SCIENCE CHINA Physics, Mechanics & Astronomy. Potential energy curves crossing and low-energy charge transfer dynamics in (BeH 2 O) 2+ complex

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1 SCIENCE CHINA Physics, Mechanics & Astronomy Article July 2012 Vol.55 No.7: doi: /s Potential energy curves crossing and low-energy charge transfer dynamics in (BeH 2 O) 2+ complex SUN QiXiang & YAN Bing * Institute of Atomic and Molecular Physics, Jilin University, Changchun , China Received November 28, 2011; accepted February 23, 2012; published online April 18, 2012 The singlet rigid Be O dissociation potential energy curves correlating to the first four molecular limits of (BeH 2 O) 2+ complex were calculated using the multi-reference single and double excitation configuration interaction theory. The radial couplings of three low-lying 1 A 1 states were calculated and combined with adiabatic potential energy curves to investigate and chargetransfer collision dynamics by using quantum-mechanical molecular orbital close-coupling methods. It is found that the total charge-transfer cross sections are dominated by the Be + ( 2 S)+H 2 O + (Ã 2 A 1 ) channel. The rate coefficients in the range of cm 3 /s are very sensitive to temperature below 1000 K. The complexation energy without charge-transfer was determined to be kcal/mol, including zero-point vibration energy corrections. This is in good agreement with the previous results. potential energy curve, adiabatic coupling, charge transfer, (BeH 2 O) 2+ complex PACS number(s): Mq, e, Gh Citation: Sun Q X, Yan B. Potential energy curves crossing and low-energy charge transfer dynamics in (BeH 2 O) 2+ complex. Sci China-Phys Mech Astron, 2012, 55: , doi: /s The interaction between metal ions, especially the alkaline and alkaline earth ions, and water is of great chemical and biological interest in order to understand the dynamical process in ionic solutions [1 5]. The interaction of doubly charged cations and water leads to a notable charge transfer (CT) arising from the avoided crossing of low-lying electronic states. The CT reactions facilitate a critical role in the field collision dynamic. In CT dynamics studies, the water-metal collision is regarded as an elementary reaction and as a mediating complex, the water-mental ionic system may also be helpful for the metal to metal CT in solution. During the last several decades, alkaline earth ions (Be 2+, Mg 2+, and Ca 2+ ) and water complexes became objects of previous ab initio studies [6 10]. The berry-water complex is one of the simplest models to investigate the CT dynamics in solution. The interaction energy of (Be+H 2 O) 2+ system was firstly calculated by using Hatree-Fock (HF) and *Corresponding author ( yanbing@jlu.edu.cn) configuration interaction (CI) methods with two extended Gaussian type basis sets. The crossing of the 1 A 1 states was also discussed [6]. The adiabatic potential energy curves (PECs) along Be O bond distance were determined with second-order quasi-degenerate perturbation theory, and quasi-diabatic PECs of 1 A 1 states were utilized to analyze the internal CT states for berry-water dication systems [10]. Most previous ab initio calculations focused on the PECs, and to our best knowledge, no previous adiabatic coupling matrix elements between states with the same space and spin symmetry are calculated, which is important for the theoretical investigation of CT dynamics. In this present study, accurate adiabatic PECs for the 1 A 1 state of (Be-H 2 O) 2+ were calculated with multireference CI (MRCI) method, the adiabatic coupling matrix elements were also obtained, and subsequently the unitary transforms from adiabatic to diabatic presentations were made. The collision CT dynamics of (Be-H 2 O) 2+ was then studied. In addition, some other PECs for singlet low-lying electronic states were Science China Press and Springer-Verlag Berlin Heidelberg 2012 phys.scichina.com

