Phosphorescence of Hydrogen-Capped Linear Polyyne Molecules C₈H₂, C₁₀H₂ and C₁₂H₂ in Solid Hexane Matrices at 20 K

Abstract

Laser-ablated polyyne molecules, H(C≡C)_nH, were separated by size in solutions and co-condensed with excess hexane molecules at a cryogenic temperature of 20 K in a vacuum system. The solid matrix samples containing C₈H₂, C₁₀H₂, and C₁₂H₂ molecules were irradiated with UV laser pulses and the phosphorescence 0–0 band was observed at 532, 605, and 659 nm, respectively. Vibrational progression was observed for the symmetric stretching mode of the carbon chain in the ground state with increments of ~2190 cm⁻¹ for C₈H₂, ~2120 cm⁻¹ for C₁₀H₂, and ~2090 cm⁻¹ for C₁₂H₂. Temporal decay analysis of the phosphorescence intensity revealed the lifetimes of the triplet state as ~30 ms for C₈H₂, ~8 ms for C₁₀H₂, and ~4 ms for C₁₂H₂. The phosphorescence excitation spectrum reproduces UV absorption spectra in the hexane solution and in the gas phase at ambient temperature, although the excitation energy was redshifted. The symmetry-forbidden vibronic transitions were observed for C₁₀H₂ by lower excitation energies of 25,500–31,000 cm⁻¹ (320–390 nm). Detailed phosphorescence excitation patterns are discussed along the interaction of the polyyne molecule and solvent molecules of hexane.

1. Introduction

Hydrogen-end-capped linear polyyne molecules, H(C≡C)_nH or C_2nH₂ (n ≥ 2), constitute a series of model compounds for sp-hybridized carbon species [1,2]. Since the discovery of cyanopolyynes, H(C≡C)_nC≡N or HC_2n+1N (n ≥ 2), in the molecular clouds and circumstellar shells of a red giant (a carbon star in AGB) by radio astronomical observations [3,4,5,6,7], they have been thought of as candidates for interstellar molecules [8]. Laboratory experiments revealed UV absorption spectra of C_2nH₂ up to n = 12, thanks to the organic synthesis in the early 1970s [9,10]. Infrared absorption spectra, as well as the UV spectra, were measured for C₆H₂ and C₈H₂ in the gas phase [11,12]. Recently, cyanopolyynes of molecular formulae, HC_2n+1N, have been synthesized in the laboratory up to n = 2 and reacted in cryogenic matrices into larger derivatives to identify their phosphorescence spectra [13,14,15,16,17,18,19,20,21]. Very recently, photosyntheses were conducted using polyynic precursors of HC₅N and C₄H₂ co-condensed in solid rare gas matrices, and the detection of phosphorescence of HC₉N was successful [18]. Using laser-ablated cyanopolyynes, the phosphorescence measurement was extended to HC₉N and HC₁₁N in solid organic molecules at 20 K as matrix hosts [22].

Polyyne molecules were formed by the laser ablation of carbon particles [23,24] as well as by the arc discharge of graphite in organic solvents [1]. The formation of hydrogen-capped polyyne molecules was confirmed up to C₂₆H₂ by the laser ablation in decalin [25]. Spectroscopic characterization has so far been performed by UV absorption [9,10], IR absorption [11,12,19,22,26], Raman [17,24], and resonance Raman spectroscopy [27,28]. In relation to the formation mechanism, ¹H-NMR and ¹³C-NMR were applied to polyynes, C₁₀H₂ and C₁₂H₂ [28], and cyanopolyynes, HC₇N and HC₉N [29]. Using the size-separated polyyne molecules of C_2nH₂ (n = 5–8), optical emission spectra were observed in solutions of hexane at ambient temperature [30]. Since the spectral range of the emission spanning from near-UV to visible [30] differs to that for the phosphorescence of cyanopolyynes of a relevant size [16,18], the emission was attributed to the fluorescence of polyyne molecules. To obtain evidence for the assignment, we planned to observe the phosphorescence of C_2nH₂ (n = 4–6) in this work.

For the measurement of phosphorescence, it is crucial to keep the molecular samples at cryogenic temperature in a condensed phase. However, the unsaturated polyyne molecules are highly reactive, leaving polymerized materials at high concentration. In solutions, the molecules are stable only under the dilute condition of less than ~1 mg/mL. We decided to allow the solution to be condensed directly on a cold surface under vacuum, where laser-induced phosphorescence measurements were performed. Dispersed phosphorescence spectra were recorded for C₈H₂, C₁₀H₂, and C₁₂H₂ within a range of 500–1000 nm by scanning the excitation wavelength in the ranges of UV, 213–302 nm, and near-UV, 302–409 nm, and converted to phosphorescence excitation spectra. Phosphorescence lifetimes were also measured and compared along the difference in size, n.

2. Materials and Methods

Polyyne molecules were produced by the laser ablation of graphite particles in liquid hexane by irradiation with the 1064 nm output at ~0.5 J/pulse from a Nd:YAG laser system operated at 10 Hz (Continuum, Santa Clara, CA, USA, Powerlite 8010). The solution after laser irradiation was filtrated to remove solid particles to obtain a yellow solution, which is subjected to high-performance liquid chromatography (HPLC, Shimadzu, Kyoto, Japan, LC-10) using a polymeric ODS column (Wako Chemicals, Tokyo, Japan, Wakosil 5C-18AR, i.d. 10 mm × 250 mm) eluted with hexane to separate the molecules of C₈H₂, C₁₀H₂, and C₁₂H₂ [24,28,29,30]. The concentration and purity of polyyne, C_2nH₂, in the solution were estimated by the measurement of UV absorption spectra.

