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Singlet−Triplet and Triplet−Triplet Transitions of Asphaltene PAHs by Molecular Orbital Calculations Yosadara Ruiz-Morales*,† and Oliver C. Mullins‡ †

Instituto Mexicano del Petróleo, Programa de Ingeniería Molecular, Eje Central Lázaro Cárdenas Norte 152, Mexico City 07730, Mexico ‡ Schlumberger-Doll Research, Cambridge, Massachusetts 02139, United States ABSTRACT: Two important features of the molecular structure of asphaltenes remain unresolved; the size distribution of the asphaltene polycyclic aromatic hydrocarbons (PAHs) and the number of PAHs per asphaltene molecule. The relatively small molecular weight of asphaltenes restricts the PAH size; if there are several PAHs per asphaltene molecule, they must be rather small. Optical spectroscopy especially when coupled with molecular orbital (MO) calculations is an excellent probe of asphaltene PAH populations and thus asphaltene molecular architecture. Previously, singlet−singlet transitions for asphaltenes were analyzed using both experiment and MO theory. Here, we describe MO calculations performed to treat triplet−triplet transitions from the ground triplet state for 103 PAHs. Qualitative comparisons with corresponding triplet−triplet transition measurements for asphaltenes are discussed. In addition, spin-forbidden transitions between the singlet and the triplet states, corresponding to phosphorescence, are calculated and discussed in terms of the probability of intersystem crossing of PAHs in asphaltenes and crude oils. Conclusions obtained here are consistent with the corresponding study of singlet−singlet transitions and support the model of a single, relatively large PAH per asphaltene molecule as the predominant asphaltene molecular architecture: the island model. This is consistent with a most probable asphaltene PAH of seven fused aromatic rings (7FAR) with a width of four to ten fused aromatic rings (4FAR-10FAR). This molecular architecture is a central feature of the Yen−Mullins model of asphaltene nanoscience.

1. INTRODUCTION Recent advances in the field of asphaltene science have been codified in the Yen−Mullins model, specifying the dominant asphaltene molecular structure and the hierarchical aggregate structures of asphaltenes in crude oils and in laboratory solvents.1,2 This asphaltene nanoscience is proving to be rather important. For example, this nanoscience has enabled the development of the first predictive asphaltene equation of state (EoS), the Flory−Huggins−Zuo (FHZ) EoS, for asphaltene gradients found in oil reservoirs.3,4 In turn, the asphaltene gradients in reservoirs have allowed unequivocal identification of asphaltene molecules,3 nanoaggregates,4 and most recently clusters5 in heavy oils, confirming key aspects of the Yen− Mullins model. This theory coupled with in situ chemical analysis of reservoir crude oils in oil wells6 allows the assessment of asphaltene equilibration across a reservoir. When asphaltenes are equilibrated, the good news of reservoir connectivity is indicated,7,8 addressing the biggest risk factor in deepwater−oil production.6 The foundation of this asphaltene nanoscience model is the asphaltene molecule. The asphaltene molecular architecture is in large measure responsible for the structure and small aggregation number of the asphaltene nanoaggregate, with its central PAH core and its peripheral alkane.1,2,9,10 In addition, asphaltene molecules can have interfacial activity and the molecular architecture is central to understanding this property. For example, direct determination by Sum Frequency Generation (SFG) of asphaltene molecular orientation in Langmuir−Blodgett films of asphaltenes shows that asphaltene PAHs are in-plane, while the alkanes are out-of-plane.11 In © XXXX American Chemical Society

these experiments, all asphaltene is forced onto the water surface by evaporation of the toluene. Only large PAHs would be expected to show such strong orientation.11 Moreover, recent work on asphaltene solution−water interfaces establishes very strong structure−function relationships for asphaltene molecules.12,13 A universal curve was obtained for interfacial tension versus relative surface coverage by asphaltene for a broad range of concentrations and conditions independent of aging time, viscosity (when scaled), and the presence or absence of nanoaggregates.12,13 This simple universal curve was fit with the Langmuir equation, where one of two parameters is the asphaltene molecular size in the interface. The value of 6.2 fused aromatic rings was obtained in close agreement with the orientation found in the SFG experiments11 and with the asphaltene PAH size determined by a multitude of measurements and MO calculations.1,2 Moreover, the lack of asphaltene nanoaggregate loading onto the surface in these pendant drop experiments is consistent with the structure of asphaltene nanoaggregates having peripheral alkanes.13 The Yen−Mullins model is also consistent with universal curves obtained for the oil−water interface, as explicitly stated by the authors.13 These studies establish the relationship between interfacial behavior and asphaltene molecular structure. The debate regarding asphaltene molecular weight is now largely resolved.1,2 All diffusion measurements and all mass spectral techniques are in reasonable agreement: asphaltene Received: January 29, 2013 Revised: August 14, 2013

