- Email: [email protected]
Ab initio study for the intermolecular potential of the water–nitric oxide complex
18 February 2000
Chemical Physics Letters 318 Ž2000. 232–239 www.elsevier.nlrlocatercplett
Ab initio study for the intermolecular potential of the water–nitric oxide complex Grzegorz Myszkiewicz, Joanna Sadlej
)
Department of Chemistry, UniÕersity of Warsaw, Pasteura 1, 02-093 Warsaw, Poland Received 26 November 1999; in final form 4 January 2000
Abstract Ab initio UMP2 gradient calculations confirm that there are a few stable structures of the complex H 2 O PPP NO ŽX 2 P .. The AX state has three minima: the N-bonded anti structure is the global minimum. Two other minima have also been located ŽN-bonded syn and O-bonded anti forms.. By contrast, the AXX has one minimum related to a T-shaped form, which lies above the AX global minimum ŽUMP2 gradient optimisation procedure followed by calculations at the CCSDŽT. level.. The comparison of the IPES for the AX and AXX states calculated from a grid of points at the UMP2 level followed by the CCSDŽT. calculations for the characteristic points on the IPES demonstrated the failure of the UMP2 calculations for the H 2 O PPP NO complex. q 2000 Elsevier Science B.V. All rights reserved.
1. Introduction The structure of numerous weakly bound complexes have been recently examined spectroscopically using many experimental techniques w1–3x. A complementary approach to obtain information on weakly bound complexes are the ab initio calculations. This method is becoming an accepted tool for the study of the structure and properties of the molecular complexes w4–6x. The method is especially useful in cases in which the existence of different conformers is difficult to determine spectroscopically. In a series of papers we are studying the intermolecular potential energy surface ŽIPES. for the ) Corresponding author. Fax: q48-22-822-59-96; e-mail: [email protected]
complexes of water with small closed-shell molecules ŽH 2 , N2 , CO, NH 3 . w7–13x. Recently, the spectroscopy of open-shell complexes has become an important source of information on the interaction between closed- and open-shell molecules. Nitric oxide ŽNO. is a stable radical. Until the middle of the 1980s it had been considered as an atmospheric pollutant and bacterial metabolite w14–16x. However, it appears that a simple molecule as NO can play a key bioregulatory function in a number of physiological responses w17x Že.g., the NO is identified with the endothelium derived relaxing factor ŽEDRF. w18x.. It is hydrophobic with respect to aqueous solutions; however it should form a weak complex with the water molecule. The H 2 O PPP NO complex was examined by infrared spectroscopy w19x. Although shifted fundamental frequencies were noted, no low-frequency vibra-
0009-2614r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. PII: S 0 0 0 9 - 2 6 1 4 Ž 0 0 . 0 0 0 3 2 - 4
G. Myszkiewicz, J. Sadlejr Chemical Physics Letters 318 (2000) 232–239
tional modes were reported. There is no other spectroscopic paper about the H 2 O PPP NO complex. On the other hand, a few microwave studies with hyperfine resolution on rare-gas complexes show a strong interaction with Ar w20–22x. Recently, the FH PPP NO complex was examined for the first time by Fourier transform microwave spectroscopy w23x. The N hyperfine coupling reveals a strong splitting of the 2 P state degeneracy into AX and AXX states. The state AX is lower in energy, in contrast to the NO PPP Ar complex w20x. Accurate ab initio calculation could provide the characterization of the adiabatic IPES in the region of the minimum. The molecule NO in its ground X 2 P electronic state corresponds to the K C K N 3s2 4s2 1p 4 5s 2 2 p 1 configuration with two components corresponding to L s 1, where L is the projection of the electron angular momentum on the NO axis. In the absence of any external field, the two states are degenerate. In the presence of an interacting molecule the degeneracy is cancelled. This gives rise to two electronic states, e.g., for the NO PPP Rg planar complexes, AX and AXX w24x. Yang and Alexander found that the AXX state is deeper than the AX state for Rg s He w25x. The AXX state has two minima Ža T-shaped one and a collinear one He PPP ON.. The AX state reveals three minima Ža T-shaped form, a collinear He PPP NO one, and He PPP ON.. Klos et al. w26x found that these states are somewhat different. The IPES of the AX state has three minima, while, in contrast, the IPES of the AXX state has two minima. Surprisingly, the complex H 2 O PPP NO was the subject of only one theoretical paper w27x. Ball showed by G2 calculations that both N-bonded and O-bonded complexes are stable at low temperature, while at 298 K four investigated complexes are higher in energy with respect to the isolated molecules. The study of Ball w27x elucidated the major quantitative features of the electronic structure of the H 2 O PPP NO complex. However, the author did not investigate the syn–anti isomers and the two electronic states of the IPES of the H 2 O PPP NO complex. In addition, the G2 method applied by this author treats the electron correlation energies only approximately. Therefore, the study of molecular complexes involving NO is still a challenging problem for the
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theory in as much H 2 O PPP NO represents a model complex of closed-shell PPP open-shell interaction with a single electron occupying the antibonding p orbital. Depending on the orientation of the singleoccupied orbital as the NO radical approaches the water molecule, structures of the complex belong to the AX and AXX electronic states. The goal of this Letter is to evaluate detailed IPES of the H 2 O PPP NO system in the interaction region with special emphasis on the manifold potential wells.