The C₈H₂ molecules isolated in a solution of hexane were condensed by using a rotary evaporator to a volume of ~1 mL at a concentration of ~1 mg/mL. Having similar molecular weights, 98 for C₈H₂ and 84 for hexane, the order of molecular number ratio of C₈H₂ to hexane is 1:1000, corresponding to the condition in which ten solvent molecules lie between two neighboring C₈H₂ molecules on average, though a fraction of C₈H₂ vaporizes together with hexane to reduce the efficiency of concentration. The concentrated solution was conducted into the vacuum system through a tubing of 0.10 mm in inner diameter. Reaching the exit of the tubing, the solution was sprayed onto a nearby cupper slab cooled at 20 K using a closed-cycle helium refrigerator (Daikin, Osaka, Japan, V202CL), where the C₈H₂ molecules and the excess hexane molecules were co-condensed as an opaque, milky white, solid matrix sample. By the rapid introduction of the solution within several seconds, even droplets were directly condensed on the cold surface. The dimerization of C₈H₂ molecules was minimized and the C₈H₂/hexane ratio in the solid matrix sample was more or less the same as the precursory condensed solution. The introduction of the room temperature solution results in the instantaneous warming of the cold surface to ~60 K. The measurement was performed after waiting for the cold surface to be cooled down to 20 K.

The solid matrix sample at 20 K was irradiated with UV laser pulses of the second harmonic of an OPO output excited with nanosecond 355 nm laser pulses (Spectra Physics, Santa Clara, CA, USA, VersaScan-MB/INDI40). Emitted photons from the surface of the UV-irradiated matrix sample were collected through an optical-fiber bundle and dispersed by a polychromator (Acton Research Corporation, Acton, MA, USA, Model 320i) and recorded on a liquid-nitrogen-cooled CCD array detector (Princeton Instruments, Trenton, NJ, USA, PyLoN:256-OE) in a spectral range of 500–1000 nm. A long-pass glass filter having an appropriate cut-off wavelength was used to reduce stray light. The excitation wavelength was slowly scanned in a range of 213–302 nm and a series of dispersed emission spectra were recorded redundantly. Spectral resolution was ~0.1 nm for dispersed phosphorescence and 0.2–0.5 nm for the excitation spectrum.

Lifetime measurement was performed for selected bands of phosphorescence by using a photomultiplier detector (Hamamatsu Photonics, Hamamatsu, Japan, R928) and a digitizing oscilloscope (LeCroy, Chestnut Ridge, NY, USA, WavePro 954). The waveform of amplified phosphorescence signals was summed over 1000 laser pulses and transferred to a PC. The same experimental procedures of the spectral measurement and the lifetime measurement for C₈H₂ were applied also to C₁₀H₂ and C₁₂H₂. For the longer wavelength excitation in 302–409 nm for C₁₀H₂, the sum-frequency mixing (SFM) of the OPO system was exploited.

3. Results

3.1. Phosphorescence Spectra and Excitation Spectra

Figure 1 shows a dispersed phosphorescence spectrum of C₈H₂ embedded in a solid hexane matrix at 20 K, observed at the excitation of 231.8 nm. Peaks are conspicuous at 532.3, 602.4, 693.2, 815.1, and 986.9 nm for the 0–0, 0–1, 0–2, 0–3, and 0–4 bands, respectively. Adjacent peaks in the series of transitions from the v = 0 level in the upper electronic state to v = 0, 1, 2, 3, and 4 levels in the lower electronic state are separated by successive increments of 2190, 2172, 2157, and 2136 cm⁻¹, which are attributable to the member of a vibrational progression of the symmetric stretching σ_g mode of the sp-carbon chain in the electronic ground state, X¹∑_g⁺. The upper state of the phosphorescence is the lowest triplet state, a³∑_u⁺. Smaller peaks are discernible between the high-intensity peaks. Appearing in a similar pattern repeatedly in the gaps, these tiny peaks are attributable to combination bands of some symmetric vibrational species with the symmetric stretching σ_g mode.

Figure 2 illustrates the phosphorescence excitation mapping for the 0–1 band of C₈H₂ at 602.5 nm. Relatively strong emission was observed when the excitation wavelength was set at 232 nm and 221 nm. The trace in white at the bottom of the panel represents the intensity of the horizontal cross section at the excitation of 232 nm. The peak at 602.5 nm is again the 0–1 band of the phosphorescence. Small peaks near 620 and 640 nm are the combinations. A few satellite peaks accompany the foot of the main peak at 602.5 nm, which are signals belonging to the same σ_g mode, but their photons of phosphorescence are emitted from molecules in different environments in the matrix sample. A less intense but almost identical phosphorescence spectrum is obtained at the excitation of 221 nm. The series of spots corresponding to the phosphorescence peaks are discernible along the horizontal line at 221 nm in the mapping. As a result, the strong phosphorescence peak at 602.5 nm appears twice, at excitation wavelengths of 232 and 221 nm. When the intensity of phosphorescence at 602.5 nm is plotted as a function of the excitation wavelength, we obtain another spectrum in yellow in the left of the panel. This action spectrum primarily represents the strength of absorption at relevant UV wavelength and is called an excitation spectrum. The upper electronic state is designated as ¹∑_u⁺, to which the UV photon lifts the molecule to be excited from the ground state, X¹∑_g⁺.