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molecular weight is ∼750 Da with a 500−1000 Da full width half-maximum (fwhm).1,2 There remains some uncertainty regarding asphaltene molecular architecture. The size distribution of asphaltene PAHs is of concern. In addition, there is the difficult question to address whether there is predominantly one PAH (island model) per asphaltene molecule or several PAHs per asphaltene molecule (archipelago). The modest molecular weight of asphaltenes provides a rather tight constraint on the asphaltene molecular architecture; the larger the PAHs, the fewer of them that can fit, in the asphaltene structure, within this asphaltene molecular weight constraint. For example, there are archipelago models being proposed with only two or three PAHs in the structure.14 The first studies to indicate that the island model predominantly applies to asphaltenes are the time-resolved fluorescence depolarization studies (TRFD).15−20 These molecular diffusion results are consistent with those from Fluorescence Correlation Spectroscopy (FCS)21,22 and Taylor dispersion.23 It is of vital interest to characterize the size distribution of PAHs and the number of PAHs per asphaltene molecule. Recently, an extensive systematic theoretical molecular orbital study24 that comprises 3264 dimer systems, in island and archipelago architectures, has concluded that if two asphaltene core PAHs are directly bonded via a single bond forming a dimer, then the optical methods would identify this as a single chromophore, therefore as an island, thereby blurring the distinction between island versus archipelago. As well, some decomposition studies would find this single-bonded pair of PAHs as a single entity.24 Direct molecular imaging of asphaltenes by scanning tunneling microscopy obtained the most probable asphaltene PAHs of six to seven fused aromatic rings (6FAR-7FAR).25 High-resolution transmission electron microscopy obtained similar results at lower resolution but investigating much more sample.26 Different groups using Raman spectroscopy obtained similar PAH results while relying on totally different physics.27−29 Laser two-step ionization mass spectroscopy (L2MS) has shown that asphaltene molecules and all-studied island model compounds resist decomposition at higher laser power, while all studied archipelago models underwent fragmentation under identical conditions.30 Moreover, detection cross sections for L2MS are fairly invariant;31 consequently, the L2MS studies indicate a predominance of island molecular architecture. These results are consistent with laserinduced acoustic desorption studies that concluded that island architecture is more consistent with their decomposition results.32 In particular, laser-induced, acoustic-desorption, electron-impact mass spectrometry (LIAD-EI MS) shows that the asphaltenes are stable against decomposition, this time with electron impact, whereas archipelago models fragment readily.33 Other studies of asphaltene decomposition using catalytic hydrogenation do indicate that asphaltenes have some fraction of archipelago14 and, as noted, some fraction pendant benzene or naphthalene groups would not register as significant in many studies that indicate island architecture dominates. One of the best methods to interrogate the size of PAHs is to determine their electronic properties, thus optical spectra. The visible−NIR spectra of asphaltenes are dominated by absorption, not scattering.34 This result was confirmed by seeing no change in the visible−NIR spectra of asphaltenes above and below various aggregation concentration thresholds.35 Moreover, crude oil and asphaltene absorption spectra exhibit the Urbach tail formalism in the visible and near-

infrared spectral ranges.36,37 The near-infrared absorption (not scattering) in the continuation of the visible absorption is expected and found based on the Boduszynski continuum model.38,39 Each π-electron has an oscillator strength of one, so all πelectrons are registered in the spectrum. Because there is a strong dependence of frequency on PAH size and aromaticity,35,40−44 the asphaltene PAH size distribution can be probed by spectral analysis with certainty that all PAHs are included. Indeed, the dark brown coloration of virgin crude oil asphaltenes is one of their canonical properties; there is no debate as to the color of asphaltenes. Different laboratories measure the same asphaltene optical spectrum. The fairly similar optical spectral properties of asphaltenes have been established for a broad array of crude oil asphaltenes, and this colorimetric similarity is now being used to quantify asphaltene content in samples.45 The color of asphaltenes cannot be washed from the sample as an impurity; the asphaltenes are inherently colored. Quantitative analysis requires detailed examination of potential asphaltene PAHs, this being best accomplished by molecular orbital calculations. The challenge is to perform such an analysis on the large number of PAHs that can potentially contribute. To explore asphaltene PAHs, first, the governing principles of PAH electronic transitions needed to be sorted out in a systematic way.40,41 The singlet electronic manifold spectra depend critically on the number of fused aromatic rings in the PAH in accord with a quantum particle in a box.40,41 This quantum principle explains the huge red-shift in going from colorless benzene to black graphite. In addition, the PAH spectrum depends critically on the geometry of the PAH and the distribution of its π-electronic density into the Clar-type representation with aromatic sextet carbon versus isolated double-bond carbon.40,41,46 Carbon X-ray Raman studies have determined that the bulk of asphaltene aromatic carbon is aromatic sextet carbon,42,47 in agreement with the results obtained with molecular orbital (MO) calculations coupled with the Y-rule.40,41 Sextets of π-electrons are located in particular hexagons of the benzenoid molecule, indicating domains of increased π-electron contents and/or local aromaticity. The Y-rule offers an original and easy-to-apply criterion for locating aromatic sextets in pericondensed benzenoids (see Theoretical Methodology). Also, the MO calculations have been used to compare with asphaltene singlet optical absorption and electronic emission properties.35,40,43,44 In these studies, concentration effects were explored and ruled out any significant optical contribution from charge transfer.35 Analysis of PAHs with heteroatoms showed small differences in electronic structure from nonheteroatom-containing PAHs.44 One key molecular attribute of the asphaltenes is the size distribution of their polycyclic aromatic hydrocarbons (PAHs). Comparison of measured spin singlet−singlet absorption and emission transitions with exhaustive molecular orbital (MO) calculations on 523 PAHs indicates that asphaltene PAHs have a population centroid of ∼7 fused aromatic rings (7FAR). Quantitative comparison of MO predictions matched asphaltene singlet electronic manifold absorption and emission spectra reasonably well when using an asphaltene PAH distribution with 7FAR, as most probable, with the bulk of the population width of 4FAR to 10FAR.44 Nevertheless, to further test the validity of this conclusion, the spectral analysis of asphaltenes needs to be extended to include the study of the triplet-state spectroscopy, which is complex especially on B