2 Sun Q X, et al. Sci China-Phys Mech Astron July (2012) Vol. 55 No present and complexation energy of (Be-H 2 O) 2+ system was determined with ab initio calculations. 1 Computational methods 1.1 Electronic structure calculations The Y-shape (Be-H 2 O) 2+ complex in C 2v symmetry is considered, and rigid PECs are calculated in this present study. The experimental structure data for neutral water are collected according to Cossi and Persico [10], and the bond distance and bond angle are fixed as a 0 and The aug-cc-pvqz basis set developed by Dunning [11] is used throughout the ab initio electronic structure calculations. The main configure of ground state 1 A 1 of (BeH 2 O) 2+ is (Core)3 4a 1 2 1b 1 2 1b 2 2 5a 1 0 2b b 2 0. (1) The core orbitals 1 2a 2 1 are corresponding to the 1s orbitals of O and Be atoms. The zero-order wavefunctions were generated by complete active space multiconfiguration self-consistent fields (CAS-MCSCF) with full valence active space. Additional valence correlation energy was evaluated by single and double excitation out of CAS- MCSCF space with internal contracted MRCI scheme implemented in the Molpro package 1). The total number of contracted configuration functions for 1 A 1 state is approximately The coupling matrix elements A ( R) i / R j, in which i and j are states with the same space and spin symmetry and / R is the differential operator with respect to Be O bond length R, were calculated in finite difference in approximation with three-point formula using MRCI vectors. 1.2 Collision theory The quantum-mechanical molecular-orbital close-coupling (QM-MOCC) method which has been described in detail in ij previous literature [12 14] was used for CT collision reaction. In adiabatic representation, transitions between channels are driven by radial and rotational coupling. The adiabatic presentation, along with first-order derivative, is conveniently transformed into diabatic representation numerically [13]: U(R) = W(R)[V(R) P(R)]W 1 (R), (2) and dw(r)/dr + W(R)A rad (R)=0, (3) in which R is the internuclear distance, U(R) is the diabatic potential matrix, V(R) is the diagonal adiabatic potential, W(R) is a unitary transformation matrix, P(R) is the given rotational matrix element [14], and A rad is the adiabatic radial coupling matrix element. To obtain the reaction matrix element K l and scattering matrix element S l, with the transformed diabatic potential and coupling, for each partial wave the coupled set of second-order differential equations was solved to match the plane wave at the asymptote limit. Thus, the CT crossection from initial channel to a charge-transfer channel can be expressed as: α πg ( E) (2l 1) ( S ). k α l β (4) α l Here k denotes the wave number for center-of mass motion of the initial ion-atom channel, and g is an approach probability factor of the initial channel. The geometry of water was fixed and the couplings between 1 A 1 and other states are neglected in the scattering calculation. 2 Results and discussion 2.1 PECs and radial couplings In Table 1, the relative energies of dissociation limits of (Be-H 2 O) 2+ complex are shown along with the molecular states correlated to each dissociation limit. The previous Table 1 The vertical excitation energies for dissociation limit of (Be-H 2 O) 2+ complex (units in ev) Dissociation limits Molecular states Energy This work a) exp. b) Theory c) Be 2+ ( 1 S)+H 2 O( XA 1 1 ) 1 A Be + ( 2 S)+H 2 O + ( XB) 2 1 1,3 B ± Be + ( 2 S)+H 2 O + (Ã 2 A 1 ) 1,3 A ± Be + ( 2 P)+H 2 O + ( XB) 2 1 1,3 (A 1,A 2,B) ± Be + ( 2 P)+H 2 O + (Ã 2 A 1 ) 1,3 (A 1,B 1,B 2 ) ± Be + ( 2 S)+H 2 O + ( BB 2 2 ) 1,3 B ± a) Energy calculated with fixed water geometry b)combine the photoelectron spectroscopy experiment in ref. [15] for water with NIST value for Berry c) Theoretical values in ref. [10] 1) Werner H J, Knowles P J, Lindh R, et al. Molpro, a package of ab initio programs, Version , 2010