Figure 3 shows the excitation spectrum for the 0–1 band in the phosphorescence at 603 nm of C₈H₂, plotted as a function of energy. The intensity is scaled according to the conversion from wavelength to energy. Two major bands, namely the 0–0 band at 43,113 cm⁻¹ and the 1–0 band at 45,243 cm⁻¹, constitute the vibrational progression of the symmetric stretching σ_g mode in the excited state, ¹∑_u⁺. The increment of 2130 cm⁻¹ is smaller than the phosphorescence counterpart of 2190 cm⁻¹, indicating a slightly shallow potential with a lower harmonic frequency in the excited state, ¹∑_u⁺. The overall shape of the excitation spectrum and the vibrational frequency in the upper state are explainable by the absorption of a UV photon via the fully allowed electric dipole transition, ¹∑_u⁺ ← X¹∑_g⁺. When the transition energy of the 0–0 band is compared with that observed at 43,960 cm⁻¹ by UV absorption in the solution of hexane, the peak in the solid matrix is redshifted by 847 cm⁻¹. Weaker bands or shoulders at the higher energy side of the major bands in Figure 3 are rather close to the bands in the UV absorption spectrum in the solution of hexane, i.e., at 227 nm (44,050 cm⁻¹) for the 0–0 band and 216 nm (46,300 cm⁻¹) for the 1–0 band. The band with a shoulder in the phosphorescence excitation curve is fitted with three Gaussian functions to provide two narrow bands and a broad component for the base line. Among the two sets of the narrow-band features, one is the major component of high intensity, and the other is the minor component at the shoulder located close to the position of peaks in the solution at ambient temperature.

Figure 4 compares the dispersed phosphorescence spectra of C₈H₂, C₁₀H₂ and C₁₂H₂ with the excitation at 231.8, 259.0, and 282.0 nm, respectively, where the phosphorescence intensity is maximum for each size. As is expected for a particle-in-a-box model, the phosphorescence wavelength, as well as the excitation wavelength, shifts to a longer wavelength as the size of the carbon chain increases. The 0–0 band of phosphorescence appears at 532.3 nm for C₈H₂, 605.1 nm for C₁₀H₂, and 658.8 nm for C₁₂H₂. The vibrational progression is conspicuous for the symmetric stretching σ_g mode for each polyyne, exhibiting an increment of ~2190, ~2120, and ~2090 cm⁻¹ for C_2nH₂ of n = 4, 5, and 6, respectively. The bands of C₁₀H₂ and C₁₂H₂ are relatively broad compared with those of C₈H₂, probably because of the lack of uniformity in the packing patterns of molecules surrounding the C_2nH₂ molecule. As is seen in the dashed line for C₁₀H₂ in Figure 4, a slightly different excitation wavelength at 261.7 nm provides a different band shape with a sharp phosphorescence peak at 599.4 nm, and with a broad distribution of satellites up to 605 nm. The detailed matrix effect is discussed in the latter Section 4.4. Despite the broadness of bands, peaks are discernible for major features: (1) the σ_g vibrational progression with three bands and (2) the combination bands between the major bands of σ_g.

Figure 5a shows the phosphorescence excitation spectrum obtained from the intensity of the 0–0 band of C₁₀H₂ in solid hexane at 20 K. The absorption spectra of C₁₀H₂ at ambient temperature are shown for comparison (b) in the solution of hexane and (c) in the gas phase. The measurement of the spectrum in the gas phase (c) is conducted as follows; a small amount of the concentrated solution of C₁₀H₂ in hexane was introduced into an evacuated quartz cell of 10 cm path length and the cell was set in the sample chamber of the double-beam UV spectrophotometer (Jasco, Hachioji, Japan, V-670). The 0–0 band peaked at 43,690 cm⁻¹ (228.9 nm) in (c) and at 39,640 cm⁻¹ (252.3 nm) in (b), indicating a solvent shift of −4050 cm⁻¹ for hexane. In the excitation spectrum (a) for the hexane matrix at 20 K, the most intense band peaked at 38,728 cm⁻¹ (258.2 nm), revealing a further redshift of −912 cm⁻¹ from the peak in the hexane solution. In general, the tight packing of the solvent molecules in cryogenic solid matrices results in a stronger interaction between the host and guest molecules, and the electronically excited state of the guest polyyne molecule is stabilized further to redshift its absorption/excitation spectrum.

Figure 6 shows the phosphorescence excitation mapping of the 0–1 band of C₁₂H₂ (left) and an excitation spectrum (right) plotted using the phosphorescence intensity at 761.7 nm (solid line). The absorption spectrum in the solution at ambient temperature is overlapped (dashed line), showing the redshift of −840 cm⁻¹ for the solid matrix relative to the liquid solution of C₁₂H₂/hexane.

Table 1. Peaks in cm⁻¹ (nm) for the phosphorescence excitation spectra of polyyne molecules, C_2nH₂ (n = 4–6), in solid hexane matrices at 20 K. Peaks in the absorption spectra in the hexane solution and in the gas phase are listed for comparison.

Molecule	Assignment 1	Solid Matrix Hexane (20 K)	Solution 2 Hexane	Gas Phase 2
C8H2	0–0	43,113 (231.9)	43,960 (227.5)	48,190 (207.5)
	1–0	45,243 (221.0)	46,080 (217.0)	50,280 (198.9)
	2–0		48,190 (207.5)	52,380 (190.9)
C10H2	0–0	38,728 (258.2)	39,640 (252.3)	43,690 (228.9)
	1–0	40,815 (245.0)	41,670 (240.0)	45,790 (218.4)
	2–0	42,909 (233.1)	43,630 (229.2)	47,820 (209.1)
	3–0	44,940 (222.5)	45,600 (219.3)
C12H2	0–0	35,420 (282.3)	36,260 (275.8)	40,370 (247.7)
	1–0	37,511 (266.6)	38,300 (261.1)	42,340 (236.2)
	2–0	39,469 (253.4)	40,230 (248.6)	44,250 (226.0)
	3–0	41,457 (241.2)	42,160 (237.2)
	4–0	43,292 (231.0)	44,010 (227.2)

¹ Change in the symmetric stretching σ_g vibrational level in the ¹∑_u⁺ ← X¹∑_g⁺ transition. ² Measurement at room temperature.

summarizes the observed peaks in the phosphorescence excitation spectra of C₈H₂, C₁₀H₂, and C₁₂H₂, together with their absorption peaks in solutions and in the gas phase. Molecular constants in the electronically excited state, ¹∑_u⁺, are listed in

Table 2. Molecular constants in cm⁻¹ of the electronically excited state, ¹∑_u⁺, of polyyne molecules, C_2nH₂ (n = 4–6) in solid/liquid hexane and in the gas phase. Vibrational constants, ω_e’ and ω_ex_e’, are for the alternating CC stretching σ_g mode.

Molecule	Constant	Solid cm−1	Solution cm−1	Gas cm−1
C8H2	T * 1	42,048	42,896	47,145
	ωe’	2130 2	2130	2090 2
	ωexe’	–	5	–
C10H2	T * 1	37,663	38,626	42,614
	ωe’	2129	2044	2170
	ωexe’	14	15	35
C12H2	T * 1	34,361	35,237	39,362
	ωe’	2141	2072	2030
	ωexe’	34	27	30

¹ T * = T₀ − ω_e”/2 + ω_ex_e”/4. Zero-point energy in the electronic ground state is included. ² Difference in the transition energies for the 1–0 and 0–0 bands.

. Figure 7 plots the transition energies of the electronic ¹∑_u⁺ ↔ X¹∑_g⁺ system of C_2nH₂ (n = 4–6), showing the solvent shift (gas–solution) and the matrix shift (solution–solid matrix).

3.2. Lifetimes

Figure 8 illustrates the typical decay profiles of phosphorescence intensity at 20 K for the 0–0 and 0–1 bands of C₈H₂ (red), C₁₀H₂ (black), and C₁₂H₂ (blue). From the slope of the logarithmic plot, phosphorescence lifetime was deduced for each trace by fitting to a single exponential component. The lifetime was ~31 ms for C₈H₂, ~8.4 ms for C₁₀H₂, and ~3.9 ms for C₁₂H₂, showing a decreasing property as the number of carbon atoms in a molecule increases. A longer polyyne such as C₁₄H₂ should exhibit a weak phosphorescence signal at a longer wavelength.

For C₁₀H₂, depending on the phosphorescence peak wavelengths within the 0–0 band (599–605 nm), the observed decay rates deviated from 6 ms to 16 ms due to the different rates of intersystem crossing and/or internal conversion in the different trapping sites in the solid matrix host.

3.3. Vibrational Bands

Vibrational overtones and combinations in the dispersed phosphorescence in Figure 1 and Figure 4 are summarized in

Table 3. Overtone and combination bands observed in the dispersed phosphorescence spectra of C_2nH₂ (n = 4–6) in solid hexane matrices at 20 K. Vibrational mode characteristics are noted for (a) the alternating C≡C and C–C stretching mode, σ_g (2100–2200 cm⁻¹), (b) the longitudinal breathing mode, σ_g’, (c) the even-numbered overtone of the trans-zigzag bending mode, π_g (~620 cm⁻¹), and (d) the even-numbered overtone of the cis-zigzag bending mode, π_g’ for C₁₀H₂ and π_u’ for C₈H₂ and C₁₂H₂ (~240 cm⁻¹).

Molecule	Observed Band cm−1 (nm)	Difference Frequency cm−1		Vibrational Mode Assignment
C8H2	18,788 (532.3)	0	$0_0^0$		0–0 band
	18,305	483	$5_1^0$	σg’	breathing b
		and/or	${16}_2^0$	πu’2	cis-zigzag d
	17,819	969	${16}_4^0$	πu’4	cis-zigzag d
	17,540	1248	${11}_2^0$	πg2	trans-zigzag c
	16,597 (602.4)	2190	$2_1^0$	σg	alternating CC str. a
	16,126	471	$2_1^0{5}_1^0$	σg + σg’	breathing b
		and/or	$2_1^0{16}_2^0$	σg + πu’2	cis-zigzag a,d
	15,646	951	$2_1^0{16}_4^0$	σg + πu’4	cis-zigzag a,d
	15,352	1245	$2_1^0{11}_2^0$	σg + πg2	trans-zigzag a,c
	14,426 (693.2)	2172	$2_2^0$	σg2	alternating CC str. a
	13,959	467	$2_2^0{5}_1^0$	σg2 + σg’	breathing b
		and/or	$2_2^0{16}_2^0$	σg2 + πu’2	cis-zigzag a,d
	13,183	1243	$2_2^0{11}_2^0$	σg2 + πg2	trans-zigzag a,c
	12,268 (815.1)	2157	$2_3^0$	σg3	alternating CC str. a
	10,133 (986.9)	2136	$2_4^0$	σg4	alternating CC str. a
C10H2	16,525 (605.1)	0	$0_0^0$		0–0 band
	16,145	380	$6_1^0$	σg’	breathing b
	16,042	483	${15}_2^0$	πg’2	cis-zigzag d
	15,560	965	${15}_4^0$	πg’4	cis-zigzag d
	15,293	1232	${13}_2^0$	πg2	trans-zigzag c
	14,405 (694.2)	2120	$3_1^0$	σg	alternating CC str. a
	14,031	374	$3_1^0{6}_1^0$	σg + σg’	breathing a,b
	13,930	475	$3_1^0{15}_2^0$	σg + πg’2	cis-zigzag a,d
	13,456	949	$3_1^0{15}_4^0$	σg + πg’4	cis-zigzag a,d
	13,172	1233	$3_1^0{13}_2^0$	σg + πg2	trans-zigzag a,c
	12,300 (813.0)	2105	$3_2^0$	σg2	alternating CC str. a
	11,902	398	$3_2^0{6}_1^0$	σg2 + σg’	breathing a,b
	11,847	453	$3_2^0{15}_2^0$	σg2 + πg’2	cis-zigzag a,d
	10,210 (979.4)	2090	$3_3^0$	σg3	alternating CC str. a
C12H2	15,178 (658.8)	0	$0_0^0$		0–0 band
	14,869	309	$7_1^0$	σg’	breathing b
	14,699	479	${23}_2^0$	πu’2	cis-zigzag d
	14,205	973	${23}_4^0$	πu’4	cis-zigzag d
	13,883	1295	${15}_2^0$	πg2	trans-zigzag c
	13,088 (764.1)	2090	$3_1^0$	σg	alternating CC str. c
	12,765	323	$3_1^0{7}_1^0$	σg + σg’	breathing a,b
	12,602	486	$3_1^0{23}_2^0$	σg + πu’2	cis-zigzag a,d
	11,008 (908.4)	2080	$3_2^0$	σg2	alternating CC str. a
	10,699	309	$3_2^0{7}_1^0$	σg2 + σg’	breathing a,b

. Figure 9 plots the observed vibrational levels for (a) C₈H₂, (b) C₁₀H₂, and (c) C₁₂H₂. The electronic transition from the lowest triplet state to the ground state, a³∑_u⁺ → X¹∑_g⁺, is spin forbidden but the other conditions are common with the fully allowed transition, ¹∑_u⁺ ↔ X¹∑_g⁺, because excited states in both transitions commonly stem from the single-electron HOMO–LUMO excitation. In this case, totally symmetric vibrational species tend to appear as overtones and combinations. The main progression with the increment of 2100–2200 cm⁻¹ is associated with the alternating C≡C and C–C stretching σ_g mode of the sp-carbon chain, i.e., ν₂σ_g of C₈H₂, ν₃σ_g of C₁₀H₂, and ν₃σ_g of C₁₂H₂, in which all the triple bonds expand and all the single bonds shrink simultaneously, and vice versa. In

Table 4. Molecular constants in cm⁻¹ obtained from the analysis of the a³∑_u⁺ → X¹∑_g⁺ phosphorescence spectra for polyyne molecules, C_2nH₂ (n = 4–6), in solid hexane matrices at 20 K. Vibrational constants are deduced for the alternating CC stretching σ_g mode in the electronic ground state, X¹∑_g⁺.

Molecule	T * 1 cm−1	ωe” cm−1	ωexe” cm−1	Mode	Raman 2 cm−1
C8H2	19,888	2205	8.1	ν2σg	2172
C10H2	17,590	2135	7.5	ν3σg	2123
C12H2	16,227	2100	5.0	ν3σg	2096

¹ T * = T₀ + ω_e’/2 − ω_ex_e’/4. Zero-point energy in the lowest spin-triplet state, a³∑_u⁺, is included. ² The Stokes Raman fundamental energy of the 1–0 transition in hexane solutions [24,25,28].

, molecular constants deduced from the σ_g progression in the dispersed phosphorescence spectra are summarized for the electronic ground state, X¹∑_g⁺.

For candidates of the combination bands appearing between the peaks of the σ_g progression, totally symmetric species are possible by the other symmetric stretching σ_g modes and by even-numbered overtones of antisymmetric stretching modes or bending modes, i.e., σ_uσ_u, π_gπ_g, or π_uπ_u. Molecular orbital (MO) calculations predict harmonic frequencies for all modes, σ_g, σ_u, π_g, and π_u (see Figure S1 in Supporting Materials) [31]. Among them, frequencies for stretching σ_g and σ_u modes of lower frequencies, <1600 cm⁻¹, are size dependent, i.e., lower frequencies for longer polyynes. Observed bands of frequencies at ~480 cm⁻¹ for C₈H₂, ~380 cm⁻¹ for C₁₀H₂, and ~310 cm⁻¹ for C₁₂H₂ follow this tendency and are attributable to the longitudinal breathing mode of the carbon chain, namely σ_g’, having the lowest frequency among the σ_g modes, i.e., ν₅σ_g for C₈H₂, ν₆σ_g for C₁₀H₂, and ν₇σ_g for C₁₂H₂. This mode is reasonably excited when the length of the molecule changes upon the a³∑_u⁺ → X¹∑_g⁺ transition (one of the HOMO–LUMO transitions), where the triple bonds are tightened and the single bonds are loosened.

The three polyynes share a common frequency of 1230–1290 cm⁻¹ for the observed highest-frequency combination band. According to the MO calculations, one of the highest-frequency bending modes of π_g stays at 650–700 cm⁻¹ independently of the molecular size for all the polyynes (see Figure S1 in Supporting Materials). This π_g mode promotes a deformation of the carbon chain into a trans-zigzag configuration, i.e., alternating displacements of adjacent carbon nuclei in opposite directions to each other perpendicularly to the molecular axis (see Figure S2 in Supporting Materials). The activation of the trans-zigzag bending motion of the carbon chain accompanies the electronic transition of a³∑_u⁺ → X¹∑_g⁺, when even numbers of vibrational quanta are excited, providing a totally symmetric species as π_{g ⊗} π_g = σ_g⁺ _⊕ δ_g. Thus, the observed band separated by 1230–1290 cm⁻¹ from the band in the major progression of σ_g is attributable to the overtone of π_g² and its combinations with the alternating CC stretching mode, i.e., nν₂σ_g for C₈H₂, nν₃σ_g for C₁₀H₂, and nν₃σ_g for C₁₂H₂ of n = 1–4.

Another series of combination bands with common frequencies at ~480 and ~960 cm⁻¹ are noted for the excitation, once and twice, of an overtone of bending modes, π_g² or π_u². The vibrational motion having a common harmonic frequency of ~240 cm⁻¹ for different molecular size represents the cis-zigzag bending mode, namely π_g’ for C₁₀H₂ and π_u’ for C₈H₂ and C₁₂H₂ (see Figures S1 and S2 in Supporting Materials). Candidates for the possible excitations are 2ν₁₆ and 4ν₁₆ of π_u’ for C₈H₂, 2ν₁₅ and 4ν₁₅ of π_g’ for C₁₀H₂, and 2ν₂₃ and 4ν₂₃ of π_u’ for C₁₂H₂.

3.4. Annealing of Matrix Samples

To study the origin of satellite bands accompanying the main peak in the bands of the σ_g progression, the matrix sample in solid hexane was subjected to warming and cooling cycles between 20 K and 80 K, then warming up to 120 K, during which the spectra were recorded redundantly from one to the next. Figure 10 shows a series of spectra for the 0–0 band at 532 nm of C₈H₂ observed in the warming–cooling cycle, namely 20–60–20–80–20 K. The intensity of the main peak was reduced for vanishing by the warming up to 60 K, then recovered by cooling back to 20 K. In this cycle, a fraction of the intensity of the main peak was lost, while the intensity of the satellite bands was retained. The next cycle to 80 K affected the main peak by reducing its intensity to an order of magnitude less than the original intensity, even after cooling back to 20 K. Similar changes were observed for the other band of 0–1 in the σ_g progression. The recovery of the C₈H₂ molecule in a trapping site associated with the main peak is reproducible upon annealing partly but not completely.

In Figure 11, the simple warming up of the matrix sample from 20 K to 120 K for the 0–1 band at 603 nm of C₈H₂ exhibited again the reduction in the intensity for the main peak up to 80 K, followed by the intensification of a broad band at 607 nm and the reduction of all the band features around 120 K, up to where the solid hexane matrix and the trapped molecules were lost by sublimation. The weaker features or satellite bands were associated with the 0–0 and 0–1 transitions in the phosphorescence of C₈H₂ molecules trapped in different circumstantial environments. The relatively sharp main peak corresponds to C₈H₂ molecules in a stable trapping condition.

4. Discussion

4.1. Electronic Transition and Vibrational Excitation

Single-electron excitation from the highest occupied molecular orbital (HOMO) to the lowest unoccupied molecular orbital (LUMO) in a linear polyyne molecule in D_∞h point group symmetry, H(C≡C)_nH, provides three electronically excited states as spin-singlet states, i.e., ¹∑_u⁺, ¹∑_u⁻, and ¹Δ_u. Among them, the ¹∑_u⁺ is the only state to which the optical transition is allowed from the ground state, X¹∑_g⁺ [32,33,34]. By the character of the electronic excitation from one degenerated molecular orbital to another, the excited state to which the optical transition is allowed, ¹∑_u⁺, enjoys the highest transition energy among the three states stemming from the HOMO–LUMO excitation, while the others, ¹∑_u⁻ and ¹Δ_u, come close at the lowest transition energies within the spin-singlet manifold [34]. The spin-flipped, lowest-energy triplet state, a³∑_u⁺, also stemming from the HOMO–LUMO excitation, lies closer to or even lower in the transition energy relative to those for the latter two.

HOMO has electron densities on the triple bonds, C≡C, and nodes on the single bonds, C–C, of the polyynic carbon chain, while LUMO has electron densities on the single bonds, C–C, and nodes on the triple bonds, C≡C. Thus, upon the transition of an electron between HOMO and LUMO, a vibrational mode in which all the triple bonds expand and all the single bonds shrink and vice versa is activated. Accordingly, a conspicuous progression for the alternating CC stretching σ_g mode constitutes a major feature in the spectra of absorption, ¹∑_u⁺ ← X¹∑_g⁺ [9,10] and ¹Δ_u ← X¹∑_g⁺ [10,12,32], fluorescence, ¹Δ_u → X¹∑_g⁺ [30], and phosphorescence, a³∑_u⁺ → X¹∑_g⁺, as shown in Figure 1 and Figure 4. The relevant modes are ν₂σ_g for C₈H₂, ν₃σ_g for C₁₀H₂, and ν₃σ_g for C₁₂H₂. Since the phosphorescence excitation spectra of C₁₀H₂ in Figure 5a corresponds to the absorption spectra in Figure 5b,c, the progression of the alternating CC stretching σ_g mode predominates the spectral feature. The same discussion applies to the excitation spectra of C₈H₂ and C₁₂H₂ in Figure 3 and Figure 6, respectively.

When the potential minimum changes or the length of the sp-carbon chain varies upon the electronic transition, this is accompanied by the excitation of the longitudinal breathing mode, namely σ_g’, where all the CC bonds expand then shrink repeatedly. The relevant modes are the lowest-frequency symmetric stretching mode of ν₅σ_g for C₈H₂, ν₆σ_g for C₁₀H₂, and ν₇σ_g for C₁₂H₂. As the size of the carbon chain, n, increases, the vibrational frequency of the breathing mode decreases as ~n⁻¹.

A sudden change in the molecular length upon the electronic excitation is to be relaxed and mitigated when some bending modes are excited simultaneously. A plausible mode which accompanies the alternating CC stretching motion is the trans-zigzag bending mode of π_g symmetry, in which the adjacent carbon atoms move in opposite directions transversely to the molecular axis. According to the MO calculations, another π_g mode of vibration, i.e., CH bending, has a similar harmonic frequency to that of the trans-zigzag bending π_g mode of the carbon chain. The calculated mode frequencies are so close that the order can be reversed depending on the theoretical model and the basis set used. Experimentally, the IR absorption spectra revealed the frequency for the CH-bending π_u mode at 625 cm⁻¹ and its combination of π_g + π_u at 1236 cm⁻¹ for C_2nH₂ (n = 3–6), independently of the size, n [11,12,26]. Disregarding the anharmonicity and other effects of perturbation, the simple subtraction provides ~611 cm⁻¹ for the CH-bending π_g mode. On the other hand, the overtone frequency of ~1232 cm⁻¹ for π_g² observed in the dispersed phosphorescence spectrum is simply divided into two, providing the frequency of ~616 cm⁻¹ for the trans-zigzag bending π_g mode. The highest-frequency π_g mode is, by definition, ν₁₀ for C₈H₂, ν₁₂ for C₁₀H₂, and ν₁₄ for C₁₂H₂. This numbering of the mode, n of ν_n, has been applied to the CH-bending π_g mode in the IR absorption spectra [26] and also to the trans-bending π_g mode of the carbon chain in the laser-induced fluorescence spectra [30]. One might better refrain from the use of the numbering, n for ν_n, because of the close proximity of the vibrational frequencies for the CH-bending π_g mode and the trans-zigzag bending π_g mode. However, for convenience throughout this article, we dare to reserve for the CH-bending the numbering of the highest-frequency π_g mode, i.e., ν₁₀ for C₈H₂, ν₁₂ for C₁₀H₂, and ν₁₄ for C₁₂H₂, while for the trans-zigzag bending of the carbon chain the numbering of the second highest-frequency π_g mode, i.e., ν₁₁ for C₈H₂, ν₁₃ for C₁₀H₂, and ν₁₅ for C₁₂H₂. Having the same frequency and belonging to the same vibrational symmetry, both π_g modes can strongly couple to gain extra activity, appearing as conspicuous spectral features.

Another relaxation is obtained upon distortion induced by the electronic transition, provided the cis-zigzag bending mode is excited simultaneously. In this mode, displacements of the adjacent C≡C units are in opposite directions transversely to the molecular axis. The symmetry of this mode is π_u for C₈H₂ and C₁₂H₂ or π_g for C₁₀H₂, namely π_u’ for the 4n series and π_g’ for the 4n + 2 series. Having smaller number of nodes along the carbon chain, the vibrational frequency of ~240 cm⁻¹ for this cis-zigzag bending mode, π_u’ or π_g’, is lower than that of ~620 cm⁻¹ for the trans-zigzag bending mode, π_g. They are ν₁₆π_u for C₈H₂, ν₁₅π_g for C₁₀H₂, and ν₂₃π_u for C₁₂H₂. With the excitation of even-numbered vibrational quanta, the π_g and π_u modes provide a totally symmetric vibrational species as π_{g ⊗} π_g = π_{u ⊗} π_u = σ_g⁺ _⊕ δ_g, and thus are excited simultaneously upon the electronic excitation with a transition moment parallel to the molecular axis, namely the ∑-∑ transition. An example for the progression of the even-numbered vibrational quanta of a bending mode is reported for the ∏-∑ transition of a simple linear molecule of C₃ [35].

4.2. Phosphorescence Lifetimes

The observed lifetimes of 31 ms for C₈H₂, 8.4 ms for C₁₀H₂, and 3.9 ms for C₁₂H₂ are comparable to the reported lifetimes of cyanopolyynes in solid rare gas matrices, i.e., 40 ms for HC₅N [13,16], 8.2 ms for HC₇N [15], and 3.9 ms for HC₉N [18]. In solid organic matrices at 20 K, phosphorescence lifetimes of HC₉N were ~9.7 ms in solid hexane and ~11.2 ms in solid acetonitrile, and the lifetime of HC₁₁N was ~7.6 ms in solid acetonitrile [22]. These observations clearly show shorter lifetimes for larger species. The tendency of decreasing lifetimes for larger species is confirmed for both series of polyynes and cyanopolyynes. With an increasing number of vibrational degrees of freedom, particularly in low-frequency bending modes for longer polyynes, non-radiative decay is promoted from the upper singlet states, as well as from the lowest triplet state, a³∑_u⁺, to vibrationally excited states of the singlet ground state, X¹∑_g⁺. The population in the electronically excited states decreases faster for larger molecules with a high density of vibrational states.

4.3. Phosphorescence versus Fluorescence

Laser-induced fluorescence spectra have been reported in the near-UV and visible regions for hydrogen-capped centrosymmetric polyyne molecules of C_2nH₂ (n = 5–8) in hexane solutions at ambient temperature, c.a. 25 °C, upon the excitation of the fully allowed transition, ¹∑_u⁺ ← X¹∑_g⁺, in the UV [30]. The optical emission was attributed to the vibronic transition in the symmetry-forbidden electronic system of ¹Δ_u → X¹∑_g⁺. The optical transition for the 0–0 band of ¹Δ_u ↔ X¹∑_g⁺ is strictly forbidden but becomes weakly allowed through vibronic coupling, when a particular vibrational mode, namely an inducing mode of π_g symmetry, is activated or deactivated simultaneously upon the electronic transition [32,33]. Under the room temperature condition of the solution, fluorescence was detectable but phosphorescence was not noticed [30], reasonably because of the fast relaxation via internal conversion at the elevated temperature. Only the fluorescence having a typical lifetime of at most a few nanoseconds could be detected. In the present work for the same series of molecules, C_2nH₂ (n = 4–6), with the same excitation energy but in the cold matrix of solid hexane at 20 K, the phosphorescence spectrum predominated while the fluorescence spectrum was not discernible.

4.4. Vibronic Bands in the Forbidden Transition

Figure 12 shows the detail of the phosphorescence mapping of C₁₀H₂, with an extension of the excitation wavelength in the near-UV range from 302 nm to 409 nm, in addition to the excitation in the UV range from 213 nm to 302 nm. In the UV excitation below 300 nm, bright spots are discernible in the map, which are attributable to the 0–1 band emission of the phosphorescence, a³∑_u⁺ → X¹∑_g⁺, upon the excitation of the allowed transition, ¹∑_u⁺ ← X¹∑_g⁺. The bottom trace in light blue is the excitation spectrum for the emission at 693.5 nm, showing again the curve of UV absorption identical to the excitation spectrum by the 0–0 band at 605 nm in Figure 5a. In the middle trace, using the emission at 687.0 nm, another peak of the excitation at 262 nm appears as the small spot in the map, which corresponds to the emission peak of the dashed line in Figure 4. This excitation spectrum exhibits complex patterns, with two sharp peaks and some overlapping bands in the slightly longer wavelength region of 266–271 nm. The upper trace using the emission at 686.0 nm shows the excitation peak at 242 nm within a complex pattern of the excitation spectrum. All these patterns appear in the phosphorescence excitation mapping of C₁₀H₂ in solid hexane and they are reproducible for different matrix samples and for the mapping using the 0–0 band emission. Couples of electronic states are predicted below the excitation energy of the allowed transition, to which the electric dipole transition is symmetry forbidden but vibronically allowed by the mechanism of intensity borrowing [36,37,38].