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Figure 1. Schematic representation of the ground singlet state, the lowest triplet state, and higher triplet states. In the present theoretical work, we have concentrated on studying neutral and even-numbered polycyclic aromatic hydrocarbons (PAHs) with fused six member rings, that is, benzenoid-type PAHs. The theoretical estimates are derived from a single “frozen” molecule in the gas phase at 0 K without corrections for thermal motions and solvent effects. No heteroatoms have been included in the structures for simplicity of the calculations. Experimentally, it is known that the replacement of a carbon atom in PAH compounds with a heteroatom typically results in a red shift (longer wavelength) of the fluorescence maximum, if there is any spectral effect.52 The total number of systems calculated for each FAR family is 4FAR: 1 system with CR = 0.3333; 5FAR: 3 systems with CR from 0.1100 to 0.6667; 6FAR: 14 systems with CR between 0.3333 and 1.0000; 7FAR: 15 systems with CR between 0.1667 and 1.3333; 8FAR: 16 systems with CR between 0.1667 and 0.6667; 9FAR: 23 systems with CR ranging from 0.3333 to 0.7778; 10FAR: 11 systems with CR ranging from 0.1333 to 0.8390, and 11FAR: 20 systems with CR ranging from 0.200 to 1.0000. The geometry optimization (structure relaxation) of all the systems in singlet ground state (S0) and triplet ground state (T1) were carried out using the high-level quantum density functional theory (DFT) approach with the self-consistent generalized-gradient GGA and the Perdew−Wang 91 (PW91) exchange-correlation potential (DFT GGA-PW91).53 The DNP basis set (double-ζ plus polarization function basis set)54 with a radial cut off of 3.0 Å was used, as implemented in the DMol3 code54−56 and instrumented in the interface of Materials Studio.57 For the triplet ground state (T1) open shell, DFT optimizations were carried out using the unrestricted selfconsistent field (SCF) formalism,58 while for the closed shell singlet ground state (S0) optimizations the restricted formalism was used.59 The energy of the lowest singlet−triplet transition (3La), or S0−T1 transition, has been obtained by subtracting the total energy of the optimized S0 state (singlet ground state) from that of the triplet ground state (T1) at the respective optimized geometries. It is reported in the literature60 that in open shell Kohn−Sham DFT calculations, the spin contamination of the triplet state is relatively low. Therefore, the effects of spin contamination on the optimized T1 structures and the calculated S0−T1 energy gaps are expected to be unimportant. The lowest triplet state (3ψ1 or T1), for all the systems considered in this study, is that state obtained by a promotion of a π-electron from the HOMO (highest occupied molecular orbital) to the LUMO (lowest unoccupied molecular orbital). For the higher triplet configurations (T2 or Tn), we consider only those electronic excitations in which the HOMO and/or LUMO MO’s are involved in order to construct the wave functions (see Figure 1). There are some difficulties in the triplet−triplet transition calculation. In tripletto-triplet absorption spectra, one is dealing with an open-shell to openshell transition, where the intershell correlation energy changes, whereas in (ground-state) singlet-to-triplet spectra or even in (groundstate) singlet-to-(excited state) singlet spectra, one is confronted with a closed-shell-to-open-shell transition, where only the intrashell correlation energy changes.

polydisperse materials such as asphaltenes. A recent publication48 has explored the triplet-state spectroscopy of asphaltenes and crude oils with both theory and experiment. The experiments included nanosecond pump−probe techniques to generate triplet-state absorption spectra and lifetime measurements. The latter included experimental parameters of the presence and absence of molecular oxygen and of temperature. In addition to asphaltenes, many different crude oils were measured as well. Only results from preliminary MO analysis were included in this earlier triplet experimental study. In the present paper, the best theoretical approach is discussed in detail and the benchmarking is described. Also the calculation of the first triplet transition S0−T1 is presented and discussed together with the T1−Tn triplet transitions. Computational chemistry approaches have revolutionized our understanding of the structure and reactivity of molecules, and computation has become the third apex of the triangle representing how we do science, with experiment and theory representing the other two apexes. Here, we extend the interrogation of asphaltene PAHs with MO calculations beyond the singlet−singlet (S0−Sn) transition. Triplet−triplet (T1−Tn) calculations are performed, enabling interpretation of the corresponding experimental data. The T1−Tn calculations are openshell, consequently far more difficult to carry out than the S0−Sn transition calculations. Benchmarking is performed on individual PAHs to evaluate these calculations. Nevertheless, the objective here is the qualitative, not quantitative, comparison with the asphaltene T1−Tn experimental data. In addition, singlet−triplet (S0−T1) calculations are performed, enabling comparison with phosphorescence data.