2. Method of calculations and computational details First, we employed the standard Gaussian gradient optimization at the UMP2 level to determine the lowest energy structures Žwithout taking into account the CP correction in the optimization procedure.. The complex binding energy De for the optimized structures has been obtained from the equation: AB D E AB Ž n . s Ecom Ž n . y EAAB Ž n . y EBAB Ž n . s De , Ž 1.
where Ž n. denotes the level of theory such as UMP2 or UMP4, and noniterative triple excitations, CCSDŽT.. All the terms in Eq. Ž1. are evaluated within the same complex basis set ŽAB. and the geometry of monomers as they are in the complex. The evaluation of the interaction energy using the dimer basis set amounts to applying the couterpoise correction of Boys and Bernardi w28x. The deformation energy of monomers Ddef is taken into account to calculate the binding energy De w29,30x. The latter quantity was computed on the basis of that of the monomer. To calculate the dissociation energy D 0 this quantity has been corrected for the zero-point vibration energy difference between the complex and the isolated monomer energies DZPE Žcalculated at the UMP2 level.. The vibrational frequencies have been calculated within the harmonic approximation. Open-shell systems cause a few additional complications. A first complication is connected with the counterpoise method. The symmetry of the NO molecule in the presence of ghost orbitals of the second molecule is lowered from C`v to C s and
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gives rise to two different corrections related to the AX and AXX symmetries w31x. The second problem is the spin contamination. In our supermolecular calculations the spin adulteration of NO and the complex was not very significant, with S 2 equal to 0.776 instead of 0.75. This contamination amounts to ; 3.5%. It should be the same spin contamination for both monomers and the complex. Next, we have performed IPES calculations at the UMP2 level. The UMP4 and CCSDŽT. calculations
for the characteristic points on the IPES are reported. In the IPES calculations the experimental monomer geometries were kept constant: r ŽOH. s 1.8088 a.u., /HOHs 104.528 and r ŽNO. s 2.1747 a.u. The coordinate system is shown in Fig. 1a. The interaction potential D EŽ2. was calculated as a function of R, defined as a radius vector connecting the center of mass Žc.m.. of the NO molecule with the oxygen atom of the water molecule. For each orientation of the intermolecular axis R, the potential was calculated as a function of two angles: a and b , where a is the angle of R with the NO molecule axis, and b is the angle of R with the C 2 axis of the water molecule. Supermolecular calculations were performed on a fine grid of points at the UMP2 level. The distance R varied from 6 to 9 a.u. with a step of 0.5 a.u.. The angular step was fixed at 308 for the angle a in the region 0 F a F 180.0 and b s Žy127.74,y 52.26,0.0,52.26,127.74,180.08.. Two molecules are in the same plane. The minima on the UMP2 interaction energy surface were determined as follows. First, the structures corresponding to the lowest computed interaction energies were found on the grid. Next, additional calculations were performed in their vicinity. In order to check if the points considered as minima correspond to minima on the IPES, simple two- and three-dimensional fits were performed. An analysis of the fitted functions confirmed that the lowest energy points are minima indeed. In all calculations we used the aug-cc-pVTZ basis set w32,33x. As shown by Xantheas et al. w34x, this basis set accurately reproduces the geometries and the energetics of bound complexes. The calculations were performed by GAUSSIAN 94 w35x.
3. Results and discussion 3.1. Optimal structures and energetics
Fig. 1. The structure of the H 2 O PPP NO complex: Ža. coordinate X X system; Žb. A state, N-bonded-H-syn structure Ž I .; Žc. A state, X N-bonded-H-anti structure Ž II .; Žd. A state, O-bonded-H-anti X XX structure Ž III .; Že. A state, O-bonded-H-syn structure Ž IV .; Žf. A X XX state, T-structure Ž Vp .; Žf . A state, T-structure Ž V ., in plane; Žg. XX XX A state, O-bonded Ž VI .; Žh. A state, N-bonded Ž VII ..
Table 1 presents the binding and dissociation energies at the UMP2 level for the minima Žfully optimized geometries obtained by gradient procedure, which did not have any symmetry elements imposed on the complex. of the H 2 O PPP NO complex corrected for the deformation error. The optimized structures for H 2 O PPP NO complexes are
G. Myszkiewicz, J. Sadlejr Chemical Physics Letters 318 (2000) 232–239
235
Table 1 X XX Binding energies De ŽUMP2, UMP4, CCSDŽT.. and the dissociation energies D 0 ŽUMP2. Žin cmy1 . for the A and A states of the y1 optimized Žat UMP2 level. structures of the complex H 2 O PPP NO Žin cm . Structure
R
a
b
De ŽUMP2.
