Determination Of Heterocyclic Molecules Ionization Potential Based On Optical Absorption Spectra Of Electromagnetic Radiation In The Visible And UV Range
An extensive field of application of such molecules requires information on the electronic structure, in particular, the first vertical ionization potentials (IP), which determine the processes of electron transfer under the influence of electromagnetic radiation in the optical region and the electron-donating ability of materials.
Molecules containing a large number of carbon atoms and heteroatoms, e. g., nitrogen, oxygen, sulfur, are known to be characterized by strong effects of exchange and Coulomb interaction of electrons, the so-called correlation interaction, which is difficult to take into account in calculations and experiments . It is known that optical spectroscopy is used to determine the first vertical IP, in addition to the methods of photoelectron spectroscopy and photoionization [10–12].
The earlier studies demonstrate the efficiency of using integral phenomenological parameters of optical spectra for determining the first effective vertical IP of the molecules [10–12]. But the additive integral parameters that are used in these studies do not sufficiently take into account the effects of electron correlation, associated with the exchange and Coulomb interaction of electrons in different energy states [13–15].
The aim of this research is to investigate the integral correlation phenomenological characteristics of the optical spectra of heterocyclic condensed media of nitrogen and oxygen-containing molecules. In particular, the study of the relationships between the integral parameters of the autocorrelation functions of the optical spectrum and the first vertical IP is within the framework of the hypothesis of a strong correlation of electronic states.
Spectra characteristic feature is that the spectra of the separate molecules under research are of a continuous nature, in the form of a system of bands associated with the interaction of vibrational electronic states.
Without resorting to the Fourier transform for the separation of bands, we shall consider energy spectrum of the molecule in the form of autocorrelation function (ACF), which depends on the frequency of the electronic transfers. We shall consider the integral value of ACF as a measure of the interaction of molecule electronic states at certain frequencies of the electronic transfers from one energy state to another. As it is known from the theory of signals [16, 17] and optical spectra , ACF has the following form:
where are the frequency distribution functions of radiation absorption intensities in the visible and UV spectra at frequencies of , respectively. As it is known [19, 20], the correlation function can be expressed in terms of resonant frequencies, using Wiener-Khinchin theorem
Formula (2) establishes a direct connection between the energy spectrum of the resonance electronic states and ACF, but the search for these frequencies by the Fourier transform method is not a part of our task.
Since the statistical analysis of the spectrum includes the near UV and visible regions in the range of 190–760 nm (6.53–10.63 eV) in this research, ACF is replaced by an integral parameter of this function (IACF), which is a particular integral having a specific numerical value in the energy scale:
where E is the radiation energy, eV; E1, E2 are spectral boundaries, eV; S (E) and S (E + ΔE) are the spectral distribution functions of the radiation absorption intensities in the visible and UV spectra with energies of E and E + ΔE, respectively.
The integral transformation is used as IACF (IA, eV) in the form of basic and retarding logarithmic function, i. e., , is the molar absorption ratio. Then
Since IACF reflects the interconnection of the resonance electronic states that correspond to electronic transfers creating the electron spectrum, this parameter reflects the correlation interaction of electrons on the one hand and the energy of electronic states on the other hand. Therefore, we should expect the interrelation of this parameter with IP, which characterizes the energy of the higher occupied molecular orbital.
To test this hypothesis, we investigated the interrelation of IACF calculated from the experimental absorption spectra of heterocyclic molecules with IP obtained by Hartree-Fock method, RHF‑6–31G** . In the calculations it is assumed that the process of absorption of radiation by molecules is ergodic and stationary, i. e. the time of light passage through the sample being researched is much shorter than the relaxation time of the electronic states.
93 spectra of heterocyclic molecules were examined, in particular, the spectra of oxygen-containing molecules belonging to the series of phenols, complex aromatic alcohols and ethers, ketones and aldehydes, polyene acids and quinines, as well the spectra of nitrogen-containing molecules belonging to the series of acridines and pyridines (Fig. 1). The spectra of hetero-containing compounds include absorption bands, the appearance of which is caused by π → π* transitions due to the presence of a conjugated chain, characterized by high intensity, as well as by low-intensity forbidden by symmetry transitions of n → π*, n → σ*.
The spectra were registred in the absorption range from 190 to 760 nm on an automatic electronic spectrometer SF‑2000 with a step of 1 nm and the output of the results via ADC to a computer. Furthermore, the spectra of individual compounds were selected from the database .
Thus, we move to the energy scale of the spectrum. By processing the data of spectroscopy and quantum calculations using least square method, the statistical relationships of the first IP and IACF are studied. In the course of calculations, for all classes of organic compounds, a physical effect is established that connects IACF to the first IP for the molecules under study:
where IP is the first vertical IP, eV; , are empirical ratios that are constant for molecules close in chemical nature, whose dimensions are eV and dimensionless, respectively.
The physical meaning of these ratios, apparently, is as follows: characterizes IP value in a given series in the absence of autocorrelation of states ; characterizes the change in IP with an increase in the correlation energy of repulsion of electrons, which is determined by the IACF growth. Graphically, the dependence (5) is shown in Fig. 2. Empirical ratios of dependences (5) for the first IP of oxygen- and nitrogen-containing molecules are given in Table 1.
Quasilinear connection of IP and ACF is confirmed by statistical data processing by the least square method. The corresponding average relative deviations are from 0.06 to 3.05 eV; determination ratios are from 0.76 to 0.99; variation ratios are from 3.99 to 6.82; root-mean-square deviations are from 0.35 to 0.64 eV; ratios are in the range from 9.35 to 11.34 eV; ratios are in the range from –2.98 to – 7.87 (Table 1). As follows from the values of the ratios, the smallest value of the correlation parameters is in the series of pyridines and acridines < quinones < ketones and aldehydes < polyenoic acids < alcohols and oxy compounds. These circumstances coincide with the conclusions of the molecules quantum theory .
Thus, there is a physical effect connecting IACF with the first UI. The reason for this is probably the correlation of electronic states belonging to different molecular orbitals of heterocyclic compounds. Therefore, it can be assumed that it is possible to determine IP directly from the electronic spectra by frequency-based IACF in the visible and near-UV ranges of the spectrum.
The established dependencies are as good as other experimental methods and quantum-chemical calculation methods in RHF‑6–31G** approximation. Table 2 shows the characteristics of adequacy of IP empirical and calculated estimates for various molecules.
On the basis of spectral representations as a plurality of interacting excited electronic states in a strongly correlated quantum system, a physical effect binding ionization potentials of oxygen- and nitrogen-containing heterocyclic molecules with an integral phenomenological characteristic of absorption of electromagnetic radiation was discovered, an integral parameter of autocorrelation function of the signal in the range 6.53 .1.63 eV (190…760 nm).
The established regularities allow reducing the estimates of the first ionization potentials of oxygen- and nitrogen-containing molecules by integral parameters of the autocorrelation function of the optical absorption spectra in the UV and visible regions with the accuracy sufficient for practical applications, ±(0.1…0.3) eV, thus providing for correct information about electronic structure of the molecules and the properties of complex molecular systems, and organic semiconductors without quantum calculations and division of spectral bands by Fourier transform.
The established regularities may be used in molecular electronics, photonics, photochemistry and physical chemistry for the study of electron transfer processes, as well as in the estimates of the characteristics of the band structure of nanoparticles in condensed matter physics.