2. THEORETICAL METHODOLOGY We have calculated the T1−Tn transitions and the lowest S0−T1 transition for a total of 103 polycyclic aromatic hydrocarbons (PAHs) with 4 to 11 fused aromatic rings (4FAR−11FAR). The PAH model compounds were selected by the same criteria we used before for the calculation of the singlet manifold spectroscopy.44 We characterize PAHs in terms of the carbon ratio (CR), which is the ratio of carbon atoms in isolated double bonds (IDB) to those in aromatic sextets. For example, naphthalene with its two IDB and a single aromatic sextet has a carbon atom ratio (IDB/sextet) of 2/3. Asphaltenes, from both petroleum and coal, have been shown to have a carbon ratio of 1/ 3.40,47 In both, the original formulation of the Clar theory,46 and its several later variants, sextets of π-electrons are located in particular hexagons of the PAH molecule, indicating domains of increased πelectronic density and/or local aromaticity. The Y-rule40,41,49−51 was used to find the most important Clar-type structure for the studied PAHs and thus to determine the actual number and localization of sextets and double bonds in the studied systems.40,41,43 C

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Table 1. Calculated Triplet S0−T1 (3La) and Singlet S0−S1 (1La)40,41,43 Adiabatic Excitation Energies, without Zero-Point Energy Correction, for PAHs with 4FAR, 5FAR, and 7FAR Rings in the Structuree

Number of fused aromatic rings in the PAH structure. bCarbon ratio (see Theoretical Methodology for description). cRef 74. dRef 73. The first number does not consider zero-point-energy correction, while the second number, in italics, does consider zero-point-energy correction. eThe experimental 0−0 excitation S0−T1 energy in solution is given in parentheses. In the last column theoretical results from the literature are tabulated73 (see text for description). a

The T1−Tn transition energy and oscillator strength calculations were carried out using the optimized (DFT GGA-PW91) structures, in triplet ground state (T1), and molecular linear response timedependent density functional theory (TDDFT),61−66 as implemented in the GAUSSIAN 09 program.67 In the past decade, TDDFT linear response theory has proven to be efficient in its predictive power and has become the most widely used electronic structure method for calculating vertical electronic excitation energies.68 Open shell DFT calculations were carried out using the unrestricted self-consistent field formalism.58 Becke’s 1988 exchange-energy functional, which includes the Slater exchange along with corrections involving the gradient of the density and a percentage of the exact exchange from the Hartree− Fock method,69 was used together with the correlation functional of Lee, Yang, and Parr,70 which includes both local and nonlocal terms (i.e., the hybrid B3LYP density functional was used). We used the 631+G(d, p) basis set,71,72 which is a valence double-ζ basis augmented with diffuse sp- functions on the C atoms and polarization functions (d on the C atoms, and p on the H atoms).

As the size of the PAH systems increases, in terms of the number of fused aromatic rings (FAR), the calculations become computationally expensive; therefore, only the first 15 T1−Tn transitions were calculated. For the case of the T1−Tn (TT) calculations, the number of calculated spectra is equal to the number of systems in each FAR family. All of the calculated spectra for each FAR family were added up and a population diagram versus the wavelength was obtained. The population is the sum of the calculated TT oscillator strength, different from zero, for all of the compounds in the given FAR family, that fall in a given wavelength range, divided by the number of occurrences in that given wavelength range. We chose wavelength ranges or regions of 10 nm: for example, 400−409, 410−419, 420−429 nm, and so on. Other means of normalization did not impact the data significantly.

3. RESULTS AND DISCUSSION 3.1. Singlet−Triplet S0−T1 Transition. Phosphorescence of PAHs. In Table 1, the validation of the S0−T1 D