De ŽUMP4.
De ŽCCSDŽT..
D 0 ŽUMP2.
55.1 52.5 128.1
110.8 y126.5 y108.6
y476.0 y431.9 y182.8
y466.0 y434.2 y250.9
y428.5 y400.5 y273.5
y118 y110 y42
72.4
44.5
y419.3
y449.9
y401.9
y283
X
A: 6.71 6.90 6.77
II I III
XX
Vp
A: 5.78
a a
The structure Vp, ŽFig. 1f., the hydrogen of the water molecule in the plane perpendicular to the NO PPP O plane.
shown in Fig. 1. The hydrogen bonding for the structures I and II occurs between the N atom of NO and the H atom of the water molecule ŽN-bonded structures.. Both these structures belong to the AX state. Depending on the orientation of the water molecule the syn Ž I . and anti Ž II . forms are found. The hydrogen bond can be formed in another way, namely between the O atom of NO and the H atom of the water molecule ŽO-bonded structures. for the AX state. The resulting structures are III and IV. However, only the anti Ž III . structure is found to be a minimum Žall harmonic frequencies are positive.. The global minimum for the AX state is the structure N-bonded-anti Ž II . with the UMP2 binding energy equal to y476 cmy1 . The energy ordering of the structures for the AX state Ž II - I - III . is the same for UMP2, UMP4 and CCSDŽT.. The binding energies are almost unaffected by the use of different methods except for the structure III. The state AXX has a global minimum for the T-type structure Ž Vp . presented in Fig. 1f. The water molecule is in the plane perpendicular to the NO PPP O plane. The UMP2 binding energy for this structure is close to the energy of the structure I. However, the zero-point energy correction changes the ordering and the structure Vp which belongs to the AXX state is the most stable. Let us compare now these results with Ball’s calculations w27x. The syn and anti forms were not found in Ref. w27x. Ball’s UMP2 ordering is Ž II Vp - III . without discussing the symmetry of the electronic state while our ordering is Ž II - I - Vp III .. The structure D ŽO PPP O interaction. found in Ref. w27x was not a stable point at either the AX or AXX state in our work.
3.2. Feature of total IPES Let us discuss now the general features of the IPES for AX and AXX states in the plane of two molecules. The interaction potential DEŽ2. was calculated first as a function of the orientation of the intermolecular axis, which defines the position of the water molecule with respect to the NO molecule. For each orientation of the intermolecular axis, the potential was investigated as a function of R and b . A table with the UMP2 interaction energies for 616 different complex configurations is available from the authors on request. We represented our ab initio IPESs by a site–site analytical formula: Us
Ý Ý xgX ygY
½
exp Ž r x y y sx y R x y .
qf 1 Ž d 1x y R x y .
yg x y
qx qy Rxy f j Ž d jx y R x y .
Ý js6, 8, 10, 12
C jx y R xj y
5
,
Ž 2.
where sites x belong to the NO molecule, sites y to the H 2 O molecule and R x y is the distance between x and y. To control the relative importance of the Ryn x y terms and make them vanish at small distances, where they are no longer relevant, we used the Tang–Toennies w36x damping function: n
f n w z x s 1 y expyz
Ý ks0
zk k!
.
Ž 3.
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G. Myszkiewicz, J. Sadlejr Chemical Physics Letters 318 (2000) 232–239
Since anisotropy of the atom–atom interactions was not negligible we were forced to include it by allow-
ing parameters r x y and sx y Žin the exchange energy. and g x y Žin the dispersion energy. to depend
Fig. 2. Two-dimensional contour plots of the interaction energy D EŽUMP2. as a function of angles a and b around the stationary points X XX for: Župper. A and Žlower. A states.
G. Myszkiewicz, J. Sadlejr Chemical Physics Letters 318 (2000) 232–239
on the orientation via a series of spherical harmonics. For the exchange energy we decided on the following improvements: 2
½
r x y Ž u 1x y , u 2 . s a 0x y 1 q
a lx y Pl cos u 1x y
Ý ls1
=Pl cos Ž u 2 .
½
5
,
Ž 4.
2
sx y Ž u 1x y , u 2 . s b 0x y 1 q
Ý
b lx y Pl cos u 1x y
ls1
=Pl cos Ž u 2 .
5
,
Ž 5.
where u 1x y s /Ž x, c.m. NO , y ., u 2 s b q 1808, and in the dispersion energy: 2
g x y Ž u 1x y . s 1 q
Ý
c lx y Pl cos u 1x y .
Ž 6.
ls1
In order to ensure a proper behaviour of the electrostatic part of our fit we placed four charges in the NO molecule: qO 1 –q Bq 2 –q Bq 3 –q N 4 and five in H 2 O: q H 5, 9 –q Bq 6, 8 –qO 7, C 2v, initially computed at the MP2 level. This combined with angular dependence of r x y , sx y and g x y gave enough flexibility to our analytical function to well reproduce the wells of our IPESs. The two-dimensional minimal interaction energy paths for the H 2 O PPP NO complex resulting from
237
the UMP2 calculations descibed above are represented in Fig. 2 for the AX Župper. and AXX Žlower. states. The topology of the PES is quite interesting. For the AX state we have located four minima, three of them are mentioned earlier ŽTable 1.. The two lowest minima can be described as the N-bonded structures I and II mentioned earlier. These two minima are separated by 137 cmy1 ŽUMP2.. There are also local minima for the O-bonded structures III and IV ŽFig. 1d and e, respectively., which are separated from the global one by barriers of 34.4 and 8.9 cmy1 ŽUMP2., respectively. Our global minimum for the AX state is the N-bonded-syn structure I at R s 6.9 a.u., a s 48.18 and b s y125.98 w D EŽUMP2. s y373.2 cmy1 x. The second minimum is found for the N-bonded- anti structure II, at R s 6.57 a.u., a s 67.98 and b s 109.6 o w DEŽUMP2. s -344.7 cmy1 x ŽFig. 1c.. In contrast, the IPES of the AXX state has three minima. The global minimum for the AXX state is found for R s 5.7 a.u., a s 62.7 and b s 8.98, with the interaction energy w DEŽUMP2. s y518.0 cmy1 x Ž V ; Fig. 1f X .. This minimum is 39% ŽUMP2. deeper than for the AX state. There are two other minima for the structures VI and VII, which are separated by barriers of 88 and 71 cmy1 , respectively. Although we started from the experimental geometry of the monomers in the IPES calculations the minima are localized for the similar geometry parameters as in the gradient standard optimization. The results of the calculations of stationary points on the potential
Table 2 X XX Interaction energies D EŽUMP2, UMP4, CCSDŽT.. for the A and A states of the complex H 2 O PPP NO a Žin cmy1 . Structure
R
a
b
UMP2
UMP4
CCSDŽT.
48.1 67.9 126.4 141.6
y125.9 109.6 y108.7 128.7
y373.2 y344.7 y238.8 y219.1
y382.9 y365.5 y282.9 y258.7
y357.8 y380.2 y271.1 y250.4
62.7 60.0 180.0 10.0
8.9 0.0 y127.7 112.3
y517.9 y498.5 y199.1 y131.3
y486.4
y326.8
y217.7 y191.7
y174.4 y295.1
X
I II III IV
A: 6.89 6.57 6.70 6.99
V Vp b VI VII
A: 5.72 6.00 7.50 8.0
XX
a b
The minima obtained from the UMP2 calculations; UMP4 and CCSDŽT. calculated for the UMP2 optimized geometries. The structure Vp ŽFig. 1f., with the hydrogen of the water molecule in the plane perpendicular to the NO PPP O plane.
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G. Myszkiewicz, J. Sadlejr Chemical Physics Letters 318 (2000) 232–239
energy surface for the AX and AXX states at the UMP2 level are shown in Table 2. Subsequent calculations at the CCSDŽT. level performed at the stationary points for the geometries corresponding to the UMP2 values revealed that the UMP2 and UMP4 methods are not accurate enough to reproduce the AX –AXX splitting. While qualitatively the shapes of the AX and AX states are reasonable, the AX –AXX splitting proved to be wrong, because the AX surface turned out to be shallower Žy373.2 cmy1 . than the AXX state Žy517.9 cmy1 . at the UMP2, Žas well as at the UMP4., but deeper at the CCSDŽT. level Žy357.8 and y326.8 cmy1 , respectively.. It seems that the calculation of an accurate IPES for H 2 O PPP NO requires the use of highly correlated methods like the CCSDŽT. method. This is a rather discouraging result, since the calculations of the full potential surface at this level is very computer time expensive. Work in this direction is in progress.
4. Conclusions In this Letter we reported the first calculations for two states of H 2 O PPP NO complex. Among a few minima the N-bonded anti structure is the global minimum for the AX state, while the T-shaped form is the global minimum for the AXX state. The well depth of the potential energy surfaces for the AX and AXX states of H 2 O PPP NO ŽX 2 P . have been estimated to be y428.5 and 401.9 cmy1 , respectively, at the CCSDŽT. level for geometry structures found by gradient optimization procedure at the UMP2 level. However, the IPES calculations started from experimental monomers geometry parametres failed at the UMP2 level. Full PES for this complex requires the CCSDŽT. method.
