Structural and Spectroscopic Study of the Linear Proton-Bound van der
Waals Complex of PN with HNP+
Supplementary Information
C. Eric Cotton and Joseph S. Francisco*
Department of Chemistry and Department of Earth and Atmospheric Science
Purdue University
West Lafayette, Indiana, USA, 49707
Alexander O. Mitrushchenkov
Université Paris-Est
Laboratoire Modélisation et Simulation Multi Echelle
MSME UMR 8208 CNRS
5 bd Descartes, 77454 Marne-la-Vallée, France
The supplementary information presents the full results of the electronic structure studies of the
PN-HNP+ complex. Supplementary information on the construction of the 2D and 4D PES is
presented. Equilibrium geometries, equilibrium rotational constants, and energetic properties
from the CCSD(T)/aug-cc-pVnZ (n = 2 – 6) levels of theory and the CCSD(T)/aug-cc-pV(n+d)Z
(n = 2 – 4) levels of theory are presented. Equilibrium vibrational frequencies for the copmplex
at the CCSD(T)/aug-cc-pVnZ and the CCSD(T)/aug-cc-pV(n+d)Z (n = 2 – 3) are reported.
Table S1 - Phosporus Species Geometries
CCSD(T)
N=2
N=3
aug-cc-pVNZ
N=4
N=5
N=6
aug-cc-pV(N+d)Z
N=4
N=2
N=3
Species
Coordinate
PN'
r(N'-P)
1.5281
1.5079
1.4992
1.4953
1.4944
1.5170
1.5028
1.4968
r(N-P)
1.4956
1.4746
1.4665
1.4627
1.4618
1.4835
1.4688
1.4639
r(N-H)
1.0242
1.0147
1.0138
1.0136
1.0136
1.0235
1.0144
1.0136
r(N'-P)
1.5125
1.4937
1.4854
1.4814
1.4805
1.5012
1.4884
1.4829
r(N-H)
1.1484
1.1318
1.1314
1.1312
1.1309
1.1436
1.1306
1.1304
r(N-P)
1.5021
1.4820
1.4738
1.4700
1.4690
1.4901
1.4764
1.4713
r(N'•••H)
1.4491
1.4658
1.4660
1.1312
1.4678
1.4581
1.4679
1.4680
r(N'-P)
r(N'-H)
1.5074
1.2746
1.4882
1.2699
1.4799
1.4760
1.4760
1.2707
1.2707
1.4827
1.2698
1.4774
1.2703
1.4958
1.2745
HNP
+
PN'-HNP
+
[PN'-H-NP+]
‡
1.2704
Table S2 Rotational Constants (MHz)
Species
PN
HNP
+
Method
Basis Set
B
CCSD(T)
aug-cc-pVDZ
aug-cc-pVTZ
aug-cc-pVQZ
aug-cc-pV5Z
aug-cc-pV6Z
aug-cc-pV(D+d)Z
aug-cc-pV(T+d)Z
aug-cc-pV(Q+d)Z
aug-cc-pVDZ
aug-cc-pVTZ
aug-cc-pVQZ
aug-cc-pV5Z
aug-cc-pV6Z
aug-cc-pV(D+d)Z
aug-cc-pV(T+d)Z
aug-cc-pV(Q+d)Z
aug-cc-pVDZ
aug-cc-pVTZ
aug-cc-pVQZ
aug-cc-pV5Z
aug-cc-pV6Z
aug-cc-pV(D+d)Z
aug-cc-pV(T+d)Z
aug-cc-pV(Q+d)Z
aug-cc-pVDZ
aug-cc-pVTZ
aug-cc-pVQZ
aug-cc-pV5Z
aug-cc-pV6Z
aug-cc-pV(D+d)Z
aug-cc-pV(T+d)Z
aug-cc-pV(Q+d)Z
22,438
CCSD(T)
PN-HNP +
CCSD(T)
[PN-H-NP+]‡
CCSD(T)
23,045
23,312
23,434
23,463
22,769
23,202
23,387
19,638
20,187
20,396
20,492
20,516
19,937
20,333
20,462
945
957
962
964
964
950
960
963
963
979
984
986
986
970
982
985
Table S3 Vibrational Frequencies
CCSD(T)
Mode
Mode
Species
Number
Description
N=2
N=3
N=4
N=5
N=2
N=3
PN
1 (S s)
PN stretch
1264
1318
1333
1341
1282
1323
HNP +
1 (S s)
NH stretch
3575
3599
3605
3600
3583
3605
2 (S s)
PN stretch
1322
1380
1395
1402
1345
1387
3 (Π)
HNP bend
616
658
677
659