3 1260 Sun Q X, et al. Sci China-Phys Mech Astron July (2012) Vol. 55 No. 7 theoretical and experimental results are also listed for comparison. As shown in Table 1, the current calculations give better agreement comparing with previous work [10]. The present calculated values of 1 A 1 states fall into the error bar of the experiment [15] or exceed the upper experimental limits within 0.02 ev, which is adequate for low-energy scattering problems. For the sixth dissociation limit, which is correlated to singlet and triplet B 2 states, the relative energy is 0.04 ev higher than the upper limit of experimental value. Since this channel is not included in the following collision problems, no further efforts are made to decrease this discrepancy. Because of the symmetry of entrance channel, Be 2+ ( 1 S) +H 2 O( XA 1 1 ), and neglecting the rotational coupling, only 1 A 1 states were included in the collision study. Each PEC is constructed from over 240 single-point energy calculations. The avoided crossing points at larger nuclear distance than 20a 0 are not included in this present work and only A 1 states were calculated. The adiabatic PECs and radial adiabatic couplings functions with respect to Be O bond distance of A 1, together with transformed diabatic PECs and couplings, are illustrated in Figures 1 and 2, respectively. The equilibrium Be O distance of water is calculated to be 2.83a 0, which is in good agreement with recent theoretical values [10]. At 2.84a 0, it also gives reasonable agreement with ab initio value a 0 at different levels [16 18]. In Figure 1, the adiabatic PECs appear four avoided crossing points, which are A 1 avoided crossing at 8.787a 0, A 1 at a 0, A 1 at 2.154a 0, and A 1 at 4.422a 0, respectively. The energy gaps of these four avoided crossing points are , 0.064, , and a.u., respectively. It should be noted that the avoided crossing at large internuclear distance (17.102a 0 ) is treated diabatically in collision calculation. In Figure 2, a sharp peaked radial coupling between 2 1 A 1 and 3 1 A 1 exists at small bond distance (2.154a 0 ), which could make contributions to the total cross section at energy higher than Figure 2 The radial adiabatic and diabatic couplings. ev according to the PECs in Figure 1. As shown in Figure 1, the adiabatic coupling at 4.422a 0 is not strong enough to make diabatic PECs of the charge-transfer channel crossed, while the diabatic PECs for A 1 become energetically close through the coupling of A 1 in small internuclear distances. The CT process through the A 1 avoided crossing is an exoergic reaction, which is expected to have significant contributions to cross section even in very-lowenergy regions. 2.2 CT cross sections and rate coefficients The QM-MOCC method was used for collision calculations with the obtained diabatic PECs and radial coupling matrix elements. The calculated state-selective and total singleelectron CT cross sections in the range of ev/u are displayed in Figure 3. Since no vibrational-rotational wavefunctions are considered, the cross sections below 0.05 ev/u are truncated. As shown in Figure 3, similar to ion-atom collision [19], few oscillation structures are present in both total cross section and individual CT cross sections. Since the water is kept frozen and no internal vibrational-rota- Figure 1 The adiabatic (solid line) and diabatic (dot line) PECs of (BeH 2 O) 2+ complex. Figure 3 Total and state-selective charge transfer cross sections.