Acknowledgements This work was supported by the 3 TO9A 056 14 KBN Grant. ICM at Warsaw University is acknowled for computer time. We thank Drs. G. Chalasinski and R. Moszynski for reading the manuscript and the discussions.
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Chemical Physics Letters 318 Ž2000. 232–239 www.elsevier.nlrlocatercplett
Ab initio study for the intermolecular potential of the water–nitric oxide complex Grzegorz Myszkiewicz, Joanna Sadlej
)
Department of Chemistry, UniÕersity of Warsaw, Pasteura 1, 02-093 Warsaw, Poland Received 26 November 1999; in final form 4 January 2000
Abstract Ab initio UMP2 gradient calculations confirm that there are a few stable structures of the complex H 2 O PPP NO ŽX 2 P .. The AX state has three minima: the N-bonded anti structure is the global minimum. Two other minima have also been located ŽN-bonded syn and O-bonded anti forms.. By contrast, the AXX has one minimum related to a T-shaped form, which lies above the AX global minimum ŽUMP2 gradient optimisation procedure followed by calculations at the CCSDŽT. level.. The comparison of the IPES for the AX and AXX states calculated from a grid of points at the UMP2 level followed by the CCSDŽT. calculations for the characteristic points on the IPES demonstrated the failure of the UMP2 calculations for the H 2 O PPP NO complex. q 2000 Elsevier Science B.V. All rights reserved.
1. Introduction The structure of numerous weakly bound complexes have been recently examined spectroscopically using many experimental techniques w1–3x. A complementary approach to obtain information on weakly bound complexes are the ab initio calculations. This method is becoming an accepted tool for the study of the structure and properties of the molecular complexes w4–6x. The method is especially useful in cases in which the existence of different conformers is difficult to determine spectroscopically. In a series of papers we are studying the intermolecular potential energy surface ŽIPES. for the ) Corresponding author. Fax: q48-22-822-59-96; e-mail: [email protected]
complexes of water with small closed-shell molecules ŽH 2 , N2 , CO, NH 3 . w7–13x. Recently, the spectroscopy of open-shell complexes has become an important source of information on the interaction between closed- and open-shell molecules. Nitric oxide ŽNO. is a stable radical. Until the middle of the 1980s it had been considered as an atmospheric pollutant and bacterial metabolite w14–16x. However, it appears that a simple molecule as NO can play a key bioregulatory function in a number of physiological responses w17x Že.g., the NO is identified with the endothelium derived relaxing factor ŽEDRF. w18x.. It is hydrophobic with respect to aqueous solutions; however it should form a weak complex with the water molecule. The H 2 O PPP NO complex was examined by infrared spectroscopy w19x. Although shifted fundamental frequencies were noted, no low-frequency vibra-
0009-2614r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. PII: S 0 0 0 9 - 2 6 1 4 Ž 0 0 . 0 0 0 3 2 - 4
G. Myszkiewicz, J. Sadlejr Chemical Physics Letters 318 (2000) 232–239
tional modes were reported. There is no other spectroscopic paper about the H 2 O PPP NO complex. On the other hand, a few microwave studies with hyperfine resolution on rare-gas complexes show a strong interaction with Ar w20–22x. Recently, the FH PPP NO complex was examined for the first time by Fourier transform microwave spectroscopy w23x. The N hyperfine coupling reveals a strong splitting of the 2 P state degeneracy into AX and AXX states. The state AX is lower in energy, in contrast to the NO PPP Ar complex w20x. Accurate ab initio calculation could provide the characterization of the adiabatic IPES in the region of the minimum. The molecule NO in its ground X 2 P electronic state corresponds to the K C K N 3s2 4s2 1p 4 5s 2 2 p 1 configuration with two components corresponding to L s 1, where L is the projection of the electron angular momentum on the NO axis. In the absence of any external field, the two states are degenerate. In the presence of an interacting molecule the degeneracy is cancelled. This gives rise to two electronic states, e.g., for the NO PPP Rg planar complexes, AX and AXX w24x. Yang and Alexander found that the AXX state is deeper than the AX state for Rg s He w25x. The AXX state has two minima Ža T-shaped one and a collinear one He PPP ON.. The AX state reveals three minima Ža T-shaped form, a collinear He PPP NO one, and He PPP ON.. Klos et al. w26x found that these states are somewhat different. The IPES of the AX state has three minima, while, in contrast, the IPES of the AXX state has two minima. Surprisingly, the complex H 2 O PPP NO was the subject of only one theoretical paper w27x. Ball showed by G2 calculations that both N-bonded and O-bonded complexes are stable at low temperature, while at 298 K four investigated complexes are higher in energy with respect to the isolated molecules. The study of Ball w27x elucidated the major quantitative features of the electronic structure of the H 2 O PPP NO complex. However, the author did not investigate the syn–anti isomers and the two electronic states of the IPES of the H 2 O PPP NO complex. In addition, the G2 method applied by this author treats the electron correlation energies only approximately. Therefore, the study of molecular complexes involving NO is still a challenging problem for the
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theory in as much H 2 O PPP NO represents a model complex of closed-shell PPP open-shell interaction with a single electron occupying the antibonding p orbital. Depending on the orientation of the singleoccupied orbital as the NO radical approaches the water molecule, structures of the complex belong to the AX and AXX electronic states. The goal of this Letter is to evaluate detailed IPES of the H 2 O PPP NO system in the interaction region with special emphasis on the manifold potential wells.
2. Method of calculations and computational details First, we employed the standard Gaussian gradient optimization at the UMP2 level to determine the lowest energy structures Žwithout taking into account the CP correction in the optimization procedure.. The complex binding energy De for the optimized structures has been obtained from the equation: AB D E AB Ž n . s Ecom Ž n . y EAAB Ž n . y EBAB Ž n . s De , Ž 1.
where Ž n. denotes the level of theory such as UMP2 or UMP4, and noniterative triple excitations, CCSDŽT.. All the terms in Eq. Ž1. are evaluated within the same complex basis set ŽAB. and the geometry of monomers as they are in the complex. The evaluation of the interaction energy using the dimer basis set amounts to applying the couterpoise correction of Boys and Bernardi w28x. The deformation energy of monomers Ddef is taken into account to calculate the binding energy De w29,30x. The latter quantity was computed on the basis of that of the monomer. To calculate the dissociation energy D 0 this quantity has been corrected for the zero-point vibration energy difference between the complex and the isolated monomer energies DZPE Žcalculated at the UMP2 level.. The vibrational frequencies have been calculated within the harmonic approximation. Open-shell systems cause a few additional complications. A first complication is connected with the counterpoise method. The symmetry of the NO molecule in the presence of ghost orbitals of the second molecule is lowered from C`v to C s and
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gives rise to two different corrections related to the AX and AXX symmetries w31x. The second problem is the spin contamination. In our supermolecular calculations the spin adulteration of NO and the complex was not very significant, with S 2 equal to 0.776 instead of 0.75. This contamination amounts to ; 3.5%. It should be the same spin contamination for both monomers and the complex. Next, we have performed IPES calculations at the UMP2 level. The UMP4 and CCSDŽT. calculations
for the characteristic points on the IPES are reported. In the IPES calculations the experimental monomer geometries were kept constant: r ŽOH. s 1.8088 a.u., /HOHs 104.528 and r ŽNO. s 2.1747 a.u. The coordinate system is shown in Fig. 1a. The interaction potential D EŽ2. was calculated as a function of R, defined as a radius vector connecting the center of mass Žc.m.. of the NO molecule with the oxygen atom of the water molecule. For each orientation of the intermolecular axis R, the potential was calculated as a function of two angles: a and b , where a is the angle of R with the NO molecule axis, and b is the angle of R with the C 2 axis of the water molecule. Supermolecular calculations were performed on a fine grid of points at the UMP2 level. The distance R varied from 6 to 9 a.u. with a step of 0.5 a.u.. The angular step was fixed at 308 for the angle a in the region 0 F a F 180.0 and b s Žy127.74,y 52.26,0.0,52.26,127.74,180.08.. Two molecules are in the same plane. The minima on the UMP2 interaction energy surface were determined as follows. First, the structures corresponding to the lowest computed interaction energies were found on the grid. Next, additional calculations were performed in their vicinity. In order to check if the points considered as minima correspond to minima on the IPES, simple two- and three-dimensional fits were performed. An analysis of the fitted functions confirmed that the lowest energy points are minima indeed. In all calculations we used the aug-cc-pVTZ basis set w32,33x. As shown by Xantheas et al. w34x, this basis set accurately reproduces the geometries and the energetics of bound complexes. The calculations were performed by GAUSSIAN 94 w35x.
3. Results and discussion 3.1. Optimal structures and energetics
Fig. 1. The structure of the H 2 O PPP NO complex: Ža. coordinate X X system; Žb. A state, N-bonded-H-syn structure Ž I .; Žc. A state, X N-bonded-H-anti structure Ž II .; Žd. A state, O-bonded-H-anti X XX structure Ž III .; Že. A state, O-bonded-H-syn structure Ž IV .; Žf. A X XX state, T-structure Ž Vp .; Žf . A state, T-structure Ž V ., in plane; Žg. XX XX A state, O-bonded Ž VI .; Žh. A state, N-bonded Ž VII ..
Table 1 presents the binding and dissociation energies at the UMP2 level for the minima Žfully optimized geometries obtained by gradient procedure, which did not have any symmetry elements imposed on the complex. of the H 2 O PPP NO complex corrected for the deformation error. The optimized structures for H 2 O PPP NO complexes are
G. Myszkiewicz, J. Sadlejr Chemical Physics Letters 318 (2000) 232–239
235
Table 1 X XX Binding energies De ŽUMP2, UMP4, CCSDŽT.. and the dissociation energies D 0 ŽUMP2. Žin cmy1 . for the A and A states of the y1 optimized Žat UMP2 level. structures of the complex H 2 O PPP NO Žin cm . Structure
R
a
b
De ŽUMP2.
De ŽUMP4.
De ŽCCSDŽT..
D 0 ŽUMP2.
55.1 52.5 128.1
110.8 y126.5 y108.6
y476.0 y431.9 y182.8
y466.0 y434.2 y250.9
y428.5 y400.5 y273.5
y118 y110 y42
72.4
44.5
y419.3
y449.9
y401.9
y283
X
A: 6.71 6.90 6.77
II I III
XX
Vp
A: 5.78
a a
The structure Vp, ŽFig. 1f., the hydrogen of the water molecule in the plane perpendicular to the NO PPP O plane.
shown in Fig. 1. The hydrogen bonding for the structures I and II occurs between the N atom of NO and the H atom of the water molecule ŽN-bonded structures.. Both these structures belong to the AX state. Depending on the orientation of the water molecule the syn Ž I . and anti Ž II . forms are found. The hydrogen bond can be formed in another way, namely between the O atom of NO and the H atom of the water molecule ŽO-bonded structures. for the AX state. The resulting structures are III and IV. However, only the anti Ž III . structure is found to be a minimum Žall harmonic frequencies are positive.. The global minimum for the AX state is the structure N-bonded-anti Ž II . with the UMP2 binding energy equal to y476 cmy1 . The energy ordering of the structures for the AX state Ž II - I - III . is the same for UMP2, UMP4 and CCSDŽT.. The binding energies are almost unaffected by the use of different methods except for the structure III. The state AXX has a global minimum for the T-type structure Ž Vp . presented in Fig. 1f. The water molecule is in the plane perpendicular to the NO PPP O plane. The UMP2 binding energy for this structure is close to the energy of the structure I. However, the zero-point energy correction changes the ordering and the structure Vp which belongs to the AXX state is the most stable. Let us compare now these results with Ball’s calculations w27x. The syn and anti forms were not found in Ref. w27x. Ball’s UMP2 ordering is Ž II Vp - III . without discussing the symmetry of the electronic state while our ordering is Ž II - I - Vp III .. The structure D ŽO PPP O interaction. found in Ref. w27x was not a stable point at either the AX or AXX state in our work.
3.2. Feature of total IPES Let us discuss now the general features of the IPES for AX and AXX states in the plane of two molecules. The interaction potential DEŽ2. was calculated first as a function of the orientation of the intermolecular axis, which defines the position of the water molecule with respect to the NO molecule. For each orientation of the intermolecular axis, the potential was investigated as a function of R and b . A table with the UMP2 interaction energies for 616 different complex configurations is available from the authors on request. We represented our ab initio IPESs by a site–site analytical formula: Us
Ý Ý xgX ygY
½
exp Ž r x y y sx y R x y .
qf 1 Ž d 1x y R x y .
yg x y
qx qy Rxy f j Ž d jx y R x y .
Ý js6, 8, 10, 12
C jx y R xj y
5
,
Ž 2.
where sites x belong to the NO molecule, sites y to the H 2 O molecule and R x y is the distance between x and y. To control the relative importance of the Ryn x y terms and make them vanish at small distances, where they are no longer relevant, we used the Tang–Toennies w36x damping function: n
f n w z x s 1 y expyz
Ý ks0
zk k!
.
Ž 3.
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Since anisotropy of the atom–atom interactions was not negligible we were forced to include it by allow-
ing parameters r x y and sx y Žin the exchange energy. and g x y Žin the dispersion energy. to depend
Fig. 2. Two-dimensional contour plots of the interaction energy D EŽUMP2. as a function of angles a and b around the stationary points X XX for: Župper. A and Žlower. A states.
G. Myszkiewicz, J. Sadlejr Chemical Physics Letters 318 (2000) 232–239
on the orientation via a series of spherical harmonics. For the exchange energy we decided on the following improvements: 2
½
r x y Ž u 1x y , u 2 . s a 0x y 1 q
a lx y Pl cos u 1x y
Ý ls1
=Pl cos Ž u 2 .
½
5
,
Ž 4.
2
sx y Ž u 1x y , u 2 . s b 0x y 1 q
Ý
b lx y Pl cos u 1x y
ls1
=Pl cos Ž u 2 .
5
,
Ž 5.
where u 1x y s /Ž x, c.m. NO , y ., u 2 s b q 1808, and in the dispersion energy: 2
g x y Ž u 1x y . s 1 q
Ý
c lx y Pl cos u 1x y .
Ž 6.
ls1
In order to ensure a proper behaviour of the electrostatic part of our fit we placed four charges in the NO molecule: qO 1 –q Bq 2 –q Bq 3 –q N 4 and five in H 2 O: q H 5, 9 –q Bq 6, 8 –qO 7, C 2v, initially computed at the MP2 level. This combined with angular dependence of r x y , sx y and g x y gave enough flexibility to our analytical function to well reproduce the wells of our IPESs. The two-dimensional minimal interaction energy paths for the H 2 O PPP NO complex resulting from
237
the UMP2 calculations descibed above are represented in Fig. 2 for the AX Župper. and AXX Žlower. states. The topology of the PES is quite interesting. For the AX state we have located four minima, three of them are mentioned earlier ŽTable 1.. The two lowest minima can be described as the N-bonded structures I and II mentioned earlier. These two minima are separated by 137 cmy1 ŽUMP2.. There are also local minima for the O-bonded structures III and IV ŽFig. 1d and e, respectively., which are separated from the global one by barriers of 34.4 and 8.9 cmy1 ŽUMP2., respectively. Our global minimum for the AX state is the N-bonded-syn structure I at R s 6.9 a.u., a s 48.18 and b s y125.98 w D EŽUMP2. s y373.2 cmy1 x. The second minimum is found for the N-bonded- anti structure II, at R s 6.57 a.u., a s 67.98 and b s 109.6 o w DEŽUMP2. s -344.7 cmy1 x ŽFig. 1c.. In contrast, the IPES of the AXX state has three minima. The global minimum for the AXX state is found for R s 5.7 a.u., a s 62.7 and b s 8.98, with the interaction energy w DEŽUMP2. s y518.0 cmy1 x Ž V ; Fig. 1f X .. This minimum is 39% ŽUMP2. deeper than for the AX state. There are two other minima for the structures VI and VII, which are separated by barriers of 88 and 71 cmy1 , respectively. Although we started from the experimental geometry of the monomers in the IPES calculations the minima are localized for the similar geometry parameters as in the gradient standard optimization. The results of the calculations of stationary points on the potential
Table 2 X XX Interaction energies D EŽUMP2, UMP4, CCSDŽT.. for the A and A states of the complex H 2 O PPP NO a Žin cmy1 . Structure
R
a
b
UMP2
UMP4
CCSDŽT.
48.1 67.9 126.4 141.6
y125.9 109.6 y108.7 128.7
y373.2 y344.7 y238.8 y219.1
y382.9 y365.5 y282.9 y258.7
y357.8 y380.2 y271.1 y250.4
62.7 60.0 180.0 10.0
8.9 0.0 y127.7 112.3
y517.9 y498.5 y199.1 y131.3
y486.4
y326.8
y217.7 y191.7
y174.4 y295.1
X
I II III IV
A: 6.89 6.57 6.70 6.99
V Vp b VI VII
A: 5.72 6.00 7.50 8.0
XX
a b
The minima obtained from the UMP2 calculations; UMP4 and CCSDŽT. calculated for the UMP2 optimized geometries. The structure Vp ŽFig. 1f., with the hydrogen of the water molecule in the plane perpendicular to the NO PPP O plane.
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energy surface for the AX and AXX states at the UMP2 level are shown in Table 2. Subsequent calculations at the CCSDŽT. level performed at the stationary points for the geometries corresponding to the UMP2 values revealed that the UMP2 and UMP4 methods are not accurate enough to reproduce the AX –AXX splitting. While qualitatively the shapes of the AX and AX states are reasonable, the AX –AXX splitting proved to be wrong, because the AX surface turned out to be shallower Žy373.2 cmy1 . than the AXX state Žy517.9 cmy1 . at the UMP2, Žas well as at the UMP4., but deeper at the CCSDŽT. level Žy357.8 and y326.8 cmy1 , respectively.. It seems that the calculation of an accurate IPES for H 2 O PPP NO requires the use of highly correlated methods like the CCSDŽT. method. This is a rather discouraging result, since the calculations of the full potential surface at this level is very computer time expensive. Work in this direction is in progress.
4. Conclusions In this Letter we reported the first calculations for two states of H 2 O PPP NO complex. Among a few minima the N-bonded anti structure is the global minimum for the AX state, while the T-shaped form is the global minimum for the AXX state. The well depth of the potential energy surfaces for the AX and AXX states of H 2 O PPP NO ŽX 2 P . have been estimated to be y428.5 and 401.9 cmy1 , respectively, at the CCSDŽT. level for geometry structures found by gradient optimization procedure at the UMP2 level. However, the IPES calculations started from experimental monomers geometry parametres failed at the UMP2 level. Full PES for this complex requires the CCSDŽT. method.
Acknowledgements This work was supported by the 3 TO9A 056 14 KBN Grant. ICM at Warsaw University is acknowled for computer time. We thank Drs. G. Chalasinski and R. Moszynski for reading the manuscript and the discussions.
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