Intramolecular rate-constant calculations based on the correlation function using temperature dependent quantum Green's functions.

A theoretical method for calculating rate constants for internal conversion (IC), intersystem crossing (ISC) and radiative (R) electronic transitions is presented. The employed method uses temperature-dependent quantum Green's functions, which give the opportunity to consider almost any nth-order polynomial perturbation operator and the influence of external electromagnetic fields on the rate constants. The rate constants of the IC, ISC and R processes are calculated for two important indocyanine molecules namely indocyanine green (ICG) and heptamethine cyanine (IR808) at the Franck-Condon level using the temperature-dependent quantum Green's function approach. Calculations at the time-dependent density functional theory level with the MN15 functional show that ICG and IR808 have only one triplet state below the S1 state. The main deactivation channel of the S1 state is the IC process with a large (kIC(S1 → S0)) rate constant of ∼109-1011 s-1. The estimated quantum yield of fluorescence (φfl) is ∼0.001-0.24 for the two studied molecules, which agrees rather well with experimental values. Thus, the present approach enables calculations of the three kinds of rate constants and the quantum yield of fluorescence using the same computational methodology.

Internal conversion induced by external electric and magnetic fields.

We have developed a new methodology for calculating contributions to the rate constants (kIC) of internal conversion that are induced by external electric (kIC-E) or magnetic (kIC-M) fields. The influence of the external electric and magnetic fields on the kIC was estimated for seven representative molecules. We show that the kIC-E contribution calculated at a field strength of 1011 V m-1 is generally as large as the kIC rate constant in the absence of the external field. For indocyanine green, azaoxa[8]circulene, and pyromitene 567, the kIC-E contribution is as large as kIC already at a field strength of 109 V m-1. Such electric-field strengths occur for example in plasmonic studies and in strong laser-field experiments. The induced effect on the kIC rate constant should be accounted for in calculations of photophysical properties of molecules involved in such experiments. The induced effect of an external magnetic field on kIC can be neglected in experiments on Earth because the magnetic contribution becomes significant only at very strong magnetic fields of 104-105 T that cannot be achieved on Earth. However, the magnetic effect on the rate constant of internal conversion can be important in astrophysical studies, where extremely strong magnetic fields occur near neutron stars and white dwarfs.

Internal conversion rate constant calculations considering Duschinsky, anharmonic and Herzberg-Teller effects.

A novel method for calculating rate constants for internal conversion (kIC) that simultaneously accounts for Duschinsky, anharmonic and Herzberg-Teller effects has been developed and implemented. This method has been applied to robust planar molecules like tetraoxa[8]circulene (4B), free-base porphyrin (H2P) and pyrometene (PM567) with small Duschinsky rotation (i.e. with almost identical normal coordinates in the ground and excited states) and to poly[n]fluorenes (P[n]F) (n = 2-14) with a substantial Duschinsky rotation. The obtained results show that the Duschinsky effect is large in the harmonic approximation, whereas it is in general much smaller in the anharmonic approximation. The Duschinsky effect is found to be large for high frequency vibrational modes with energies of ∼3300 cm-1 such as the X-H (X = C, N and O) stretching modes that mix in the S1 → S0 electronic transition. However, even in this case, the increase in kIC due to the Duschinsky effect does not exceed one order of magnitude. The calculations show that anharmonic contributions to kIC are larger than Herzberg-Teller contributions which in turn are larger than contributions from the Duschinsky effect ANH > HT > Du. We also show that an approximation, where only X-H bonds are considered in the kIC calculation, is accurate even for P[n]F (n = 2-14).

Fast estimation of the internal conversion rate constant in photophysical applications.