In the near-UV excitation of 310–395 nm in Figure 12, four bands with an increment of ~2050 cm⁻¹ are found in the mapping using phosphorescence 0–1 band of C₁₀H₂. By the proximity to those observed as absorption bands in the symmetry-forbidden transition in solutions [10,30], these bands belong to the excitation of the ¹Δ_u ← X¹∑_g⁺ system of the HOMO–LUMO transition.

Table 5. Observed peaks in nm for the excitation spectrum of C₁₀H₂ in solid hexane matrix at 20 K. For the vibronic transition in near UV, ¹Δ_u ← X¹∑_g⁺, absorption bands observed in hexane solution at ambient temperature are listed for comparison [30].

Transition	Excitation 686.0 nm	Excitation 687.0 nm	Excitation 693.5 nm	Separation cm−1	Solution 1 nm	Mode	Symmetry
1Δu ← X1∑g+	395.3	392.8	397.8
			390.3	0
	387.8	387.8	387.8	165	384	${13}_0^2$	πg2
			381.8	571
			379.3	173
	365.3	363.8	367.3
			361.3	2057
	359.3	359.3	359.3	154	357	$3_0^1{13}_0^2$	σg + πg2
			353.8	587
			351.8	161
	339.8	339.8	340.8
			336.3	2058
	334.8	334.8	334.8	133	333	$3_0^2{13}_0^2$	σg2 + πg2
			330.3	540
	312.8	313.8	314.8	2031	312	$3_0^3{13}_0^2$	σg3 + πg2
1Δu ← X1∑g+	270.2	271.2
	268.2	268.2
	266.2	266.2
1∑u+ ← X1∑g+	261.7	261.7	258.8	0		0–0
	255.3	257.3	245.3	2116		$3_0^1$	σg
	250.8	251.3	233.4	2084		$3_0^2$	σg2
	242.3	242.8	222.9	2008		$3_0^3$	σg3
	233.9	239.9
	230.9	231.4
	222.9
	220.5

¹ Reference [30].

compares the observed bands in the forbidden transition by phosphorescence excitation in solid hexane at 20 K in the present work and those by absorption in hexane solutions at ambient temperature [30]. In the excitation spectrum using the phosphorescence 0–0 band in Figure 5a, identical features are discernible in 32,300–25,300 cm⁻¹. The intensity of these features in the excitation spectrum in Figure 5a is relatively stronger than the intensity in absorption in the solutions shown in Figure 5b. The difference is rationalized as follows: in different wavelengths of UV, where the molecule strongly absorbs the incident light, and near-UV, where the molecular absorption is orders of magnitude weaker, the thickness of the sample is common for the transmission measurement of the absorption in solutions, while in the phosphorescence measurement, the penetration depth of the incident light for the excitation is different, i.e., thin for the UV and thick for the near-UV, to gain intensity for the near-UV relative to the UV.

As the probing wavelength is shortened from 694 nm to 686 nm, the band shape of the forbidden transition changes, but rather simply compared with those in the allowed transition in shorter wavelengths. Since the appearance of the phosphorescence signal of the 0–1 band in 685–695 nm coincides well with the excitations of the allowed transition, ¹∑_u⁺ ← X¹∑_g⁺, and the forbidden transition, ¹Δ_u ← X¹∑_g⁺, all the spectral features in Figure 12 belong to C₁₀H₂, despite the complex shifts in wavelengths and the alternating intensities.

4.5. Relevance to Interstellar Molecules

Finally, we briefly mention the relevance to interstellar molecules. Cyanopolyynes, H(C≡C)_nC≡N, have been a series of leading interstellar molecules since their discovery by radio astronomical observations in the late 1970s [3,4,5,6,7]. It is natural to consider that the simplest analog of hydrogen-end-capped polyynes, H(C≡C)_nH, shares the same place [8]. However, their detection in space has been limited by the selection rule for the pure rotational transition to take place, i.e., the detectable molecule must have a permanent electric dipole. Since the radio-frequency pure rotational transition for the centrosymmetric polyyne molecule, H(C≡C)_nH, is forbidden, vibrational transitions or electronic transitions are the possibilities for detection.

Infrared absorption has been reported in relevance to the abundance of hexatriyne, C₆H₂, and octatetrayne, C₈H₂, in the atmosphere of Titan [11,12]. In this case, vibrational modes associated with heteronuclear, dipolar CH bonding are detectable, i.e., the asymmetric CH stretching σ_u mode at ~3330 cm⁻¹ and the synchronized CH bending π_u mode at 622 cm⁻¹, and its combination of π_u + π_g at ~1230 cm⁻¹. For the characteristic localized vibration on the two terminal CH bonds, the vibrational frequencies of these modes are independent of the size of the carbon chain. On the other hand, transition energies of the electronic spectra are size dependent because of the property of the HOMO–LUMO excitation of the electron in the doubly degenerate π-orbitals on the carbon chain, as plotted in Figure 13. Absorption bands of vibronic transitions in the forbidden transition, ¹∑_u⁻ ← X¹∑_g⁺ and ¹Δ_u ← X¹∑_g⁺ [33], have been the subject of astronomical observation. Concerning the phosphorescence, a³∑_u⁺ → X¹∑_g⁺, the size-dependent property is clearly shown for the wavelength of their 0–0 bands, as demonstrated in Figure 4 and Figure 13. Although the observable condition is limited to the place where the UV excitation occurs for cold molecules, phosphorescence in the visible and near-infrared regions can be a promising probe for the detection of centrosymmetric linear polyyne molecules of C_2nH₂ in space.