4 Sun Q X, et al. Sci China-Phys Mech Astron July (2012) Vol. 55 No tional structure is considered, the collision between Be 2+ ion and water can be treated as a quasi ion-atom process. The same physical mechanisms [19] are responsible for the oscillations in low energy regions. As discussed in sect. 2.1, in the low-energy region, the contribution of total cross section is completely dependent on the Be + ( 2 S)+H 2 O + (Ã 2 A 1 ) channel until the energy increasing to 0.15 ev/u, where the Be + ( 2 P)+H 2 O + ( X 2 B 1 ) channel contributes to the total cross section with values as large as cm 2. At the energy becomes larger than 0.5 ev/u, the state selective cross section arising from the Be + ( 2 P)+H 2 O + ( XB) 2 1 channel becomes dominant, which maybe attributed to the extra energy made in the CT probability, increasing the short inter-nuclear distance. The Be + ( 2 S)+H 2 O + (Ã 2 A 1 ) CT cross section has a minimum at 1.5 ev/u for the completions between two exit channels in the range of 1 10 ev/u. For the energy above 10 ev/u, the contribution from the Be + ( 2 S) +H 2 O + (Ã 2 A 1 ) channel is about 2 7 times larger than that from the Be + ( 2 P)+H 2 O + ( XB), 2 1 because the former channel is energetically preferred and strong couplings with exit channel exist both in large and short inter-nuclear distances. The rate coefficients of CT were determined by using; 3/2 kt (5) Et 1 2 ( T) ( E) Eexp( E/ kt)d E, π where, is the reduced mass of (BeH 2 O) 2+, E t is the threshold energy, and E=v 2 /2 is the center of mass energy. The calculated total and state-selective rate coefficients as function of temperature are presented in Figure 4. It is clear that the most important channel is the Be + ( 2 S)+H 2 O + (Ã 2 A 1 ), particularly in the low-temperature (<1000 K) region. Almost all contributions are from the Be + ( 2 S)+H 2 O + (Ã 2 A 1 ) channel. For the most chemically interesting temperature regions, that is a few hundred K, the rate coefficients in- crease exponentially. For instance, as the temperature increasing from 300 to 400 K, the rate coefficient increased 16 times. 2.3 Complexation energy and adiabatic PECs of singlet low-lying electronic states In order to examine the adiabatic dissociation process of the (BeH 2 O) 2+ complex, the adiabatic PECs for singlet lowlying electronic states including A 1, B 1, B 2, and 1 A 2 symmetry of the (BeH 2 O) 2+ complex were calculated using MRCI methods as shown in Figure 5. Previous report [10] on complexation energy of (BeH 2 O) 2+ are discrepant to each other with values from to kcal/mol. Most results are in (130±20) kcal/mol. In Figures 1 and 5, the adiabatic dissociation along channel 1 (Table 1) need to overcome the barrier at 4.6 Å, the complexation energy along adiabatic charge-transfer path Be + ( 2 S)+ H 2 O + ( XB) 2 1 is determined as kcal/mol without the zero-point vibrational energy included. The present calculated complexation energy value agrees the previous reported values and kcal/mol obtained with different theoretical treatments [10]. The complexation energy referred to the Be 2+ ( 1 S)+H 2 O( XA 1 1 ) asymptote without CT is kcal/mol, which is in good agreement with that of Cossi and Persico [10] (146.4 kcal/mol). The zero-point vibration energy correction for complexation energy is rather small, which is determined as 0.59 kcal/mol by second-order Møller-Plesset perturbation theory calculations. Briefly, the complexation energy without CT process included is kcal/mol and that with CT process included is kcal/mol according to the current MRCI/ aug-cc-pvqz calculations. Excluding the A 1 states, all other calculated states are dominated by coulomb repulsion. The lowest crossing point between the 1 1 A 1 and 1 1 B 1 adiabatic states is located at Å. If the orientation of the incident ion changes Figure 4 Total and state-selective rate coefficients as function of temperature. Figure 5 The adiabatic PECs for low-lying singlet states of (BeH 2 O) 2+ as function of internuclear distance of Be O with fixed water geometry.

