Charge-Transfer and Dispersion Energies in Water Clusters

Transcription

1 II.26 Charge-Transfer and Dispersion Energies in Water Clusters Suehiro Iwata 1,2, Pradipta Bandyopadhyay 3, Sotiris S. Xantheas 4 1)Toyota Physical and Chemical Research Institute ( , fellow) 2) Faculty of Science and Engineering, Keio Univ. (2012, visiting Prof.) 3) Jawaharlar Nehru University 4) Pacific Northwest National Laboratory 1

2 Purpose for a series of the research To find a practical way to study the molecular clusters consisting of many molecular units with the effect of the BSSE as small as possible. Present status The purpose was accomplished at the closed shell Hartree- Fock level by the 2nd and 3rd order Single excitation Perturbation Theory based on Locally Projected Molecular Orbitals (LP MO 2&3SPT). Now the dispersion term can be evaluated with the LP MO double excitation perturbation theory. Now it is time to use the studies of the molecular clusters. 2

3 Locally Projected Molecular Orbitals (LP MO) and the many-electron wave function for a cluster a Slater determinant mol Ψ LPMO PT = Φ LP MO + a X r X A ax,r X + b X s Y mol mol X a,r X mol X mol Y>X b X s Y Local Excitation Charge-Transfer + a X b Y r X s Y A ax,r X,b Y,s Y + a X b X r X s X X Y>X a,r X b,s Y mol X a,r X b,s X Dispersion type Intra-molecule correlation A bx,s Y A ax,r X,b X,s X determined with the perturbation theory The MO coefficient matrix is block-diagonal as The coefficient matrix is determined variationaly under the absolute locality constraint. The excited MOs can be determined under the locality condition using a proper projection operator. Reference:1)JPC A114(2010)8697, 2)JCP 135(2011) , 3)PCCP 14(2012)7787 3

4 Binding Energy in LP MO 2nd &3rd order Single Excitation + Dispersion correction E BindE LP MO E Φ ( LP MO ) HF E X X electrostatic + induction + exch. repulsion E 2&3SPT LP BindE E MO BindE + E 2&3SPT CP corrected HF E BindE SPT + Disp E E + E + E 2&3 LPMO 2&3SPT 2 DPT _ Disp BindE BindE if the augument functions are used Some features of LP MO PT No charge-transfer (CT, electron delocalizaion) between the LP molecules is allowed in MO (Φ LP MO ). E BindE CT type single excitations make correction of the binding energy, and the energy evaluated with the 2nd and 3rd order perturbation theory (2&3SPT) is close to the counterpoise corrected Hartree- Fock energy. Dispersion type excitations can be selected in the 2nd order perturbation theory without introducing the configuration basis inconsistency (BSSE). 4

5 A uniqueness of the method is that once the first order wave function was obtained, the CT and dispersion terms can be evaluated for every pair of molecules in the cluster without an extra heavy computation. The method is applied to water clusters (H2O)11. The number of possible digraphs of (H2O)11 is 460,066,726. The number of stable isomers is much smaller than that. The prescreening with the empirical potential using various searching algorithms is required. In addition to the published isomers (Bulusu, Yoo, Apra, Xantheas, Zeng, JPC A 110 (2006) 11781), the new isomers are found. All geometries are fully optimized with MP2/aug-cc-pvdz. NWChem package was used for the optimization. 5

6 Isomers examined X434 X515 X443 X551 PX3189 PI1226 X4412 PI2476 PX4205 PI2877 Label of PZssss is a new isomer. 6

7 Relative Binding Energy [Reference: ~-420kJ/mol with Dispersion energy] The discrepancy of LPMO 2&3SPT +Disp from MP2 is about 4kJ/mol all within~10kj/mol What is the determining factor of the relative stability? 7

8 Relative Binding Energy and Energy Decomposition SPT + Disp E E + E + E 2&3 LPMO 2&3SPT 2 DPT _ Disp BindE BindE LP E MO BindE electrostatic + induction + exch. repulsion E 2&3SPT E CT E 2DPT_Disp The dispersion term is the largest contribution to the binding energy, but it does not necessarily mean it determines the most stable isomer. 8

9 The correlation of the O--O distance with the CT and dispersion energies CT Strong correlation between E pair Dispersion and E pair Hydrogen bonding E CT pair, defined by LP MO 2&3SPT, is a good measure for the measure of the hydrogen bond strength. 9

10 The relation of the CT and dispersion energies, and the type of hydrogen donor waters A water molecule in the cluster is classified by DnAm, where n is the number of donating hydrogens, and m is the number of accepting hydrogens in the molecule. The strong hydrogen bond if the hydrogen donor water is of type D1A2. 10

11 The relation of the CT and dispersion energies, and the type of hydrogen acceptor waters The strong hydrogen bond if the hydrogen acceptor water is of type D2A1. The hydrogen bond between D1A2 as hydrogen donor and D2A1 as hydrogen acceptor is stronger than the other types of hydrogen bonds, and the effects are cooperative of the dispersion and CT terms. 11

12 Structural characteristics of the clusters and the relative stability Cluster The number of HBs H donor - H acceptor D1A2- D2A1 the number of waters rings c) D1A1 D2A1 D1A2 D2A2 n4,n5,n6 c) X b 0 6,2,2 X ,4,1 X ,4,3 X ,2,1 PX ,5,3 PI ,2,3 X ,2,3 PI ,2,3 PX ,3,4 PI a ,0,5 a) A pair D1A2-D2A2 is included. b) D1A3 is included c) The number of ns membered rings in the cluster Roughly, the numbers of D1A2-D2A1 pairs, D2A1 waters and D1A2 waters correlate with the relative stability. 12

13 Examples of the detailed analysis X434 [6, 2, 2] PX3189 [3, 5, 3] w11 w10 w2 w9 w1 w2 w3 CT w4 w w8 w w7 w Disp w3 w w w7 w5 w6 w10 w w4 w8(o22) is D1A3 6 membered rings: membered rings:

14 Summary Charge-Transfer energy of a hydrogen bonded water molecules is well-correlated with the dispersion energy of the pair, and it is a good measure of the strength of the hydrogen bonds. Hydrogen bond of a D1A2 type water as a hydrogen donor and a D2A1 type water as a hydrogen acceptor is stronger than that of the other types. So if the cluster has many these types of bonds, it is more stable than the others. More systematic studies of larger hydrogen-bonded clusters of more complex networks are required. The present theoretical technique makes it possible with the parallel implementation. The effect of the intramolecular correlation on the hydrogen bond has to be examined, and the efficient way should be developed without the configuration basis inconsistency (CBI). 14

15 The work is a tribute to the memory of Dr. Takeshi Nagata, with whom this series of research was started in summer of 2000 in Hiroshima. 15