632
675
1 (S s)
NH stretch
1709
1815
1817
1814
1757
1831
2 (S s)
N'P stretch
1349
1398
1413
1420
1369
1404
3 (S s)
NP stretch
1091
1163
1173
1172
1126
1174
4 (S s)
N'••H stretch
197
197
202
196
198
202
5 (Π)
HNP bend
1165
1190
1186
1185
1171
1203
6 (Π)
PN'-HN asym tor
182
186
189
182
186
193
7 (Π)
PN'-HN sym tor
89
80
81
68
91
91
1 (S s)
NP sym stretch
1438
1489
1501
1508
1458
1494
2 (S s)
NP asym stretch
1366
1420
1433
1441
1388
1426
3 (S s)
NH sym stretch
333
337
338
336
335
338
4 (S s)
H-migration
590i
655i
685i
697i
609i
663i
5 (Π)
PNH bend
1236
1281
1277
1274
1247
1290
6 (Π)
PN'-HN asym torsion
184
194
198
191
188
197
7 (Π)
PN'-HN sym torsion
91
90
92
79
93
94
PN'-HNP
+
[PN'-H-NP+]‡
aug-cc-pVNZ
aug-cc-pV(N+d)Z
Table S4 - Uncorrected and ZPE Corrected PN Proton Affinities
PN
Proton Affinity
Method
Basis Set
De
D0
CCSD(T)
aug-cc-pVDZ
191.6
184.7
aug-cc-pVTZ
194.8
187.7
aug-cc-pVQZ
195.3
188.1
aug-cc-pV5Z
195.4
188.2
aug-cc-pV6Z
195.4
188.2
CCSD(T)
aug-cc-pV(D+d)Z
aug-cc-pV(T+d)Z
aug-cc-pV(Q+d)Z
CBSa
192.9
195.4
195.5
195.4
185.9
188.3
188.4
188.2
CBSb
195.3
188.1
Table S5 Total and Relative Energetics
Total Energies (Hartree)
Method
Basis Set
PN
HNP+
CCSD(T)
aug-cc-pVDZ
aug-cc-pVTZ
aug-cc-pVQZ
aug-cc-pV5Z
aug-cc-pV6Z
-395.47408
-395.55373
-395.57812
-395.58688
-395.58982
CCSD(T)
aug-cc-pV(D+d)Z
aug-cc-pV(T+d)Z
aug-cc-pV(Q+d)Z
-395.48213
-395.55712
-395.57998
+
+ ‡
PN-HNP+
Binding Energy
De
D0
[PN-H-NP+]‡
H-Migration Barrier
De
D0
-395.77948
-395.86412
-395.88929
-395.89824
-395.90115
PN-HNP
-791.29662
-791.46087
-791.51031
-791.52786
-791.53362
[PN-H-NP ]
-791.29635
-791.46047
-791.50987
-791.52742
-791.53318
27.0
27.0
26.9
26.8
26.8
27.3
27.1
27.1
27.1
27.1
0.2
0.2
0.3
0.3
0.3
-1.4
-1.4
-1.4
-1.3
-1.3
-395.78950
-395.86852
-395.89160
-791.31503
-791.46883
-791.51448
-791.31472
-791.46841
-791.51403
27.2
27.1
26.9
27.4
27.2
27.0
0.2
0.3
0.3
-1.4
-1.4
-1.4
1. Analytical representation of 2D and 4D surfaces
The PES is represented by starting with the 4 internal coordinates described above.
It is
important to note that degrees of freedom involving bending motions are not taken into
consideration, and this constrains the system to a linear geometry in the treatment. Noting the
general symmetry of the system, namely that the energy and the Hamiltonian are invariant under
operations that would yield q2 ↔ -q2 and q3 ↔ q4, reduces the number of parameters required to
represent the surface. In 1D, 2D, and 4D energies are represented as follows:
The 1D solution corresponds to fully optimized values of q1, q3, and q4 for a fixed q2, so the
corresponding energy is a symmetric function of q2 taking the form:
𝐸1𝐷 = 𝐸1𝐷 (𝑞2 )
(4)
The values of the function are plotted over the interval 0 Å and 9 Å and are presented in Figure
1.
The 2D solution corresponds to having both variables 𝑞1
(𝑞1 , 𝑞2 ) the coordinates q3 and q4 are fully optimized.
and 𝑞2
active. For each pair
The energy that results from the
optimizations is the corresponding 2D energy, 𝐸2𝐷 (𝑞1 , 𝑞2 ). It is found, and can be seen from
Figure 1, that for a fixed q2 the energy dependence on 𝑞1 takes the shape of a typical Morse-like
function.
Therefore, the 2D energy is written as:
𝐸2𝐷 (𝑞1 , 𝑞2 ) = 𝐸1𝐷 (𝑞2 ) + ∆𝐸2𝐷 (𝑞1 − 𝑞10 (𝑞2 ); 𝑞2 )
(5)
where 𝑞10 (𝑞2 ) is the optimized value of 𝑞1 for a given 𝑞2 . The 2D correction to the overall
energy, ∆𝐸2𝐷 , is taken as a simple Morse function in the form:
∆𝐸2𝐷 (∆𝑞1 ; 𝑞2 ) = 𝐶1 (𝑞2 )𝑦12 (∆𝑞1 ; 𝑞2 )
(6)
Where the coefficient 𝐶1 is a symmetric function of 𝑞2 , and 𝑦1 is a Morse coordinate, with the
corresponding Morse parameter being a symmetric function of 𝑞2 as well, and it is written:
y1 (∆𝑞1 ; 𝑞2 ) =
1− 𝑒 (−𝐴1 (𝑞2 )∆𝑞1 )
𝐴1 (𝑞2 )
(7)
It is found that this form gives a very accurate representation of the full 2D surface (see below
for more details), so the full description of the 2D energy surface is given by the 1D energy
(discussed above) and 3 symmetric functions of 𝑞2 , namely 𝑞10 , 𝐶1 , and 𝐴1 . These functions are
plotted on the interval 0 Å and 9 Å and shown in Figures 2a, 2b, and 2c.
The 4D potential energy surface is a function of all four internal coordinates𝑞1 , 𝑞2 , 𝑞3 , and 𝑞4 .
For 𝑞3 and 𝑞4 , both being diatomic molecular bond lengths, it is natural to assume a Morse-type
function. This function has Morse parameters consisting of the functions for 𝑞1 and 𝑞2 .
Specifically written:
𝐸4𝐷 (𝑞1 , 𝑞2 , 𝑞3 , 𝑞4 ) = 𝐸2𝐷 (𝑞1 ; 𝑞2 ) + ∆𝐸4𝐷 (𝑞3 − 𝑞3𝑜𝑝𝑡 (𝑞1 , 𝑞2 ), 𝑞4 − 𝑞4𝑜𝑝𝑡 (𝑞1 , 𝑞2 )
(8)
With ∆𝐸4𝐷 taking a simple quadratic form in Morse coordinates around the optimal values
𝑞3𝑜𝑝𝑡 (𝑞1 , 𝑞2 ) and 𝑞4𝑜𝑝𝑡 (𝑞1 , 𝑞2 ):
∆𝐸4𝐷 (∆𝑞3 ; ∆𝑞4 ; 𝑞1 , 𝑞2 ) = 𝐶3 𝑦32 (∆𝑞3 ) + 𝐶4 𝑦42 (∆𝑞4 ) + 𝐶𝑚 𝑦3 (∆𝑞3 )𝑦4 (∆𝑞4 )
(9)
Here, 𝐶3 , 𝐶4 , and 𝐶𝑚 are the functions of 𝑞1 and 𝑞2 , and 𝑦3 and 𝑦4 are the Morse coordinates for
𝑞3 and 𝑞4 , (the same form as for 𝑞1 ) and the parameters 𝐴3 and 𝐴4 are functions of 𝑞1 and 𝑞2 .
Because of the symmetry mentioned above, it is found that all quantities related to 𝑞4
(𝑞4𝑜𝑝𝑡 , 𝐶4 , and A4 ) can be obtained from those of 𝑞3 via:
𝐴4 (𝑞1 , 𝑞2 ) = 𝐴3 (𝑞1 , −𝑞2 )
(10)
while 𝐶𝑚 is a symmetric function of 𝑞2 . Therefore, the full 4D potential energy surface is
described by three functions of 𝑞1 and 𝑞2 (𝑞3𝑜𝑝𝑡 , 𝐶3 , and A3 ) on the full interval (negative and
positive) for coordinate 𝑞2 , and one symmetric function in 𝑞2 (a function of 𝑞1 , 𝑞2 , and Cm ).
Then in turn, to separate out the 𝑞1 dependence, these functions are fit to a second order
polynomial in the Morse coordinate corresponding to 𝑞1 , namely:
𝑝(𝑞1 , 𝑞2 ) = 𝑝0 (𝑞2 ) + 𝐵1𝑝 (𝑞2 )𝑦1 (∆𝑞1 ; 𝑞2 ) + 𝐵2𝑝 (𝑞2 )𝑦12 (∆𝑞1 ; 𝑞2 )
(11)
where p stands for any of 𝑞3𝑜𝑝𝑡 , 𝐴3 , 𝐶3 , or 𝐶𝑚 . This produces nine functions of 𝑞2 on the full
interval (positive and negative) and 3 functions on the positive 𝑞2 interval only, all
corresponding to 𝐶𝑚 . These functions are plotted on their respective intervals and presented in
Figures 3a and 3b. The specifics of fitting the above are discussed in the results below.
For the 1D fit, the energies are simply calculated for a set of 𝑞2 coordinates with fully
optimized 𝑞1 , 𝑞3 , and 𝑞4 . To acquire the 2D parameters, 𝐴1 and 𝐶1 , three additional 2D energy
calculations are made for a selected subset of 𝑞2 geometries. The 2D calculations require that 𝑞1
and 𝑞3 are fixed, and that 𝑞2 and 𝑞4 are optimized. The three calculations, each for a fixed 𝑞2 ,
correspond to 𝑞1 = 𝑞10 ± 0.2Å and 𝑞1 = 𝑞10 ± 0.4Å. Then, for each 𝑞2 , the four points
(together with 𝑞1 = 𝑞10 ) are used to fit the two parameters 𝐴1 and 𝐶1 . In this case, it happens
that the parameters 𝐴1 and 𝐶1 are smooth functions of 𝑞2 . To verify that the Morse form
correctly represents the dependence on 𝑞1 for the energy, additional points for 𝑞1 are calculated
at the 2D level for other values of 𝑞2 . Finally, to calculate the full 4D surface, namely fitting the
𝐴3 , 𝐶3 , and 𝐶𝑚 parameters, 10 additional energy calculations were performed (without geometry
optimization) for each 2D point (i.e. for 64 (𝑞1 , 𝑞2 ) pairs). To do this, for each 𝑞3 and 𝑞4 point
three calculations are performed. These calculations correspond to a 𝑞3 or 𝑞4 change by ±0.1 Å
and ±0.2 Å. From these calculations, 𝐴3 and 𝐶3 are produced (𝐴4 and 𝐶4 are used to produce 𝐴3
and 𝐶3 with negative 𝑞2 ). Then, four additional points with ∆𝑞3 = ±0.1Å and ∆𝑞4 = ±0.1Å,
are used to find 𝐶𝑚 . For each 𝑞2 , the four values corresponding to different 𝑞1 are fit to a second
order polynomial in 𝑞1 . This produces the 𝐵1and 𝐵2 coefficients for all 4D parameters.
As explained above, the whole 4D PES is described by 16 functions of 𝑞2 . These functions are
rather irregular so they can not be represented using simple analytic form. After some tests, the
sophisticated expressions were found that describe quite well these functions, but later we
checked that the 2D and 4D levels obtained this way were practically identical (different by
much less than 1 cm-1) to those obtained with representing these 16 functions as cubic splines.
Therefore, for the results presented in this work, the cubic splines form was used. The
FORTRAN code generating 2D and 4D surfaces, is available from authors upon request.
Figure S1 - Plot from the 1D fit
Figure S2a - Plot from the 2D fits
Figure S2b - Plot from the 2D fits
Figure S2c - Plot from the 4D fits
Figure S3 - Plot from the 4D fits showing the functions on the positive interval only.