State-to-state dissociative photoionization of molecular nitrogen: the full story

Figures & data

Figure 1. MRCI/aug-cc-pV5Z potential energy curves of the gerade (top) and ungerade (bottom) electronic states of N₂⁺. The reference energy is taken as that of N₂ (X¹∑_g⁺, v” = 0). The adiabatic ionization energy of N₂ is taken from Ref [74]. The lowest dissociation limit (L1 @ 24.2884 eV) is located as given in Ref [56]. L2 (@ 26.1874 eV) and L3 (@ 26.6724 eV) were located using the excitation energies of N⁺ and N, respectively. The thick line corresponds to N₂⁺ ground state PEC

Figure 2. Adiabatic (left) and diabatic (right) PECs of the ungerade excited states of N₂⁺ involved in the predissociation branching ratios calculations of the N₂⁺(C²∑_u⁺) state. The reference energy is taken as that of N₂(X¹∑_g⁺, v” = 0). For obtaining the diabatic PECs from the adiabatic ones, we used the B – C radial coupling from Ref [43]. in addition to the couplings presented in Figure 3

Table 1. Spectroscopic constants of the electronic states of N₂⁺ investigated in the present work. We give the equilibrium distance ($R_e$ in Å), vibrational constants (${\omega }_e$, ${\omega }_e{x}_e$, ${\omega }_e{y}_e$, in cm⁻¹) and the rotational constants ($B_e$, ${\alpha }_e$, in cm⁻¹). T₀ (in eV) is the adiabatic excitation energy calculated as the difference between the energies of the minimum of the ground state and the minimum of the considered excited state including the zero point vibrational energy corrections

State	Method	$R_e$	${\omega }_e$	${\omega }_e{x}_e$	${\omega }_e{y}_e$	$B_e$	${\alpha }_e$	T0
X^2∑g^+	This work ^a)	1.1186	2202	16.47	0.16	1.923	0.018	0
	Calc. ^b)	1.126	2200	16.10	0.04	1.897	0.018	0
	Calc. ^c)	1.1257	2140	16.7			0.012	0
	Calc. ^d)	1.1696	2075					0
	Calc. ^h)	1.1167	2207	16.62	0.03	1.930	0.018	0
	Calc. ^i)	1.1191	2198	16.09		1.922	0.018	0
	Exp. ^e)	1.1164	2207			1.931		0
	Exp. ^j)		2207	16.25		1.931	0.018	0
A^2Πu	This work ^a)	1.1800	1926	15.29	0.007	1.728	0.019	1.16
	Calc. ^f)	1.1870	1850					1.10
	Calc. ^g)	1.1812	1903					1.13
	Calc. ^h)	1.1750	1904	15.03	0.006	1.744	0.018	1.12
	Calc. ^i)	1.1772	1900	14.96		1.735	0.018	1.14
	Exp. ^e)	1.1749	1903	15.02		1.744	0.018	1.14
	Exp. ^j)		1903	15.11		1.744	0.018	1.13
B^2∑u^+	This work ^a)	1.0855	2487	23.51	2.10	2.042	0.024	3.23
	Calc. ^f)	1.0834	2370					3.14
	Calc. ^g)	1.0829	2442					3.20
	Calc. ^h)	1.0748	2419	21.53	1.15	2.084	0.021	3.17
	Calc. ^i)	1.0771	2406	23.37		2.074	0.020	3.15
	Exp. ^e)	1.0742	2419	23.19	0.53	2.07456	0.024	3.16
	Exp. ^j)		2421	24.07		2.083	0.021	3.15
a^4∑u^+	This work ^a)	1.3467	1161	8.02	1.71	1.327	0.048	4.90
	Calc. ^b)	1.353	1173	17.8		1.315	0.023	4.75
	Calc. ^d)	1.42	1186					3.5
	Calc. ^f)	1.3727	1080					4.61
	Calc. ^h)	1.3482	1182	16.90	0.02	1.325	0.023	4.78
D^2Πg	This work ^a)	1.4802	973	12.2	0.05	1.098	0.016	6.56
	Calc. ^c)	1.5235	772					6.26
	Calc. ^d)	1.5494	968					5.90
	Calc. ^h)	1.4705	909	11.9	0.03	1.1051	0.018	6.49
	Calc. ^i)	1.4740	904	11.98		1.10473	0.019	6.47
	Exp. ^e)	1.471	907	11.91	0.01	1.113	0.020	6.49
C^2∑u^+	This work ^a)	1.2585	1984	10.38	0.36	1.519	0.017	8.06
	Calc. ^f)	1.2717	1980					7.73
	Calc. ^g)	1.2643	2044					7.95
	Calc. ^h)	1.2531	2070		0.25	1.447	0.007	8.02
	Exp. ^e)	1.2628	2071	9.29	0.43	1.509	89	8.01
G^2∑g^+	This work ^a)	1.6901	923	25.04	8.12	0.881	0.002	10.07
	Calc. ^h)	1.6318	883	24.51	7.89	0.896	0.001	9.82
c^4∆u	This work ^a)	1.3384	1326		0.07	1.343	0.026	6.34
	Calc. ^b)	1.339	1258	17.5		1.341	0.021	6.23
	Calc. ^d)	1.39	1302					5.7
	Calc. ^f)	1.3585	1160					6.19
	Calc. ^c)	1.3383	1258					6.24
	Calc. ^h)	1.3355	1261	15.72	0.04	1.350	0.020	6.30
d^4∑u^−	This work ^a)	1.3321	1296	16.27	0.12	1.356	0.024	7.24
	Calc. ^b)	1.335						7.14
	Calc. ^d)	1.38						6.6
	Calc. ^h)	1.3320	1286	15.39	0.06	1.357	0.020	7.22
1^4∑g^−	This work ^a)	1.7911	586	8.12	0.47	0.766	0.017	10.19
	Calc. ^h)	1.7803	543	7.52	0.32	0.759	0.012	10.04
1^2∆u	This work ^a)	1.3670	1152	53.14	4.60	1.287	0.007	8.20
	Calc. ^f)	1.3839	1095					7.98
	Calc. ^g)	1.3785	1139					7.97
1^2∑u^−	This work ^a)	1.3491	1393	24.04	0.33	1.322	0.011	8.26
	Calc. ^f)	1.3547	1208					8.04
	Calc. ^g)	1.3489	1228					8.03
	Calc. ^h)	1.3325	1309	28.23	2.03	1.353	0.002	8.09
1^6∑u^+	This work ^a)	2.6622				0.339	0.362	8.93
f^4Πu Inner potential	This work ^a)	1.1488	2148	23.15	0.06	1.823	0.041	9.43
	Calc. ^d)	1.19	2054					9.2
	Calc. ^f)	1.1600	1986					9.44
	Calc. ^c)	1.1580	2038					9.37
	Calc. ^g)	1.1537	2104					9.40
	Calc. ^h)	1.1515	2099	22.42	0.03	1.820	0.020	9.39
f^4Πu Outer potential	This work ^a)	1.9925	413	12.35	2.74	0.606	0.025	8.39
	Calc. ^b)	2.008						8.19
	Calc. ^d)	1.84	783					7.5
	Calc. ^h)	2.0103	452	8.76	0.47	0.595	0.012	8.35
b^4Πg	This work ^a)	1.4389	1021	12.13	0.26	1.1562	0.019	5.86
	Calc. ^h)	1.4483	1008	11.41	0.11	1.1477	0.017	5.75
2^2Πu	This work ^a)	1.8929	639	7.18	0.17	0.671	0.004	9.93
	Calc. ^d)	1.7594	911					9.30
	Calc. ^c)	1.8726	705					9.13
	Calc. ^h)	1.8857	657	4.98	0.39	0.677	0.007	9.67
2^4Πu	This work ^a)	2.4106	399	3.22	2.09	0.414	0.019	10.36
	Calc. ^h)	2.4278	353	2.94	0.27	0.408	0.004	10.29
2^4∑u^−	This work ^a)	1.9897	532	14.55	3.38	0.60792	0.002	10.42
1^2Φu	This work ^a)	1.9661	599	21.07	1.20	0.62254	0.011	10.50
1^2Φg	This work ^a)	1.4663	1009	9.76	0.27	1.1304	0.02	7.66
	Calc. ^h)	1.4606	997	9.80	0.15	1.1287	0.016	7.53
3^2Πu	This work ^a)	2.8691	302	7.94	0.05	0.29234	0.001	11.57
3^2∑u^+	This work ^a)	3.1711	222	16.90	2.89	0.23995	0.012	11.81

a.MRCI/aug-cc-pV5Z.

b.MRCI/AVQZ. Ref [41].

c.MRDCI/6-311 +G(2d). Ref [57].

d.CI. Ref [58].

e.Ref [59].

f.MRDCI/6-311 +G(2d). Ref [57].

g.Extended Gaussian basis sets and large CASSCF/multireference CI wave functions/(13s 8p 6d 4f)/[4s 3p 2d 1f] ANO. Ref [67].

h.icMRCI+Q/56+CV+DK. Ref [60].

i.MRCI/aug-cc-pCV5Z. Ref [61].

j.Molecular constants have been measured using fast-ion-beam laser spectroscopy. Ref [62].

Figure 3. Radial couplings between the ²∑_u⁺ states (in A) and those between the ⁴π_u states (in B). In C), we give the transition dipole moments between the C²∑_u⁺ state and some electronic-excited states of N₂⁺. In D), we plot the spin-orbit couplings between the electronic states depicted in Figure 2

Table 2. Radiative (τ_radiative), predissociative (τ_{predissociative}) and natural (τ_natural) lifetimes of the N₂⁺(C²∑_u⁺, 0 ≤ v⁺ ≤ 15) vibrational levels. All values are in ns. ${\tau }_{C-X}^{rad}$ and ${\tau }_{C-D}^{rad}$ correspond to the radiative lifetimes associated with the C²∑_u^+_X²∑_g⁺ and C²∑_u^+_D²π_g transitions. ${\tau }_{global}^{rad}$ is the global radiative lifetime computed as $\frac{1}{{\tau }_{global}^{rad}}$ = $\frac{1}{{\tau }_{C-X}^{rad}}$ + $\frac{1}{{\tau }_{C-D}^{rad}}$. ${\tau }_{C-1}^{prediss}$, ${\tau }_{C-2}^{prediss}$ and ${\tau }_{C-3}^{prediss}$ correspond to the C state spin-orbit induced predissociation lifetimes by the 1⁴π_u, 2⁴π_u and 2⁴∑⁻_u states respectively. ${\tau }_{Cglobal,SO}^{prediss}$ is for the global predissociation lifetime computed as $\frac{1}{{\tau }_{global}^{prediss}}$ = $\frac{1}{{\tau }_{C-1}^{prediss}}$ + $\frac{1}{{\tau }_{C-2}^{prediss}}$ + $\frac{1}{{\tau }_{C-3}^{prediss}}$. . ${\tau }_C^{prediss}$ is the predissociation lifetime estimated by the time-dependent method and ${\tau }_C^{prediss}$ is due to the coupling between the C and B states only . τ_natural is deduced as $\frac{1}{{\tau }_{natural}}$ = $\frac{1}{{\tau }_{radiative}}$ + $\frac{1}{{\tau }_{predissociative}}$

	${\tau }_{C-X}^{rad}$						${\tau }_{C-D}^{rad}$	${\tau }_{global}^{rad}$	${\tau }_{C-1}^{prediss}$	${\tau }_{C-2}^{prediss}$	${\tau }_{C-3}^{prediss}$	${\tau }_{CglobalSO}^{prediss}$	${\tau }_C^{prediss}$	${\tau }_{C-B}^{prediss}$	τnatural ^a)
	Calc. ^a)	Calc. ^b)	Exp. ^c)	Exp. ^d)	Exp. ^e)	Exp. ^f)	Calc. ^a)	Calc. ^a)	Calc. ^a)	Calc. ^a)	Calc. ^a)	Calc. ^a)	Calc. ^g)	Calc. ^h)
0	68.9	65.1	70.2	800	90		677	62.57
1	62.9	62.6	66.6		90	77.0 ±3.0	607	57.01
2	61.8	60.9	64.4		90	78.9 ±3.0	770	57.24
3	60.7	59.5	62.9			4 ±1	729	56.04	28.7			28.7		7.19	18.97
4	59.2	58.5	62.1			5 ±1	783	55.03	0.585			0.585	1.67	2.46	0.573
5	62.9	57.9	62.1			5 ±1	151	44.40	2.29			2.29	1.29	1.62	2.278
6	62.2	57.5	62.6				311	51.83	1.75			1.75	1.94	1.08	1.692
7	69.9						13.4	11.24	0.0642			0.0642	2.52	0.74	0.063
8	71.6						9.18	8.13	0.0802			0.0802	0.71	0.51	0.079
9	71.3						7.83	7.15	0.0464			0.0464	0.38	0.36	0.046
10	70.6						7.16	6.50	0.341			0.341	0.98	0.29	0.324
11	20.4						80.4	16.27		5360x10^9		5360x10^9	0.32		16.26
12	10.08						81.5	8.98		2.23x10^9		2.23x10^9	0.24		8.97
13	68.3						80.3	36.91			449	449	0.31		34.01
14	176						80.9	55.42			5.16	5.16	0.21		4.72
15	71.18						7.11	6.46			978	978	0.0017		6.41

a.This work, Fermi Golden rule with spin-orbit channels.

b.CASSCF/MRCI computations where the valence orbitals are considered in the active space. Ref [67].

c.Derived using an RKR potential using available experimental data. Ref [67].

d.Ref [21].

e.Govers and co-workers. Refs. [24,25].

f.Erman [26] using high-resolution High Frequency Deflection technique.

g.This work, time-dependent method.

h.Fermi Golden rule with B state, Ref [43].

Figure 4. Intensity of dissociative ionization events yielding N⁺ fragments recorded at a photon energy of 27.2 eV, as a function of electron kinetic energy (Ele KE) and N⁺ kinetic energy. Diagonal white dashed lines point the three accessible dissociation limits, while the white vertical lines represent the expected position of the N₂⁺(C²∑_u⁺) vibrational levels from v⁺ = 3 until v⁺ =15, according to Yoshii et al. [75]

Figure 5. Kinetic energy release distributions of the N⁺ fragment generated from N₂⁺ (C²∑_u⁺) v⁺ =11 to 15, recorded at a fixed photon energy of 27.2 eV. The dashed diagonal lines show the three different dissociation limits available. For v⁺ =14 and v⁺ =15, the curves are also shown after multiplication by an order of magnitude to accentuate the weak dissociation to L2 and L1. The branching ratios to the three dissociation limits are provided for the five vibrational levels in Table 3

Figure 6. Number of dissociation events towards the three available limits, L1 (black), L2 (blue) and L3 (red), recorded at hv = 27.2 eV as a function of the electron kinetic energy. The relative intensity of the curves corresponds to the branching ratios to the three dissociation limits. The positions of the N₂⁺(C²∑_u⁺) vibrational levels from Yoshii et al. [75] are marked in magenta, as well as four different progressions in gray S1(2²Π_g), S2(²∑_u⁻), S3(²Δ_u) and S4(²Π_u) from the same reference

Table 3. Experimental and calculated branching ratios (in %) for the N₂⁺ (C²∑_u⁺, v⁺) vibrational levels. The energies of the vibrational levels (E_v, in eV) are given with respect to N₂ (X¹∑_g⁺, v” = 0). L₁, L₂ and L₃ refer to the first, second, and third dissociation limits as specified in Figure 1

Vib. Level	Ev					Branching ratios
			exp.			Calc. ^a)						Calc. ^b)
						^d)			^e)			^d)			^f)			^g)
			L1	L2	L3	L1	L2	L3	L1	L2	L3	L1	L2	L3	L1	L2	L3	L1	L2	L3
3 ≤ v^+ ≤ 9	-	This work	100.0	0.0	0.0	100.0	0.0	0.0	100.0	0.0	0.0	100.0	0.0	0.0	100.0	0.0	0.0	100.0	0.0	0.0
		Ref. [28] ^c)	100	0	0
v^+ = 10	25.961	This work	100.0	0.0	0.0	100.0	0.0	0.0	100.0	0.0	0.0	90.9	9.1	0.0	90.9	9.1	0.0	99.0	1.0	0.0
		Ref. [28] ^c)	100	0	0
v^+ = 11	26.174	This work	74 ±4	26 ±6	0.0	98.0	2.0	0.0	99.0	1.0	0.0	99.8	0.2	0.0	99.8	0.2	0.0	88.2	11.8	0.0
		Ref. [28] ^c)	40	60	0
v^+ = 12	26.382	This work	45 ±2	55 ±2	0.0	74.1	25.9	0.0	88.0	12.0	0.0	80.5	19.5	0.0	79.2	20.8	0.0	88.8	11.2	0.0
		Ref. [28] ^c)	50	50	0
v^+ = 13	26.583	This work	43 ±2	57 ±1	0	46.5	53.5	0.0	54.1	45.9	0.0	83.8	16.2	0.0	33.3	66.7	0.0	79.0	21.0	0.0
		Ref. [28] ^c)	40	60
v^+ = 14	26.778	This work	14 ±2	10 ±8	76 ±3	1.0	99.0	0.0	0.0	4.1	95.9	0.0	0.1	99.9	0.0	0.22	99.78	3.1	2.4	94.4
		Ref. [28] ^c)	0.0	0.0	100.0
v^+ = 15	26.966	This work	7 ±2	10 ±6	84 ±9	0.0	100.0	0.0	0.0	3.1	96.9	0.0	0.05	99.95	0.0	0.1	99.9	0.8	10.4	88.8
		Ref. [28] ^c	0.0	0.0	100.0

a.Time-independent dynamical computations.

b.Time-dependent dynamical computations.

c.Threshold photoelectron-photoion coincidence spectroscopy.

d.Branching ratios calculated due to predissociation by the 1⁴Π_u, 2⁴Π_u and 3⁴Π_u states

e.Branching ratios calculated due to predissociation by the 1⁴Π_u, 2⁴Π_u, D²Π_u and 2⁴∑_u⁻ states

fBranching ratios calculated due to predissociation by the 3²∑_u⁺ 1⁴Π_u, 2⁴Π_u, 3⁴Π_u and 2⁴∑_u⁻ states

gBranching ratios calculated due to predissociation by the 3²∑_u⁺ B²∑_u⁺1⁴Π_u, 2⁴Π_u, 3⁴Π_u and 2⁴∑_u⁻ states

Figure 7. Threshold photoelectron photoion coincidence (TPEPICO) curves obtained for N⁺ (red) and N₂⁺ (black) by selecting only the photoionization events that correlate with the emission of a threshold electron. The threshold selection is achieved using the slow photoelectron method outlined by Poully et al. [77] and the parameters are set to deliver a total resolution of 15 meV. The vertical-dashed line represents the first dissociation limit towards N⁺(³P) + N(⁴S). Positions of the N₂⁺ (C²∑_u⁺) 0 ≤ v⁺ ≤ 3 vibrational levels are from Yoshii et al. [75]

Figure 8. Photodissociation cross-sections of a Franck-Condon wave packet computed in three electronic basis sets. Panels (a) and (b): three ²∑_u⁺, three ⁴Π_u and one ⁴∑_u⁻ states; panels (c) and (d): three ²∑_u⁺ states; panels (e) and (f): B²∑_u⁺and C²∑_u⁺ states only

Figure 9. Time evolution of the wavepacket initially prepared in the v⁺ = 0, 4, 10, 11, 12, 13, 14 and 15 vibrational levels of the C²∑_u⁺ state of N₂⁺ populating the C²∑_u⁺, B²∑_u⁺, 3²∑_u⁺, 1⁴Π_u, 2⁴Π_u, 3⁴Π_u and 2⁴∑_u⁻ states. These evolutions are confirmed by longer dynamics (not shown). For v⁺ = 15, the populations are almost those at t = 12 ps

Figure 10. In A): Average position of the first 100 vibrational eigenstates of the C²∑_u⁺ state with a discretization of the dissociation continuum. In the blue region, we give those located mainly in the inner potential well of the C state (i.e. v⁺ = 0–15). The v⁺ quantum number does not correspond to the eigenstate number for v⁺ > 10 but continues the series of eigenstates located in the inner well with an increasing number of nodes. The v⁺ = 0–15 levels are marked by red crosses. In the red region, those located in the outer potential well. In the yellow region, those delocalised in the continum (but artificially localized at long distance due to the finite grid). In the inset, we give an enlargement for the 20 first eigenstates where we can distinguish the v⁺ =0 – 12 eigenstates located in the inner potential well of the C state (red region). In B-F), we plot the vibrational wavefunctions of the N₂⁺(C²∑_u⁺) state for v⁺ = 0, 4, 13, 14 and 15, respectively. The energies of these levels with respect to the vibrationless N₂ ground state are also given. See text for more details

Merkt F, Softley TP. Rotationally resolved zero-kinetic-energy photoelectron spectrum of nitrogen. Phys Rev A. 1992;46:302.

 PubMed Web of Science ®Google Scholar

Tang X, Hou Y, Ng CY, et al. Pulsed field-ionization photoelectron-photoion coincidence study of the process N2+hν → N+ + N+ + e−: bond dissociation energies of N2 and N2+. J Chem Phys. 2005;123:074330.

 PubMed Web of Science ®Google Scholar

Paulus B, Pérez-Torres JF, Stemmle C. Time-dependent description of the predissociation of N2+ in the C2Σu+ state. Phys Rev A. 2016;94:053423.

 Web of Science ®Google Scholar

Hochlaf M, Chambaud G, Rosmus P. Quartet states in the N2+ radical cation. J Phys B: At Mol Opt Phys. 1997;30:4509.

 Web of Science ®Google Scholar

Bruna PJ, Grein F. The X2Σg+ and B2Σu+ states of N2+: hyperfine and nuclear quadrupole coupling constants, electric quadrupole moments, and electron-spin g-factors. A theoretical study. J Mol Spectrosc. 2004;227:67.

 Web of Science ®Google Scholar

Thulstrup EW, Andersen A. Configuration interaction studies of bound, low-lying states of N2−, N2, N2+ and N22+. J Phys B. 1975;8:965.

 Web of Science ®Google Scholar

Access date: 10/09/2020. Available from: http://Webbook.nist.gov

 Google Scholar

Langhoff SR, Bauschlicher CW Jr. Theoretical study of the first and second negative systems of N2+. J Chem Phys. 1988;88:329.

 Web of Science ®Google Scholar

Liu H, Shi D, Wang S, et al. Theoretical spectroscopic calculations on the 25 Λ–S and 66 Ω states of cation in the gas phase including the spin–orbit coupling effect. J Quant Spectrosc Radiat Transf. 2014;147:207.

 Web of Science ®Google Scholar

Shi D, Xing W, Sun J, et al. Spectroscopic constants and molecular properties of X2Σg+, A2Πu, B2Σu+ and D2Πg electronic states of the N2+ ion. Comput Theor Chem. 2011;966:44.

 Web of Science ®Google Scholar

Scholl TJ, Holt RA, Rosner SD. Fine and Hyperfine Structure in 14N2+: the B2Σ+u-X2Σ+g(0,0) Band. J Mol Spectrosc. 1998;192:424.

 PubMed Web of Science ®Google Scholar

Wankenne H, Momigny J. Monomolecular and collision-induced predissociation in the mass spectrum of N2+. Int J Mass Spectrom Ion Phys. 1971;7:227.

 Google Scholar

Fournier P, van de Runstraat CA, Govers TR, et al. Collision-induced dissociation of 10 keV N2+ ions: evidence for predissociation of the C2Σu+ state. Chem Phys Lett. 1971;9:426.

 Web of Science ®Google Scholar

Van de Runstraat CA, de Heer FJ, Govers TR. Excitation and decay of the C2Σu+ state of N2+ in the case of electron impact on N2. Chem Phys. 1974;3:431.

 Web of Science ®Google Scholar

Erman P. Direct Measurement of the N2+ C state predissociation probability. Phys Scr. 1976;14:51.

 Web of Science ®Google Scholar

Yoshii H, Tanaka T, Morioka Y, et al. New N2+ electronic states in the region of 23-28 eV. J Mol Spectrosc. 1997;186:155.

 PubMed Web of Science ®Google Scholar

Nicolas C, Alcaraz C, Thissen R, et al. Dissociative photoionization of N2 in the 24–32 eV photon energy range. J Phys B: At Mol Opt Phys. 2003;36:2239.

 Web of Science ®Google Scholar

Poully JC, Schermann JP, Nieuwjaer N, et al. Photoionization of 2-pyridone and 2-hydroxypyridine. Phys Chem Chem Phys. 2010;12:3566.

 PubMed Web of Science ®Google Scholar