5 1262 Sun Q X, et al. Sci China-Phys Mech Astron July (2012) Vol. 55 No. 7 and subsequently the point group is lowered from C 2v to Cs, the radial couplings of 1 1 A 1 and 1 1 B 1 (notations in C 2v ) become non-zero and the contributions from the Be + ( 2 S)+H 2 O + (X 2 B 1 ) should be concluded in total cross sections. Additionally, the effect of rotational coupling between singlet A 1 and singlet A 2, B 1 is also of great interest. The related calculations are undertaken, and the anisotropy of cross sections will be discussed in the future. 3 Conclusions Using the multi-reference single and double excitation CI theory, the rigid interaction potentials and the radial couplings of 1 A 1 states of berry-water dication complex were calculated. The CT dynamics arising from the adiabatic avoided crossings were investigated by quantum-mechanical molecular orbital close-coupling methods in the center-of mass energy range ev/u with a simple three-states coupling model. The charge-transfer rate coefficients are dominant by the Be + ( 2 S)+H 2 O + (Ã 2 A 1 ) contributions in the range of cm 3 /s, and is sensitive to temperature below 1000 K. The complexation energy without charge-transfer is determined as kcal/mol and agrees with previous results. The authors thank Dr WU Yong and Prof. WANG JianGuo for their help on collision theoretical calculations. We acknowledge the High Performance Computing Center (HPCC) of Jilin University for supercomputer time. 1 Clementi E, Corongiu G J. Structure of aggregates of water and Li +, Na +, or K + counterions with nucleic acid in solution. Bio Phy, 1983, 11: Duguid J, Bloomfield V A, Benevides J, et al. Raman spectroscopy of DNA-metal complexes. Biophys J, 1993, 65: Trachtman M, Markham G D, Glusker J P, et al. Interaction of metal ions with water: Ab initio molecular orbital studies of structure, bonding Enthalpies, vibrational frequencies and charge distributions. Inorg Chem, 1998, 37: Kritayakornupong C, Plankensteiner K, Rode B M. Structure and dynamics of the Cr(III) ion in aqueous solution: Ab initio QM/MM molecular dynamics simulation. J Comput Chem, 2004, 25: Clementi E, Corongiu G. Study of the structure of molecular complexes. XVI. Doubly charge cations interacting with water. J Chem Phys, 1978, 69: Zhao L Z, Liu S H, Zhu D B. The study of DISP 4 charge transfer complex using XPS. Chin Sci Bull, 1983, 28: Blake I O, Leś A. On the dissociation of doubly charged cations: (Mg-H 2 O) 2+ and [Mg-(H 2 O) 2 ] 2+. J Chem Phys, 1980, 73: Wasserman E, Rustad J R, Xantheas S S. Interaction potential of Al 3+ in water from first principles calculations. J Chem Phys, 1997, 106: Cachau R E, Villar H O, Castro E A. Theoretical study of the calcium dication hydrates. Theor Chim Acta, 1989, 75: Cossi M, Persico M. Charge transfer and curve crossings in the [BeH 2 O] 2+ system. Theor Chim Acta, 1991, 81: Dunning T H J. Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen. J Chem Phys, 1989, 90: Kimura M, Lane N F. The low-energy, heavy-particle collisions a close-coupling treatment. Adv At Mol Opt Phys, 1990, 26: Zygelman B, Cooper D L, Ford M J, et al. Charge transfer of N 4+ with atomic hydrogen. Phys Rev A, 1992, 46: Wang J G, Stancil P C, Turner A R, et al. Charge transfer of O 3+ ions with atomic hydrogen. Phys Rev A, 2003, 67: Brundle C R, Turner D W. High resolution molecular photoelectron spectroscopy. II Water and deuterium oxide. Proc R Soc, 1968, 307: Cammi R, Hofmann G J, Tomasi J. Decomposition of the interaction energy between metal cations and water or ammonia with inclusion of counterpoise corrections to the interaction energy terms. Theor Chem Acta, 1989, 76: Probst M M, Limtrakul J P, Rode B M. A study of the Be 2+ -H 2 O system by means of ab initio calculations. Chem Phys Lett, 1986, 132: Hashimoto K, Yoda N, Iwata S. Theoretical study of hydrated Be 2+ ions. Chem Phys, 1987, 116: Krstic P S, Macek J H, Ovchinnikov S Y, et al. Analysis of structures in the cross sections for elastic scattering and spin exchange in lowenergy H + +H collisions. Phys Rev A, 2004, 70: