347, (1993). 16 For Peer Review Only 17 18 [20] Brett Bode’s MacMolPlt, available from 19 20 http://www.msg.ameslab.gov/GAMESS/GAMESS.html 21 22 [21] K. Hirao, Chem.Phys.Lett., 190, 374, (1992). 23 24 25 [22] K. Hirao, Chem.Phys.Lett., 196, 397, (1992). 26 27 [23] H. Nakano, Chem.Phys.Lett., 207, 372, (1993). 28 29 [24] H. Nakano, J.Chem.Phys., 99, 7983, (1993). 30 31 32 [25] P.O. Widmark, P.A. Malmqvist, B. Roos, Theor. Chim. Acta, 77, 291, (1990). 33 34 [26] K.B. Wiberg, J. Comp. Chem., 25, 1342, (2004). 35 36 [27] P. Tarakeshwar, H. S. Choi, S. J. Lee, J. Y. Lee, K. S. Kim, T. K. Ha, J. H. Jang, J. G. 37 38 39 Lee, H. Lee, J. Chem. Phys., 111, 5838, (1999). 40 41 [28] F. G. Kalatzis, D. G. Papageorgiou, I. N. Demetropoulos, Comp. Phys. Comm., 175, 359, 42 43 (2006). 44 45 [29] A. Courty, M. Mons, I. Dimicoli, F. Piuzzi, M.-P. Gaigeot, V. Brenner, P. Pujo, P. 46 47 48 Millie, J. Phys. Chem. A, 102, 6590, (1998). 49 50 [30] M. Raimondi, G. Calderoni, A. Famulari, L. Raimondi, F. Cozzi, J. Phys. Chem. A, 107, 51 52 772, (2003). 53 54 55 [31] S. Suzuki, P.G. Green, R. E. Bumgarner, S. Dasgupta, W.A. Goddard III, G.A. Blake, 56 57 Science, 257, 942, (1992). 58 59 60

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1 2 3 4 5 6 7 8 9 Table 1: The NEVPT2(10,7)/6-31+G* and NEVPT2(2,2)/6-31+G* energetic results of the 10 11 ethene-water computations at the MP2/6-31+G* optimized geometry. 12 13 Active Eth-Water Interaction δBSSE Theory Monomers Ghost Basis 14 Space Complex Kcal/mol Kcal/mol 15 (1) (2) (3) 16 AB For EAB(AB) Peer EA(A)+E BReview(B) EA(AB) EOnlyB(AB) ∆Ε ∆ΕCP 17 18 CASSCF -154.10386090 -154.10221763 -78.06321495 -76.03959923 -1.03 -0.66 -0.37 19 NEVPT2 20 10,7 -154.50146957 -154.49700326 -78.30623862 -76.19286636 -2.80 -1.48 -1.32 21 (SC) 22 NEVPT2 -154.50440783 -154.49966987 -78.30630703 -76.19541629 -2.97 -1.68 -1.29 23 (PC) 24 25 CASSCF -154.08124464 -154.07966753 -78.06321495 -76.01694641 -0.99 -0.68 -0.31 26 NEVPT2 27 2,2 -154.52204591 -154.51746019 -78.30623862 -76.21323151 -2.88 -1.61 -1.27 28 (SC) 29 NEVPT2 -154.52211224 -154.51753196 -78.30630703 -76.21323151 -2.87 -1.61 -1.26 30 (PC) 31 (1) (2) (3) 32 A=Ethene, B=Water, AB=Ethene-Water dimer. The uncorrected interaction energy. The CP-corrected 33 interaction energy. 34 35 36 37 Table 2: The uncorrected, CP-corrected and the BSSE of the C2H4-H2O NEVPT2 38 39 40 calculations at different optimized geometries and basis sets. All values are in Kcal/mol. 41 42 Geometry G1 G2 G3 G4 43 NEVPT2 6-311++G** aug-cc-pVDZ ANO-1 6-311++G** 44 Basis

45 (1) (2) (3) 46 CAS SC PC CAS SC PC CAS SC PC CAS SC PC 47 48 (10,7) Active Space 49 ∆Ε -0.49 -1.63 -1.85 -0.30 -2.45 -2.75 -0.09 -3.21 -3.53 -0.63 -1.71 -1.91 50 ∆ΕCP -0.32 -0.79 -0.99 -0.03 -1.01 -1.25 0.01 -1.04 -1.29 -0.48 -0.90 -1.08 51 BSSE -0.16 -0.84 -0.86 -0.27 -1.44 -1.49 -0.10 -2.17 -2.24 -0.15 -0.81 -0.83 52 (2,2) Active Space 53 54 ∆Ε -0.82 -2.56 -2.56 -0.71 -3.56 -3.55 -0.44 -4.38 -4.38 -0.93 -2.57 -2.57 55 ∆ΕCP -0.65 -1.65 -1.65 -0.45 -2.01 -2.01 -0.27 -1.97 -1.97 -0.77 -1.70 -1.70 56 BSSE -0.17 -0.91 -0.91 -0.27 -1.55 -1.54 -0.18 -2.41 -2.41 -0.15 -0.87 -0.87 57 (1)Unperturbed CASSCF calculation. (2)Strongly Contracted approach. (3)Partially Contracted Approach. 58 59 60

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1 2 3 4 5 6 7 Table 3: The uncorrected, CP-corrected and the BSSE of the C H -H O calculations at the 8 2 4 2 9 10 CCSD(T) level of theory. All values are in Kcal/mol. 11 12 Geometry G1 G2 G3 G4 13 CCSD(T) 6-311++G** aug-cc-pVDZ ANO-1 6-311++G** 14 Basis 15 ∆Ε -2.63 -3.67 -4.49 -2.64 16 For Peer Review Only ∆ΕCP -1.63 -2.01 -2.01 -1.68 17 BSSE -1.00 -1.65 -2.48 -0.96 18 19 20 21 22 Table 4: The NEVPT2(6,6)/6-31G** energetic results of the benzene-water complex at the 23 24 MP2/6-31G** optimized geometry (see reference 28). 25 26 Active Eth-Water Interaction δBSSE 27 Theory Monomers Ghost Basis 28 Space Complex Kcal/mol Kcal/mol 29 (1) (2) (3) AB EAB(AB) EA(A)+EB(B) EA(AB) EB(AB) ∆Ε ∆ΕCP 30 31 CASSCF -306.81307843 -306.80952443 -230.78764062 -76.02319278 -2.23 -1.41 -0.82 32 33 NEVPT2 6,6 -307.76826517 -307.76238099 -231.54143727 -76.22333726 -3.69 -2.19 -1.50 34 (SC) 35 NEVPT2 36 -307.76888266 -307.76298235 -231.54205706 -76.22333726 -3.70 -2.19 -1.51 (PC) 37 38 (1)A=Benzene, B=Water, AB=Benzene-Water dimer. (2)The uncorrected interaction energy. (3)The CP-corrected 39 interaction energy. 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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1 2 3 4 5 6 7 8 9 Figure 1 10 11 12 13 14 15 16 For Peer Review Only 17 18 19 20 21 22 23 24 25 26 27 (a) (b) 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 (c) (d) 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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1 2 3 4 5 6 Figure 2 7 8 9 10 11 12 13 14 15 16 For Peer Review Only 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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1 2 3 4 5 6 7 Figure 3 8 9 10 11 12 13 14 15 16 For Peer Review Only 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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1 2 3 4 5 6 7 Figure 4 8 9 10 11 12 13 14 15 16 For Peer Review Only 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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1 2 3 4 5 6 7 Figure 5 8 9 10 11 12 13 14 15 16 For Peer Review Only 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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1 2 3 4 5 6 Figure 1: (a) The MP2/6-31+G* optimized geometry of the ethene-water dimer. (b) The π 7 8 9 active orbital of ethene. (c) The π* active orbital of ethene. (d) The molecular orbital of water 10 11 that was included in the active space. 12 13 14 15 16 For Peer Review Only 17 18 Figure 2: The active space of the CASSCF(2,2)/6-31+G* computation along with the 19 20 appropriate MO reordering. 21 22 23 24 25 26 27 Figure 3: The active space of the CASSCF(10,7)/6-31+G* computation along with the 28 29 appropriate MO reordering. 30 31 32 33 34 35 36 Figure 4: The reordering of the MOs of the ethene monomer with “ghost” functions 37 38 39 concerning the CASSCF(2,2)/6-31+G* calculation. 40 41 42 43 44 45 Figure 5: The reordering of the MOs of the water monomer with “ghost” functions 46 47 48 concerning the CASSCF(8,5)/6-31+G* calculation. 49 50 51 52 53 54 55 56 57 58 59 60

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1 2 3 4 5 6 A BSSE-corrected CASSCF/NEVPT2 procedure. An application to 7 8 9 10 11 weakly bonded OH.. πππ heterodimer complexes. 12 13 FANIS G. KALATZIS† and IOANNIS N. DEMETROPOULOS *§ 14 For Peer Review Only 15 † Department of Chemistry, University of Ioannina, GR45110, Ioannina, Greece. 16 § Department of Information and Telecommunications Engineering, Section of Applied Informatics, 17 University of West Macedonia, Park Agiou Dimitriou, Kozani, GR50100, Greece. 18 19 *Corresponding author. Email: [email protected] 20 21 In this work a stable NEVPT2-based computational procedure was developed, capable to study weakly 22 bonded OH.. π heterodimer complexes. The procedure was applied to the evaluation of the weak OH.. π 23 24 intermolecular interaction energy of the ethene-water C 2H4-H2O complex, as a model case. The counterpoise 25 method of Boys and Bernardi was used with the strongly contracted (SC) and partially contracted (PC) 26 variants of the NEVPT2 method and the energetic results were benchmarked against CCSD(T) calculations. 27 In particular, for the first time a computational methodology is proposed for the appropriate specification of 28 the active space in order to study weakly bonded OH.. π heterodimer complexes, using the super-molecular 29 30 approach. The treatment of weakly bonded OH.. π and van der Waals complexes using CASSCF 31 wavefunctions with second order perturbation theory seems to render trustable and accurate results. Also, the 32 present methodology suggests an efficient way for the specification of the “ghost” basis functions in the 33 multiconfigurational heterodimer case. The Basis Set Superposition Error (BSSE) was eliminated in both 34 CASSCF(2,2) and CASSCF(10,7) selected case studies of the C 2H4-H2O dimer. The behavior of BSSE 35 lowering as the basis set increases was verified. The computational procedure which was developed in this 36 37 paper can be easily adapted to the multiconfigurational NEVPT2 treatment of a large variety of weakly 38 bonded heterodimers. Finally, the procedure was successfully tested in the benzene-water heterodimer. 39 40 Keywords: CASSCF; NEVPT2; BSSE; weakly bonded complexes; OH.. π intermolecular interactions. 41 42 1. Introduction 43 44 45 An accurate exploitation of the weakly bonded intermolecular potential energy surface may benefit by the 46 inclusion of electron correlation through multiconfigurational wavefunctions. Recalling the classification of 47 Jeffrey [1], weak-bound hydrogen bonded complexes are associated with energies below 4 Kcal/mol and the 48 quantitative determination of these relative weak forces between molecules is experimentally and theoretically 49 demanding [2]. The simplest case of a OH.. π type intermolecular interaction is the ethene-water complex, 50 51 which can be sufficiently deployed to develop new computational procedures concerning the study of weakly 52 bonded heterodimer complexes [3]. Previous experimental results using the molecular beam electric 53 resonance technique [3] and a thorough matrix isolation study [4] exhibited a weak OH.. π hydrogen bond 54 perpendicular to the ethene plane. In both cases the hydrogen atom is directed toward the center of the π- 55 orbital of ethene. 56 57 58 59 60 URL: http://mc.manuscriptcentral.com/tandf/tmph Molecular Physics Page 28 of 45

1 2 3 The extension of the single reference self-consistent field wavefunction to the multiconfigurational self- 4 5 consistent field (MCSCF) wavefunction has been proved an accurate estimate of the non-dynamical electron 6 correlation. A well-applied implementation of the MCSCF method is known as the complete active space 7 (CASSCF) [5] or full-optimized reaction space (FORS) [6] method. The non-dynamical correlation energy 8 may be defined as the difference between full configuration interaction (CI) within the space of all valence 9 orbitals and a single determinant of molecular orbitals (Hartree–Fock theory). The exact calculation of 10 11 nondynamical correlation energy, involves computational complexity that grows exponentially with molecular 12 size. 13 An improved description of the multiconfigurational intermolecular potential energy surface can be enhanced 14 by the inclusion ofFor dynamical Peer electron correlation. Review The largest cOnlyontribution of the dynamical electron 15 correlation is recovered by the perturbation theory approach which essentially preserves the size-consistency 16 of the reference multiconfigurational wavefunction [7]. To the best of our knowledge, several methods have 17 18 been developed in order to extend single-reference perturbation theory to multireference perturbation theory, 19 based on a zeroth-order MCSCF wavefunction. The most popular variant is the CASPT2 (second-order 20 perturbation theory based on a CASSCF reference wavefunction) method [8,9]. 21 Recently, a new variant of multireference perturbation theory, based on a CASSCF zeroth-order wave 22 function, called n-electron valence state perturbation theory NEVPT2, has been proposed [10,11,12]. The 23 24 main advantages of this formulation are the strict separability (size-consistency) and the absence of intruder 25 states [13], at least in principle. Three different variants of this method have been formulated, the strongly 26 contracted (SC), partially contracted (PC), and uncontracted variants. The SC and PC variants to second order 27 NEVPT2, utilizing Dyall’s Hamiltonian [14], have been implemented in the Dalton 2.0 program [15]. The two 28 variants differ by the number of perturber functions employed in the perturbation summation. The PC– 29 NEVPT2 uses a richer function space and is in general more accurate than the SC–NEVPT2. The results of 30 31 SC–NEVPT2 and PC–NEVPT2 are anyway usually very close to one another. 32 In this work, a stable NEVPT2-based computational procedure was developed, capable to allow the efficient 33 study of weakly bonded OH.. π heterodimer complexes. Besides, this procedure provides a methodology for 34 the identification of the appropriate active space required to evaluate the intermolecular interaction energy of 35 π 36 OH.. heterodimers. Considering the C 2H4-H2O heterodimer as a model case, the procedure was applied to 37 the investigation of its intermolecular interaction energy using the SC and PC variants of the NEVPT2 38 method. Preliminary CI calculations using small basis sets were performed to determine the active molecular 39 orbitals (MOs) and visualization tools were involved. Actually two different active spaces were used in this 40 study with a variety of basis sets. The stable convergence of the NEVPT2 method was achieved in all cases. 41 The size-consistency of CASSCF and NEVPT2 methods efficiently allows such multireference calculations. 42 43 Another feature of the developed procedure is related with the elimination of the basis set superposition error 44 (BSSE) at the NEVPT2 theory, using the super-molecular approach. The most common procedure to remove 45 the BSSE is the counterpoise (CP) method of Boys and Bernardi [16]. The CP method calculates each of the 46 monomers’ energy on the basis set of the other, using “ghost” atoms. The procedure eliminates the BSSE 47 content of the interaction energy according to the following formula: 48 BSSE 49 δ = Ε Α (ΑΒ ) − Ε Α (Α) + ΕΒ (ΑΒ ) − ΕΒ (Β) (1) 50 where subscripts denote an individual molecule, while values in brackets refer to the basis set. The total CP- 51 corrected potential energy of the dimer is defined as: 52 CP BSSE 53 Ε = E AB (AB ) − δ (2) 54 while the CP-corrected interaction energy of the dimer is given by: 55 Ε CP = E (AB ) − E (AB ) − E (AB ) (3) 56 AB A B 57 58 59 60 URL: http://mc.manuscriptcentral.com/tandf/tmph Page 29 of 45 Molecular Physics

1 2 3 The NEVPT2 computations of the monomers using “ghost” functions at the basis of the dimer, proved to be 4 5 feasible with the appropriate reordering of the MOs. The CP-corrected intermolecular interaction energy at the 6 NEVPT2 method was found to exhibit accurate quantitative results at various basis sets. 7 The purpose of the methodology developed in this paper focuses to its applicability in larger heterodimer 8 molecular complexes. In a previous study [17] of the weakly bonded phenol-N2 dimer, there was difficulty in 9 achieving convergence, using the CASPT2 method and “ghost” functions calculations. Also, in a recent 10 11 cytosine homodimer study [18] successful CASPT2(12,12) CP-corrected intermolecular interaction energies 12 were retrieved. Generally, there is difficulty in performing multireference CASSCF CP-corrected 13 computations, especially on heterodimers where the MOs cannot be easily distinguished. 14 The details of the computationalFor Peer procedure, the Review discussion and the conclusi Onlyons are presented in the following 15 sections respectively. 16 17 2. Development of the computational procedure 18 19 20 In this section the computational procedure is displayed and analyzed. The C 2H4-H2O heterodimer is used as 21 an ideal case to simplify the development and the methodological approach. The GAMESS-US [19] and 22 Dalton 2.0 [15] packages were used. All geometric optimizations, preliminary CI and CASSCF calculations 23 were performed with the GAMESS-US package. The Dalton 2.0 package was used for the NEVPT2 24 calculations at the specific points that were determined. 25 26 At a large intermolecular distances R, the C 2H4-H2O heterodimer energetic CASSCF computations should 27 obey the following formula: 28 R EAB [CASSCF (n, m)] = EA [CASSCF (n1 ,m1 )]+ EB [CASSCF (n2 ,m 2 )] (4) where, 29 30 n = n1 + n2 and m = m1 + m2 , 31 meaning that a strictly separable method such as CASSCF and NEVPT2 should be applied to the study. The 32 subscripts A and B denote the C 2H4 and H 2O monomers respectively. The n, n 1, n 2 and correspond to active 33 electrons while m, m 1, m 2 correspond to the active orbitals of AB, A and B molecules respectively. The index 34 35 R represents the relative intermolecular distance, suggesting size-consistency of the dimer at large separation 36 distances R. 37 Considering equation 4, the computational procedure that was developed to study weakly bonded OH.. π 38 heterodimer complexes should retain the following steps: 39 a. Select an experimental or optimized geometry of the heterodimer. 40 41 b. Perform preliminary CI/STO-3G (with double excitations) computations to identify the π orbitals to be 42 included in the active space. (Also, other orbital identification schemes may be used). 43 c. Perform a single point RHF calculation at the geometry obtained in step a, using an arbitrary basis set B. 44 d. Decide the core and active spaces using the optimized MOs of steps b and c. 45 e. Perform a CASSCF/B computation using as initial MOs the optimized from step c. The MOs should be 46 reordered in most cases, according to instructions provided in the manuals of the ab-initio computational 47 48 packages. 49 f. At a large intermolecular separation distance of the experimental or optimized geometry perform a 50 CASSCF/B computation using as initial MOs the optimized from step c. 51 g. Repeat the steps c, d, e twice for each separate monomer in its own active space. 52 h. Check the size-consistency at the CASSCF level of theory, using results from steps f and g. 53 54 i. If the size-consistency fails, the core and active orbitals of the monomers do not coincide with those used in 55 step e and the process should be repeated from step d. 56 j. If the size-consistency verified, continue with the NEVPT2 computations. Also, the optimized CASSCF/B 57 MOs from step e can be used without reordering. 58 59 60 URL: http://mc.manuscriptcentral.com/tandf/tmph Molecular Physics Page 30 of 45

1 2 3 The active molecular orbitals, which was included in the active space of the C H -H O case, were determined 4 2 4 2 5 by a preliminary CI calculation using the STO-3G basis set. The doubly-excited determinants, using all the 6 valence electrons of the dimer, were included at the CI expansion. The small STO-3G basis set offers the 7 capability to construct a CI wavefunction using all possible doubly-excited determinants of the 20 valence 8 electrons of the dimer to the 18 active MOs. 9 10 Figure 1: (a) The MP2/6-31+G* optimized geometry of the ethene-water dimer. (b) The π active orbital of ethene. (c) The π* active 11 orbital of ethene. (d) The molecular orbital of water that was included in the active space. 12 13 14 The natural orbital For occupation Peer numbers (NOONs) Review of the preliminary Only CI calculation clearly indicated two 15 partially occupied molecular orbitals to be included in the active space. These orbitals were characterized as 16 the π and π* of the ethene monomer (figure 1b, 1c) according to their shape. The active space of the 17 heterodimer should be composed of these two active MOs, denoting a CASSCF(2,2) computation. The 18 examination of the NOONs suggested another MO to be included in the active space. This MO belongs to 19 20 water molecule (figure 1d). The selection of this MO led to a more extended CASSCF(10,7) computation of 21 the C 2H4-H2O dimer. The choice of MOs for both active spaces was also validated by performing CI 22 calculations using the small 3-21G and 6-31+G* basis sets. 23 Once the active spaces were determined, the CASSCF computations were carried out with the GAMESS-US 24 package. The strict separability of equation 4 implies that the total CASSCF electronic energy of the C H - 25 2 4 26 H2O dimer should confirm the following equations: R 27 EC2H4 -H2O [CASSCF )2,2( ] = EC2H4 [CASSCF )2,2( ]+ EH2O [RHF ] (5), 28 R 29 EC2H4 -H2O [CASSCF 10( )7, ] = EC2H4 [CASSCF )2,2( ]+ EH2O [CASSCF )5,8( ] (6) 30 The CASSCF(2,2)/6-31+G* and CASSCF(10,7)/6-31+G* calculations of the dimer were carried out at the 31 MP2/6-31+G* optimized geometry (figure 1a), using the MOs from a preliminary RHF/6-31+G* calculation. 32 The identification of the core and active MOs was verified by visual inspection of their shapes using the 33 34 MacMolPlt program [20]. 35 The CASSCF(2,2)/6-31+G* computation was carried out using 12 core orbitals and the two π, π* active 36 orbitals of ethene (figure 2). Actually, the ordering of the initial 69 RHF/6-31+G* MOs requires the 37 accommodation of the 16th π* ΜΟ inside the active space, by swapping the 14th and 16th MOs. The 38 reordering procedure was necessitated by the requirement to preserve the active orbitals’ shapes. In figure 2 39 40 the active space of the CASSCF(2,2)/6-31+G* and the appropriate MO reordering is depicted. 41 42 Figure 2: The active space of the CASSCF(2,2)/6-31+G* computation along with the appropriate MO reordering. 43 44 The total electronic energy of the CASSCF(2,2)/6-31+G* calculation at the MP2/6-31+G* optimized 45 0 46 geometry (R=0 Å) was found to be EC2H4 -H2O [CASSCF )2,2( ] = -154.08124 466 a.u 47 To test the size-consistency using equation 2 the CASSCF(2,2)/6-31+G* calculation was performed at the 48 relative large (R=200Å) intermolecular distance, resulting E 200 [CASSCF )2,2( ] = -154.07966 75 a.u. The 49 C2H4 -H2O 50 subsequent CASSCF(2,2)/6-31+G* and RHF/6-31+G* energetic calculations of the C 2H4 and H 2O monomers 51 were found to be EC2H4 [CASSCF )2,2( ] = -78.063130 15 a.u. and EH2O [RHF ] = -76.016537 35 a.u. respectively. 52 53 These results successfully validate the size-consistency of the equation 5 by mixing the multiconfigurational 54 CASSCF and the single reference RHF method. 55 The 7 active MOs of the CASSCF(10,7) calculation were selected by inspecting and reordering the initial 56 RHF/6-31+G* MOs as depicted in figure 3. 57 58 59 60 URL: http://mc.manuscriptcentral.com/tandf/tmph Page 31 of 45 Molecular Physics

1 2 3 The CASSCF(10,7) computation demands the reordering of 8 MOs to construct the appropriate core and 4 5 active spaces. According to equation 6 the core space of the dimer should contain one MO of water and seven 6 MOs of ethene. The 4th and 7th MOs of the dimer belong to water (figure 3) and should be swapped with the 7 9th and 11th MOs which belong to ethene, respectively. The 30th MO of the water monomer (figure 1d) 8 should be inserted in the active space along with the 16th π* MO of ethene. The total energies of the 9 0 10 CASSCF(10,7)/6-31+G* calculation are: EC2H4 -H2O [CASSCF 10( )7, ] = -154.10386 090 a.u and 11 E 200 [CASSCF 10( )7, ] = -154.10221 76 a.u. . The monomers’ computations concerning the right part of 12 C2H4 -H2O 13 equation 6 are: EC2H4 [CASSCF )2,2( ] = -78.063130 1 a.u. and EH2O [CASSCF )5,8( ] = -76.039087 5 a.u. resulting 14 the size-consistencyFor of the (10,7) Peer active space. Review Only 15 16 Figure 3: The active space of the CASSCF(10,7)/6-31+G* computation along with the appropriate MO reordering. 17 18 19 As long as the size-consistency of both active spaces was verified, the CP-corrected heterodimer 20 intermolecular interaction energy was obtained by carrying out computations with “ghost” functions. The 21 calculations of the monomers at the dimer’s basis with “ghost” functions require reordering of the core and 22 active MOs of the dimer. Specifically, the core and active space of the dimer should be reduced to that of each 23 24 monomer. Adopting the notation of equation 4, the core and active space of each monomer A and B can be 1 2 k1 1 2 m1 1 2 k 2 1 2 m2 25 denoted as: C AC A ⋅⋅⋅ C A AA AA ⋅⋅⋅ AA and CBCB ⋅⋅⋅ CB AB AB ⋅⋅⋅ AB . The subscripts denote each one of the A 26 and B monomers which are composed of k1, m1 and k2, m2 core and active orbitals respectively. The 27 CASSCF heterodimer computation should contain k=k1+k2 core and m=m1+m2 active orbitals, expanded as: 28 1 2 k 1 2 m k m 29 C AB C AB ⋅⋅⋅ C AB AAB AAB ⋅⋅⋅ AAB . It is possible to map the CAB and AAB orbitals of the heterodimer back to each 30 monomer by inspecting orbital energies and shapes. This reverse mapping leads to the reduction of the 31 dimer’s core and active space to that of each monomer. The CASSCF computations with “ghost” functions 32 33 were achieved by reordering the core and active MOs of the heterodimer, so as to construct the reduced 34 monomers’ orbital spaces in the whole basis of the complex. 35 The CASSCF(2,2)/6-31+G* calculation of the ethene monomer with “ghost” functions leads to the swapping 36 of MOs as depicted in figure 4. The core and active spaces were reordered so as to contain only the MOs of 37 ethene. 38 39 Figure 4: The reordering of the MOs of the ethene monomer with “ghost” functions concerning the CASSCF(2,2)/6-31+G* 40 calculation. 41 42 43 The calculation of water monomer with “ghost” functions was performed at the RHF level of theory. The 44 GHOST GHOST results are: EC2H4 [CASSCF )2,2( ] = -78.063214 95 a.u. and EH2O [RHF ] = -76.016946 41 a.u. 45 46 The computation of ethene with “ghost” functions at the CASSCF(10,7)/6-31+G* case was obtained using the 47 same reordering as shown in figure 4. The CASSCF(8,5)/6-31+G* evaluation of the water monomer with 48 “ghost” functions requires the reordering of MOs as depicted in figure 5. Eight pairs of the dimer’s MOs were 49 swapped in order to construct an active space which is composed only of the water’s MOs. 50 51 Figure 5: The reordering of the MOs of the water monomer with “ghost” functions concerning the CASSCF(8,5)/6-31+G* 52 calculation. 53 54 GHOST 55 The result of the water computation using “ghost” functions is: EH2O [CASSCF )5,8( ] = -76.039599 23 a.u. 56 The computational treatment of the heterodimer was accomplished by the addition of electron correlation 57 58 using the NEVPT2 method. All the aforementioned CASSCF calculations on GAMES-US were also validated 59 60 URL: http://mc.manuscriptcentral.com/tandf/tmph Molecular Physics Page 32 of 45

1 2 3 using the Dalton 2.0 package. The CASSCF optimized MOs from the GAMESS-US calculations were 4 5 modeled as initial MOs to the Dalton package. By applying the CASSCF optimized MOs as input to Dalton, 6 the reordering was avoided except for the calculations with ghost atoms. 7 The CASSCF and NEVPT2 results of both active spaces at the MP2/6-31+G* optimized geometry are 8 presented in table 1. The NEVPT2 and the MP2 methods was found to coincide at the computations of the 9 water monomer with and without “ghost” functions using the NEVPT2(2,2)/6-31+G* active space. The SC 10 11 and PC variants of the NEVPT2 method confirm the size consistency at both active spaces. The BSSE and the 12 CP-corrected intermolecular interaction energy of the C 2H4-H2O heterodimer were evaluated using the 13 equations 1-3. The CP-corrected NEVPT2(2,2)/6-31+G* evaluation proposes a stable computational scheme 14 of combining the multireferenceFor Peer second-order Review NEVPT2 perturbation Only theory with the single reference MP2 15 theory. 16 The study of the C H -H O dimer was expanded with NEVPT2 computations using larger basis sets at their 17 2 4 2 18 corresponding MP2 optimized geometries. The C 2H4-H2O dimer was optimized at the MP2/6-311++G**, 19 MP2/aug-cc-pVDZ, MP2/ANO-1 and the MRMP2(10,7)/6-311++G** levels of theory; the optimized 20 geometries are notated as G1, G2, G3 and G4 respectively. The MRMP2 method of Hirao [21,22] and Nakano 21 [23,24] was implemented in the GAMESS-US package with numerical derivatives. The ANO-1 basis set of 22 Roos and coworkers [25] was applied using the contraction [3s2p] for the H atom and [4s3p2d] for the C and 23 24 O atoms. The 6-311++G** basis set is of triple-zeta quality for the valence electrons and energetically 25 performs better than the double-zeta quality aug-cc-pVDZ basis set [26]. 26 27 Table 1 : The NEVPT2(10,7)/6-31+G* and NEVPT2(2,2)/6-31+G* energetic results of the ethene-water 28 computations at the MP2/6-31+G* optimized geometry. 29 Active Eth-Water Interaction δBSSE Theory Monomers Ghost Basis 30 Space Complex Kcal/mol Kcal/mol 31 (1) Ε (2) Ε (3) 32 AB EAB (AB) EA(A)+E B(B) EA(AB) EB(AB) CP 33 34 CASSCF -154.10386090 -154.10221763 -78.06321495 -76.03959923 -1.03 -0.66 -0.37 35 NEVPT2 36 10,7 -154.50146957 -154.49700326 -78.30623862 -76.19286636 -2.80 -1.48 -1.32 37 (SC) 38 NEVPT2 -154.50440783 -154.49966987 -78.30630703 -76.19541629 -2.97 -1.68 -1.29 39 (PC) 40 41 CASSCF -154.08124464 -154.07966753 -78.06321495 -76.01694641 -0.99 -0.68 -0.31 42 43 NEVPT2 2,2 -154.52204591 -154.51746019 -78.30623862 -76.21323151 -2.88 -1.61 -1.27 44 (SC) 45 NEVPT2 46 -154.52211224 -154.51753196 -78.30630703 -76.21323151 -2.87 -1.61 -1.26 (PC) 47 48 (1) A=Ethene, B=Water, AB=Ethene-Water dimer. (2) The uncorrected interaction energy. (3) The CP-corrected interaction energy. 49 50 3. Discussion 51 52 In former theoretical and experimental studies the binding energy of C H -H O complex has been determined 53 2 4 2 54 between 1.50–2.0 kcal/mol [4,27]. According to table 1, the NEVPT2/6-31+G* CP-corrected intermolecular 55 interaction energies Ε CP provide good agreement with the literature. The richer space of the PC-NEVPT2 56 approach performs slightly better in the relative small 6-31+G* basis set. Both unperturbed CASSCF(2,2)/6- 57 31+G* and CASSCF(10,7)/6-31+G* computations failed to predict a good estimate of the CP-corrected 58 59 60 URL: http://mc.manuscriptcentral.com/tandf/tmph Page 33 of 45 Molecular Physics

1 2 3 intermolecular interaction energy. The NEVPT2 results that were determined at the G1, G2, G3 and G4 4 5 optimized geometries are presented in table 2. Single point NEVPT2 calculation were carried out at the 6 optimized G1, G2, G3 and G4 geometries using their corresponded basis set. At the larger basis sets, the 7 initial MOs were accommodated using reordering instructions to preserve the required orbital shapes for both 8 (2,2) and (10,7) active spaces. The procedure of MOs’ swapping was achieved as described in the previous 9 section. 10 11 12 Table 2 : The uncorrected, CP-corrected and the BSSE of the C 2H4-H2O NEVPT2 calculations at different 13 optimized geometries and basis sets. All values are in Kcal/mol. 14 Geometry G1 G2 G3 G4 NEVPT2 For Peer Review Only 15 6-311++G** aug-cc-pVDZ ANO-1 6-311++G** 16 Basis 17 18 CAS (1) SC (2) PC (3) CAS SC PC CAS SC PC CAS SC PC 19 20 (10,7) Active Space 21 Ε -0.49 -1.63 -1.85 -0.30 -2.45 -2.75 -0.09 -3.21 -3.53 -0.63 -1.71 -1.91 22 Ε CP -0.32 -0.79 -0.99 -0.03 -1.01 -1.25 0.01 -1.04 -1.29 -0.48 -0.90 -1.08 23 BSSE -0.16 -0.84 -0.86 -0.27 -1.44 -1.49 -0.10 -2.17 -2.24 -0.15 -0.81 -0.83 24 25 (2,2) Active Space 26 Ε -0.82 -2.56 -2.56 -0.71 -3.56 -3.55 -0.44 -4.38 -4.38 -0.93 -2.57 -2.57 27 Ε CP -0.65 -1.65 -1.65 -0.45 -2.01 -2.01 -0.27 -1.97 -1.97 -0.77 -1.70 -1.70 28 BSSE -0.17 -0.91 -0.91 -0.27 -1.55 -1.54 -0.18 -2.41 -2.41 -0.15 -0.87 -0.87 29 (1) Unperturbed CASSCF calculation. (2) Strongly Contracted approach. (3) Partially Contracted approach. 30 31 32 In all cases, the PC-NEVPT2 method performs more accurately and efficiently than the SC approach. The 33 evaluations that were accomplished at the (2,2) active space exhibit identical accuracy of the SC and PC 34 variants. Also, all the NEVPT2 Ε CP results at the (2,2) active space exhibit very good agreement with the 35 former theoretical and experimental studies [4,27]. 36 The behaviour of BSSE lowering as the basis set increases was verified by comparing the SC and PC variants 37 38 of the NEVPT2/6-31+G* and NEVPT/6-311++G** results. Besides, all the PC-NEVPT2 evaluations provide 39 larger BSSE values than the SC approach. The equivalent results of the aug-cc-pVDZ and ANO-1 basis sets 40 arise from their matching double-zeta quality. The much different G1 and G4 optimized geometries provided 41 similar quantitative values using the NEVPT2/6-311++G** method; this fact illustrates the very flat potential 42 around the equilibrium geometry [4]. Moreover, the experimental notion of the very weak C H -H O 43 2 4 2 44 intermolecular interaction was also validated by the NEVPT2/6-311++G** calculations. 45 In order to verify the accuracy of the energetic results, CCSD(T) calculations were carried out, accordingly to 46 the optimized geometries and basis sets of table 2. In table 3 are illustrated the CCSD(T) results as a 47 benchmark against the NEVPT2 calculations. The CP-corrected intermolecular interaction energy exhibits 48 actually the same CP-corrected values compared with the corresponded values obtained by the NEVPT2 49 computations at the (2,2) active space. 50 51 52 Table 3 : The uncorrected, CP-corrected and the BSSE of the C 2H4-H2O calculations at the CCSD(T) 53 level of theory. All values are in Kcal/mol. 54 Geometry G1 G2 G3 G4 55 CCSD(T) 6-311++G** aug-cc-pVDZ ANO-1 6-311++G** 56 Basis 57 Ε -2.63 -3.67 -4.49 -2.64 58 59 60 URL: http://mc.manuscriptcentral.com/tandf/tmph Molecular Physics Page 34 of 45

1 2 3 Ε CP -1.63 -2.01 -2.01 -1.68 4 BSSE -1.00 -1.65 -2.48 -0.96 5 6 7 In a previous theoretical single-reference MP2 study [27] of the C 2H4-H2O complex somewhat higher Ε CP 8 values were obtained, while the multi-reference NEVPT2 method used in this work, followed by CCSD(T) 9 calculations, seems to register more accurately the weakly bonded character of the dimer. 10 11 The computational procedure that was developed in this study was also tested by computations performed to 12 the benzene-water complex. In our previous work [28] an exploration of the benzene-water intermolecular 13 potential energy surface was carried out. The equilibrium geometry [29] demands the oxygen of the water 14 monomer to be locatedFor on the C Peer6 axis of the benzeneReview while both hydrogens Only point toward the benzene plane. 15 The NEVPT2 method was applied to the benzene-water dimer using an active space composed of 6 electrons, 16 π π 17 the 6 and * orbitals of benzene and 23 core orbitals. The initial MOs that were employed for the 18 NEVPT2(6,6)/6-31G** computation, were generated at the RHF/6-31G** level. The results of the benzene- 19 water computation are presented in table 4 and lie well within the experimental values of 1.4–2.8 kcal /mol 20 [29,30,31]. Between the ethene-water and benzene-water cases, the only difference concerns the active orbital 21 selection and active orbital reordering. 22 23 Table 4 : The NEVPT2(6,6)/6-31G** energetic results of the benzene-water complex at the MP2/6-31G** 24 optimized geometry (see [28]). 25 Active Eth-Water Interaction δBSSE 26 Theory Monomers Ghost Basis 27 Space Complex Kcal/mol Kcal/mol 28 (1) (2) (3) AB EAB (AB) EA(A)+E B(B) EA(AB) EB(AB) Ε Ε CP 29 30 31 CASSCF -306.81307843 -306.80952443 -230.78764062 -76.02319278 -2.23 -1.41 -0.82 32 NEVPT2 6,6 -307.76826517 -307.76238099 -231.54143727 -76.22333726 -3.69 -2.19 -1.50 33 (SC) 34 NEVPT2 35 -307.76888266 -307.76298235 -231.54205706 -76.22333726 -3.70 -2.19 -1.51 36 (PC) 37 (1) A=Benzene, B=Water, AB=Benzene-Water dimer. (2) The uncorrected interaction energy. (3) The CP-corrected interaction energy. 38 39 4. Conclusions 40 41 42 This work proposes a stable CASSCF/NEVPT2 procedure which can be applied to study the CP-corrected 43 OH.. π intermolecular interaction of heterodimer molecular complexes. All computations were performed 44 using the GAMESS-US and Dalton 2.0 packages. The calculated CASSCF results were validated between the 45 two packages. It was found that the transfer of the CASSCF optimized MOs from GAMESS-US to Dalton 46 efficiently ensures the convergence of the NEVPT2 method. 47 48 The well-established strict-separability of the NEVPT2 method, make it a suitable target to apply the Boys 49 and Bernardi counterpoise scheme. The SC and PC variants of the NEVPT2 method were successfully applied 50 to study the CP-corrected intermolecular interaction energy of the weakly hydrogen bonded ethene-water 51 complex. The calculations concerning the ethene-water heterodimer were carried out using the small 52 CASSCF(2,2) and the medium CASSCF(10,7) wavefunctions with a variety of basis sets. The reliability of 53 the NEVPT2 method was confirmed by all calculations and was also validated by benchmark computations at 54 55 the CCSD(T) level of theory. The two different active spaces that were used in this study, exhibit the more 56 accurate performance of the PC-NEVPT2 approach, as expected. The CP-corrected ethene-water 57 intermolecular interaction energy was remarkably improved by the NEVPT2 method against the unperturbed 58 59 60 URL: http://mc.manuscriptcentral.com/tandf/tmph Page 35 of 45 Molecular Physics

1 2 3 CASSCF results. A very good agreement between NEVPT2 calculated and experimental results was observed 4 5 in this extremely weak heterodimer intermolecular interaction case. Furthermore, the developed NEVPT2 6 computational procedure was successfully testified to the benzene-water complex ensuring stability and 7 convergence using the (6,6) active space. 8 The strict-separability of the NEVPT2 method seems to offer an efficient multireference second order 9 perturbation theory capable to treat heterodimer molecular complexes more easily. Finally, it seems that the 10 11 multiconfiguration character of the CP-corrected OH.. π intermolecular interactions can be attractively 12 enhanced by the employment of the NEVPT2 method; this claim may advance future developments on 13 heterodimers’ studies which exhibit degenerate states and the multiconfigurational treatment is necessitated. 14 For Peer Review Only 15 Acknowledgements 16 17 The authors would like to acknowledge Prof. Kenneth Ruud for his insightful comments and suggestions 18 19 concerning this work. Also, it is gratefully acknowledged the computer time provided by the Computer Center 20 and the Computational Materials Science Laboratory of the University of Ioannina in Greece. 21 22 23 References 24 25 [1] G. A. Jeffrey, An Introduction to Hydrogen Bonding , Oxford University Press , Oxford, (1997). 26 27 [2] A. J. Stone, The Theory of Intermolecular Forces , Clarendon , Oxford, (1996). 28 [3] K. I. Peterson, W. Klemperer, J Chem. Phys. 85 , 725 (1986). 29 [4] A. Engdahl, B. Nelander, Chem. Phys. Lett. 113 , 49 (1985). 30 [5] B.O. Roos, P.R. Taylor, P.E.M. Siegbahn, Chem. Phys. 48 , 157 (1980). 31 [6] K. Ruedenberg, M. W. Schmidt, M. M. Gilbert, S. T. Elbert, Chem. Phys. 71 , 41 (1982). 32 [7] A. Szabados, Z. Rolik, G. Toth, P. R. Surjan, J. Chem. Phys. 122 , 114104 (2005). 33 34 [8] K. Andersson, P.-A. Malmqvist, B. O. Roos, J. Chem. Phys. 96 , 1218 (1992). 35 [9] K. Andersson, P.-A. Malmqvist, B. O. Roos, A. J. Sadlej, K. Wolinski, J. Phys. Chem. 94 , 5483 (1990). 36 [10] C. Angeli, R. Cimiraglia, S. Evangelisti, T. Leininger, J. P. Malrieu, J. Chem. Phys. 114 , 10252 (2001). 37 [11] C. Angeli, R. Cimiraglia, J. P. Malrieu, Chem. Phys. Lett. 350 , 297 (2001). 38 [12] C. Angeli, R. Cimiraglia, J. P. Malrieu, J. Chem. Phys. 117 , 9138 (2002). 39 40 [13] H. A. Witek, Y.-K. Choe, J. P. Finley, K. Hirao, J. Comp. Chem. 23 , 957 (2002). 41 [14] K. G. Dyall, J. Chem. Phys. 102 , 4909 (1995). 42 [15] Dalton, a molecular electronic structure program, Release 2.0 (2005), see 43 http://www.kjemi.uio.no/software/Dalton/Dalton.html. 44 [16] S. F. Boys, F. Bernardi, Mol. Phys. 19 , 553 (1970). 45 [17] M. J. Watkins, K. Muller-Dethlefs, M. C. R. Cockett, Phys. Chem. Chem. Phys. 2, 5528 (2000). 46 47 [18] G. Olaso-González, D. Roca-Sanjuán, L. Serrano-Andrés, M. Merchán, J. Chem. Phys. 125 , 231102 48 (2006). 49 [19] M. W. Schmidt, K. K. Baldridge, J. A. Boatz, S. T. Elbert, M. S. Gordon, J. H. Jensen, S. Koseki, N. 50 Matsunaga, K. A. Nguyen, S. Su, T. L. Windus, M. Dupuis, J. A. Montgomery, J. Comput. Chem. 14 , 1347 51 (1993). 52 53 [20] Brett Bode’s MacMolPlt, available from http://www.msg.ameslab.gov/GAMESS/GAMESS.html 54 [21] K. Hirao, Chem.Phys.Lett. 190 , 374 (1992). 55 [22] K. Hirao, Chem.Phys.Lett. 196 , 397 (1992). 56 [23] H. Nakano, Chem.Phys.Lett. 207 , 372 (1993). 57 [24] H. Nakano, J.Chem.Phys. 99 , 7983 (1993). 58 59 60 URL: http://mc.manuscriptcentral.com/tandf/tmph Molecular Physics Page 36 of 45

1 2 3 [25] P. O. Widmark, P. A. Malmqvist, B. Roos, Theor. Chim. Acta 77 , 291 (1990). 4 5 [26] K. B. Wiberg, J. Comp. Chem. 25 , 1342 (2004). 6 [27] P. Tarakeshwar, H. S. Choi, S. J. Lee, J. Y. Lee, K. S. Kim, T. K. Ha, J. H. Jang, J. G. Lee, H. Lee, J. 7 Chem. Phys. 111 , 5838 (1999). 8 [28] F. G. Kalatzis, D. G. Papageorgiou, I. N. Demetropoulos, Comp. Phys. Comm. 175 , 359 (2006). 9 [29] A. Courty, M. Mons, I. Dimicoli, F. Piuzzi, M.-P. Gaigeot, V. Brenner, P. Pujo, P. Millie, J. Phys. Chem. 10 11 A 102 , 6590 (1998). 12 [30] M. Raimondi, G. Calderoni, A. Famulari, L. Raimondi, F. Cozzi, J. Phys. Chem. A 107 , 772 (2003). 13 [31] S. Suzuki, P. G. Green, R. E. Bumgarner, S. Dasgupta, W. A. Goddard III, G. A. Blake, Science 257 , 942 14 (1992). For Peer Review Only 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 URL: http://mc.manuscriptcentral.com/tandf/tmph Page 37 of 45 Molecular Physics

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