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calculation method is presented for several PAHs together with the calculated singlet S0-S1 transition energy40,41,43 for comparison purposes. Some of the calculated S0−T1 energy transitions are compared with the values calculated by Nguyen et al.73 (last column in Table 1), who optimized the PAH structures at the DFT B3LYP level with the 6-31G+(d, p) basis set. The experimental S0−T1 energy transitions presented in Table 1 correspond to the 0−0 transition between the lowest triplet state and the ground state and correspond to the highest energy peak of the phosphorescence experimental spectra. The S0−T1 transition energies in solution at low temperature are used because excitation energies in the gas phase are not available. Phosphorescence normally must be conducted on chilled samples and the readings are typically taken between 70 and 100 K. As can be seen in Table 1, there is a very good agreement between the theoretical and the experimental values for the energy of the (S0−T1) transitions. Our calculated values do not include zero-point energy correction. The information presented in the last column corresponds to calculations published by Nguyen et al.73 The first number in the last column in Table 1 corresponds to the calculated adiabatic ΔE (S0−T1) transition energy, while the second number, in italics, corresponds to the calculated zero-point-corrected ΔE (S0−T1) transition energies, showing that this correction is small for PAHs. The experimental and the theoretical S0−T1 energies, that do not include solvent effects, are in good agreement; evidently, the experimental PAH phosphorescence is not affected by solvent effects at low temperatures. Nguyen et al.73 systematically examine the ability of the TDDFT approach with the B3LYP functional to predict experimental nonlinear absorption of organic and organometallic dyes, including free-base porphyrins, phthalocyanines, and their metal complexes. Good agreement of the theory to the experimental S0−T1 and T1−Tn excitation energies and oscillator strengths was obtained. Nguyen et al.73 tried various methods and found that the 6-31+G(d,p) basis set for both the geometry optimization and the T1−Tn transition calculation provides good agreement with the experimental value, in agreement with our findings. In previous studies on the calculation of the singlet HOMO− LUMO electronic excitation of PAHs (S0−S1 transition),41 the validation of the best combination of theoretical methods that involved (1) the structure optimization method, followed by (2) the energy gap calculation method, was carried out. The best agreement between theory and experiment was obtained for (a) semiempirical compass force field optimization of the PAH structure followed by a ZINDO transition energy calculation and (b) semiempirical compass force field structure optimization, followed by a single point B3LYP calculation for the transition-energy calculation (see Figure 2). As can be seen in Figure 2,41 for the calculation of the singlet HOMO−LUMO gap transition, the PAH structure optimization methodology is crucial. In the present work, the optimization of the structures were carried out at the DFT GGA-PW91 level with the DNP basis set, which is a double-ζ, plus a polarization function basis set. Nguyen et al.73 optimized the chromophore structures at the DFT B3LYP level using the 6-31G+(d, p) basis set. The good agreement between the MO predictions, herein, and the experiment indicates that the methodology presented in this work, to calculate the

Figure 2. Diagram of the experimental and calculated HOMO− LUMO energy gap (S0−S1 singlet transition energy)41 at various levels of theory (geometry structure optimization method/energy gap calculation method) for the case of PAH systems with six fused aromatic rings (6FAR).

phosphorescence (S0−T1 transition) for PAHs, has a good predictive power. In Figure 3, the calculated S0−T1 transition energy, expressed in wavelength, is presented for 103 calculated PAHs, with 4

Figure 3. Phosphorescence (S0−T1 transition) wavelength for 103 calculated PAHs from 4FAR to 11FAR.

fused aromatic rings to 11 fused aromatic rings in the structure (4FAR−11FAR). Each dot in Figure 3 represents the S0−T1 transition energy of a PAH system. For a given FAR family, each dot represents an isomer system with same number of fused aromatic rings in the structure and different aromaticity or carbon ratio. Because the S0−T1 transition was calculated by subtracting the total energy of the optimized S0 state (singlet ground state) from that of the excited triplet (T1) state, at the respective optimized geometries, only one value for each system is obtained and presented as a dot in Figure 3. The vibrational coupling and the effect of heteroatoms were not calculated. However, the calculated data agrees with the E

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Helicenes, which are nonplanar PAHs,78 combine the characteristics of a conjugated π-electron system with nonplanarity, which is observed to trigger spin−orbit coupling and large intersystem crossing rates. It is found that within a FAR family, PAHs with a high carbon ratio (see Theoretical Methodology) (i.e., with a high content of carbon atoms in isolated double bonds) present the lowest S0−T1 energies or larger wavelength, for example 5FAR systems in Table 1. The three 5FAR isomers have same molecular formula (C20H12), but different carbon ratios. Benzo[e]pyrene has a carbon ratio of 0.1111 and a S0−T1 energy transition of 2.28 eV or 543.52 nm. Benzo[a]pyrene has a carbon ratio of 0.6667 and a S0−T1 energy transition of 1.74 eV or 712.20 nm (see Table 1). For each FAR family, the PAH systems with low carbon ratio (high content of carbon atoms in sextets) are on the left side of the line of dots (see Figure 3), while the PAH systems with a high carbon ratio (low content of carbon atoms in sextets or high content of isolated double bonds) are on the right side of the line of dots in Figure 3. These findings are in accordance with observed tendencies in singlet S0−S1 transitions for PAHs.35,40,41,43,44 In a recent publication, the triplet state spectroscopy of asphaltenes and crude oil samples has been explored. The experiments included nanosecond pump−probe techniques to generate the triplet state absorption spectra and lifetime measurements.48 The pump excitation wavelength of 355 nm was used to excite the samples. This wavelength selects only a population of a range of PAHs that absorb at 355 nm (3.49 eV).43 Some of the selected population within the singlet manifold undergoes intersystem crossing from the S1 electronic state to the T1 electronic state. The probe laser then excited the triplet state manifold48 (in the following section the T1−Tn transitions are discussed). In a polydisperse sample, such as asphaltenes, the optical absorption at a particular wavelength includes excitation from the HOMO to the LUMO (S0−S1 singlet manifold electronic transition) of certain chromophores as well as excitation of higher excited states of lower energy chromophores. With rare exception, fluorescence emission of PAHs (in dilute solution) consists of fluorescence emission from the lowest-lying excited state.76 Thus, in fluorescence emission for asphaltenes, a spectral map of the HOMO−LUMO profiles of the asphaltene PAHs is obtained. Asphaltene fluorescence emission spectra excited with UV generally exhibit a maximum emission at 450 nm. As a very rough approximation, we used this emission spectrum as a guide to the population distribution of asphaltene fluorophores.43 Table 2 shows the systematics observed for energies of the S0−Sn transitions and S0−T1 transitions. The energy difference ΔE (S1−T1), as an approximation to the probability for the intersystem crossing, is obtained from eq 1. In Figure 4, the involved states are shown (S0−S1 and S0− T1).

reported experimental results, as shown in Table 1 and discussed above. In Figure 3, it is observed that the phosphorescence (S0−T1 transition), for the studied FAR families (4FAR−11FAR), starts at around 500−600 nm (2.07−2.45 eV) and as the number of fused aromatic rings (nFAR) is increased, going from 4FAR to 11FAR, there is an increasing red shift of the S0−T1 transition energy. For the case of pyrene (4FAR), the S0−T1 transition energy is 598 nm or 2.07 eV (see Figure 3 and Table 1), while for the 11FAR family, the calculated S0−T1 transition energy goes from around 700 nm or 1.77 eV to as far as 2400 nm or 0.52 eV, depending on the type of isomer and its aromaticity.40,41,43 Also, the S0−T1 transition is substantially red-shifted, in comparison to the singlet state S0−S1 transition (see Table 1). The S0−S1 transition of pyrene (4FAR) is 343 nm (Table 1), while the S0−T1 transition corresponds to 598 nm (see Table 1 and Figure 3). For perylene (5FAR), for example, the S0−S1 transition corresponds to 431 nm (see Table 1), while the S0−T1 transition corresponds to 837 nm (see Table 1 and Figure 3). The red shift in the wavelength for the S0−T1 transition (phosphorescence) compared with the S0−S1 transition is due to the fact that in PAHs the T1 energy level is lower in energy than the S1 energy level; therefore the S0−T1 transition energy is smaller (longer wavelength) than the S0−S1 energy transition (see Figure 4).

Figure 4. Jablonski diagram representing the energies of the various low-lying states of a typical aromatic hydrocarbon molecule with respect to the ground state S0. The spin singlet and triplet electronic manifolds are shown together with the spin of electrons and the occupation.

Transitions of the system between states of different electronic spin manifolds (intersystem crossing, ISC), such as the S0−T1 transition, are spin forbidden and are ordinarily less probable by a factor of ∼10−6 than symmetry and spin-allowed transitions. The probability of intersystem crossing between states of different manifolds increases in the presence of a heavy atom, or with vibrational coupling, which enables spin−orbit coupling75 by mixing the singlet and triplet wave functions (like in τ13 and τ30) (see Figure 4). The coupling of a photon and electron occurs via the orbital wave function of the electron. Without some spin−orbit coupling, the electron spin remains unchanged in photoabsortion or photoemission. Consequently, emission from a triplet excited state to a singlet ground state (phosphorescence) is formally forbidden, but it can occur by spin−orbit coupling induced by heavy atoms or vibrational coupling.76,77 Suitable modes usually involve out-of-plane bending modes, often C−H bending, or a ring twist.78 For small conjugated molecules such as benzene and naphthalene, the out-of-plane bending modes provide the route by which phosphorescence occurs.79

ΔE (S1 − T) 1 = ΔE (S0 − S1) − ΔE (S0 − T) 1

(1) 48

The excitation wavelength of 355 nm (3.49 eV), used in the pump−probe experiments (see following section) to ultimately generate the first triplet state, would excite, within the singlet electronic manifold, mainly the asphaltene-PAHs with a HOMO−LUMO energy lower or equal to 3.49 eV, which corresponds to the 5FAR−10FAR PAHs (see Table 2). Some of this selected population then undergoes intersystem crossing from the S1 electronic state to the T1 electronic state, which is lower in energy (see Figure 4), through spin−orbit F

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(S1−T1) = 0.5 eV (see Table 2). 10FAR chromophores would have a low probability of undergoing intersystem crossing. However, other factors have to be taken into account, as discussed below. El Sayed’s rule indicates that spin−orbit coupling is allowed between states of different symmetry and electronic configurations.80 Therefore, spin−orbit coupling between the singlet and triplet states of identical electronic configuration is forbidden, that is, for example, between S1 1ππ* and T1 3ππ* states. Intersystem crossing is expected to be remarkably fast in molecules with low-lying nπ* states, where n represents a nonbonding electron, for example, in the nitrogen or oxygen atom. In contrast, intersystem crossing is expected to be slow in the S1 1ππ* state of aromatic hydrocarbons with no nonbonding electrons. Intersystem crossing has, nevertheless, been considered important in the S1 state dynamics of molecules such as benzene, naphthalene, and anthracene.81 Intersystem crossing is very fast in the S1 1nπ* state of Nheterocyclic aromatic hydrocarbons because of strong spin− orbit coupling with the T1 3ππ* state. Singlet−triplet mixing gives rise to a magnetic moment in the single rotational line of the S1 state, and this has very recently been experimentally proven by measuring the Zeeman splitting for each rotational line in the high-resolution spectrum.81 Singlet−triplet absorption intensity is augmented by a heavy atom fairly near to the region of the molecule within which an electronic transition is localized. Sulfur containing organics can

Table 2. Energy Difference S1−T1, Obtained from the Calculated S0−S1 (HOMO−LUMO) Energy43 and Phosphorescence (S0−T1, Figure 3), and the Associated Wavelength, for PAH Families (4FAR−10FAR) ΔE (S0−S1) from ref 43a

ΔE (S0−T1) from Figure 3

ΔE (S1−T1) from eq 1

PAH Family

eV

nm

eV

nm

eV

4FAR 5FAR 6FAR 7FAR 8FAR 9FAR 10FAR 11FAR

3.65 2.82 2.64 2.63 2.46 2.25 2.06

340 440 470 471 507 550 606

2.07 2.28 2.51 2.47 2.27 2.21 2.42 1.82

596 544 494 502 546 561 512 674

1.58 0.50 0.13 0.16 0.19 0.04 −0.36

a The S0−S1 energy is taken from ref 43. For each FAR family, the S0− S1 energy corresponds to the maximum value of a Gaussian distribution.

coupling, and the probability of the intersystem crossing is expected to decrease as the S1−T1 energy gap is increased. Therefore, as can be seen in Table 2, mostly the 5FAR−9FAR PAH populations would undergo intersystem crossing to the T1 level because there ΔE (S1−T1) (see Table 2 and Figure 4) is relatively small (∼0.2 eV). The 5FAR population would undergo intersystem crossing but with less probability, ΔE

Table 3. Calculated and Experimental T1−Tn Transitions Together with Their Symmetry for Several Pericondensed PAHsa

a

The comparison with experimental results considers only the most prominent bands. G

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Figure 5. Calculated low lying T1−Tn excited states for 103 PAHs with numbers of FARs varying from 4 to 11. The carbon ratios and number of systems calculated for each FAR family are provided in Theoretical Methodology. Comparison with Figure 6 shows the importance of large PAHs (around 7 fused aromatic rings, 7FAR, for asphaltene T1−Tn spectra).

experiments included nanosecond pump−probe techniques to generate the triplet state absorption spectra and lifetime measurements. In addition to asphaltenes, many different crude oils were measured as well.48 Only results from preliminary MO analysis were included in this earlier triplet experimental study.48 In the following text, the best theoretical approach for the calculation of the T1−Tn triplet transitions is presented and discussed. In Table 3, the validation of the calculated T1−Tn transitions, for the most predominant bands, is compared with the available experimental data. The experimental T1−Tn spectra on condensed phases have been compiled and thoroughly reviewed by Carmichael et al.85,86 and compared with MO predictions herein. The comparison with the experimental data considers only the most prominent bands with the corresponding oscillator strength. The calculated T1−Tn excitation energies presented in Table 3 are, in general, in quantitative agreement with the experimental values. The average error is 0.13 eV, thus establishing the fact that the methodology used here is adequate. Nguyen et al.73 have reported an average error of 0.11 eV for the predicted T1−Tn excitation energies for organic and organometallic dyes, including free-base porphyrins, phthalocyanines, and their metal complexes using the same methodology to calculate the T1−Tn excitation energies, yielding similar deviations to results in Table 3. In the present work, the geometry optimization of the PAH structures was carried out at the lower and cheaper DFT GGAPW91 level with the DNP basis set, while the electronic T1−Tn triplet transitions are calculated at the TDDFT B3LYP level with the 6-31G+(d, p) basis set, using the cheaper geometry

exhibit spin−orbit coupling. Much of the sulfur in asphaltenes is in aromatic thiophene rings82 and could contribute to spin− orbit coupling in the measured asphaltene triplet electronic manifold spectrum. It is not necessary that the heavy atom be permanently attached to the molecule undergoing transition. Indeed, solvent adjacent heavy atom effect is such an example.83 In the case of asphaltenes, there are heavy atoms in the structure, S, N, O, and in the surroundings there are metalloporphyrins of nickel and vanadium. The presence of metals (especially with unpaired spins) increases the probability of the spin−orbit coupling and the intensity of the singlet− triplet absorption.84 The mechanisms for intersystem crossing involve vibrational coupling between the excited singlet state and a triplet state. In consideration that the singlet−triplet processes are less probable than singlet−singlet processes by a factor of 10−5 to 10−6 and radiationless vibrational processes, such as internal conversion, occur in approximately 10−13 s, the time required for a spin-forbidden vibrational process would be approximately 10−8 to 10−7 s, which is the same order of magnitude as the lifetime of an excited singlet state. Therefore, intersystem crossing can compete with the fluorescence emission from the zeroth vibrational level of an excited singlet state but cannot compete with the vibrational deactivation from a higher vibrational level of a singlet state. 3.2. Triplet−Triplet T1 → Tn Transitions (TT). To further test the understanding of asphaltene PAHs, it is desirable to consider the dynamics of their triplet states. Nevertheless, triplet state spectroscopy is complex, especially on polydisperse materials such as asphaltenes. A recent publication48 (see Introduction) has explored the triplet-state spectroscopy. The H

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Figure 6. Nanosecond pump−probe T1 → Tn absorption spectra of several crude oils and UG8 asphaltene diluted in benzene. The pump excitation wavelength is 355 nm, thereby selecting a population of a range of PAHs.48 Samples were deoxygenated using a freeze−pump−thaw method. All spectra show similar features. For lighter crude oils (right three panels), the selected PAHs exhibit a subtle blue shift. For somewhat heavier crude oils (left, lower two panels) the spectra are red-shifted. Asphaltenes (upper left panel) are deficient in small PAHs and exhibit the largest red shift. The negative absorption is due to population depletion from the pump laser (or “hole burning”).48

shift accounts for the additional red shift.48 Very low energy transitions (long wavelength) are observed (see Figure 5) but are not that numerous and occur for compounds rich in isolated double bond carbon; these compounds are not expected to contribute much to asphaltenes due to their chemical instability.40,47 In Figure 6, the experimental nanosecond pump−probe T1− Tn absorption spectra of several crude oils, light and heavy, and Kuwait-UG8 asphaltene, diluted in benzene, are shown. In these pump−probe experiments the asphaltene molecules were excited within the singlet manifold by a pump laser at 355 nm and underwent intersystem crossing to the lowest triplet. After formation of the T1 state, a flash lamp then further excited the T1 state to higher Tn levels, giving the corresponding T1−Tn excited-state absorption spectra.48 The triplet state spectra are red-shifted compared to corresponding singlet states (see Figure 6) as discussed above and also as observed in the theoretical results (see Figure 5). The asphaltenes (Figure 6, upper left panel) show an additional red shift beyond that of the light crude oils (Figure 6, right three panels) and the somewhat heavier crude oils (Figure 6, lower left panels).

optimized structures, which provides a good result (see Table 3). In the case of the calculated oscillator strength, the comparison with the experimental data is more qualitative than quantitative, but the calculated data in general follows the experimental trend (see Table 3). Some deviation may be attributed to the uncertainty in the T1−Tn experimental coefficients. The experimental spectral maximum does not always correspond to a single vertical excitation, since it often is subject to overlap between neighboring electronic or vibronic bands, which creates long tails that complicate the spectral band integration for estimating the experimental oscillator strength.73,86 In Figure 5, the results of the analysis of the T1−Tn spectra for 103 PAHs, with 4 to 11 fused aromatic rings, are presented for each FAR family. The carbon ratios and number of systems calculated are provided in Theoretical Methodology. In general, the T1−Tn transitions are much lower in energy than the S0−Sn transitions, as discussed above, and because of considerations related to the Rydberg equation.48 The ground triplet state already has one electronically excited electron due to the Pauli Exclusion Principle, thereby reducing the transition energies out of the lowest energy triplet state. In addition, the Stokes I

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Research Laboratory at the Wright-Patterson Air Force Base for fruitful discussions.

The lighter oils (Figure 6, right three panels) show appreciable T1−Tn absorption in the 425−550 nm range; the somewhat heavier oils (Figure 6, lower left two panels) show appreciable T1−Tn absorption in the 450−600 nm range, and the asphaltenes (Figure 6, first left panel) show appreciable T1− Tn absorption in the 550−800 nm range.48 Figures 5 and 6 show that this spectral trend in longer wavelength is consistent with the increasing importance of larger PAHs for heavier samples. In the former section, it was concluded that mainly the 5FAR−9FAR PAH chromophores are likely to undergo intersystem crossing to the T1 triplet state from the S1 state, at the pump excitation wavelength of 355 nm and in the calculated sample distribution. By a comparison of Figures 5 and 6, it can be concluded that the UG8-asphaltene contains appreciable spectral contribution from PAHs in the range of 6FAR to 8FAR. The sharp contrast of asphaltenes versus the lighter crude oils clearly shows a marked difference that includes a larger PAH size distribution for asphaltenes.

■

■

CONCLUSIONS Optical spectral analysis using both experimental and theoretical methods is an excellent procedure to investigate the distribution of asphaltene PAHs. Specifically, molecular orbital calculations are mandated for the interpretation of optical spectra. For investigation of the singlet manifold, the optical measurements border on trivial, while the requirements for MO calculations are laborious due to the large number of contributing PAH types and structures for asphaltenes. Corresponding previous experimental and theoretical work within the singlet manifold indicate that asphaltene PAHs have a distribution centered at ∼7 fused aromatic rings (7FAR) with the bulk of the distribution in the range from 4 to 10 fused aromatic ring systems (4FAR−10FAR). The present work extends these concepts to the triplet electronic manifold; both the theoretical and experimental methods are significantly more challenging for the triplet manifold than for the singlet manifold. Previous optical spectroscopy and lifetime experimental results for asphaltenes and crude oils within the triplet electronic manifold showed expected spectral red shifts for increasingly heavier samples. This paper reviews the demanding MO calculations for (open shell) triplet electronic manifold to interpret the experimental results. The specific MO methods selected are discussed in detail. Benchmarking of these calculations with both S0−T1 and T1−Tn experimental data reported in the literature for PAHs is discussed, establishing validity of the methods herein. The importance of this work is to interpret the first reported triplet state spectroscopy of asphaltenes. The results show excellent consistency with interpretation of the singlet manifold, namely that the distribution of asphaltene PAHs is maximum for ∼7 fused aromatic rings (7FAR) and has significant population in the 4FAR to 10FAR range.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS We would like to thank Dr. Thomas M. Cooper from the Materials and Manufacturing Directorate of the Air Force J

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