An efficient method for estimating non-adiabatic coupling matrix elements (NACME) and rate constants for internal conversion (kIC) is presented. The method, based on Plotnikov's theory, requires only calculations of the electronic wave functions and the corresponding electronic excitation energies. Computationally expensive calculations of the derivatives of the electronic wave function with respect to the nuclear coordinates are avoided. When the main accepting modes of the electronic excitation energy are X-H vibrations, the present method can be used for estimating the efficiency of the energy transfer between donor and acceptor molecules. It can also be used in studies of the influence of hydrogen bonding or solvent effect on fluorescence quenching, in studies of vibronic effects of TADF (thermally activated delayed fluorescence) emitters, and for calculating kIC. Here, kIC and NACME are calculated for free-base porhyrin, magnesium porphyrin, azulene, naphthalene, pyrene and fluorenone interacting with a solvent molecule. Reverse kIC and NACME are further calculated for the T1→ T2 transition of dibenzothiophene-S,S-dioxide (PTZ-DBTO2), which is used in TADF applications. Finally, we estimate the efficiency of the energy transfer between two large porphyrinoid dimers.

First-principles calculations of anharmonic and deuteration effects on the photophysical properties of polyacenes and porphyrinoids.

A new method for calculating internal conversion rate constants (k[combining low line]IC), including anharmonic effects and using the Lagrangian multiplier technique, is proposed. The deuteration effect on k[combining low line]IC is investigated for naphthalene, anthracene, free-base porphyrin (H2P) and tetraphenylporphyrin (H2TPP). The results show that anharmonic effects are important when calculating k[combining low line]IC for transitions between electronic states that are energetically separated (ΔE) by more than 20 000-25 000 cm-1. Anharmonic effects are also important when ΔE < 20 000-25 000 cm-1 and when the accepting modes are X-H stretching vibrations with a frequency larger than 2000 cm-1. The calculations show that there is mixing between the S1 and S2 states of naphthalene induced by non-adiabatic interactions. The non-adiabatic interaction matrix element between the S1 and S2 states is 250 cm-1 and 50 cm-1 for the normal and fully deuterated naphthalene structure and this difference significantly affects the estimated fluorescence quantum yield. Besides aromatic hydrocarbons H2P and H2TPP, the k[combining low line]IC rate constant is also calculated for pyrometene (PM567) and tetraoxa[8]circulene (4B) with a detailed analysis of the effect of the vibrational anharmonicity.

Aromaticity and photophysics of tetrasila- and tetragerma-annelated tetrathienylenes as new representatives of the hetero[8]circulene family.

The electronic structure, absorption and emission spectra, aromaticity and photophysical behavior of the recently synthesized tetrasilatetrathia[8]circulene and tetragermatetrathia[8]circulene compounds have been studied computationally. Both compounds demonstrate a specific bifacial aromaticity, which is unusual for hetero[8]circulenes; the inner eight-membered core sustains an expected strong paratropic magnetically-induced ring current, while the outer perimeter contains saturated Si(Et)2 and Ge(Et)2 moieties which break the conjugation between the thiophene rings. The overall magnetically-induced ring current for both studied circulenes is close to zero because of the strong local diatropic currents in each thiophene ring that compensate the paratropic counterpart. The electronic absorption and emission spectra of tetrasilatetrathia[8]circulene and tetragermatetrathia[8]circulene demonstrate a clear visible vibronic progression. The 0-0 band is the most active one in the absorption spectra, while in the fluorescence spectra the 0-1 band composed of several normal vibrations is more intense compared with the 0-0 band in excellent agreement with experiment. Accounting for spin-orbit coupling effects, an analysis of the photophysical constants for the two compounds demonstrates: (1) a clear manifestation of the internal heavy atom effect on the inter-system crossing efficiency; (2) one to two order domination of non-radiative rates over the fluorescence rate; and (3) that the S1-S0 internal conversion is extremely slow and can not compete with the fluorescence, while the S1-Tn inter-system crossing is a main deactivation channel of the S1 excited state. These results provide new insight into the electronic structure and photophysics of tetrasilatetrathia[8]circulene and tetragermatetrathia[8]circulene as novel standalone representatives of hetero[8]circulenes - tetraannelated derivatives of tetrathienylene.

First-principles method for calculating the rate constants of internal-conversion and intersystem-crossing transitions.

A method for calculating the rate constants for internal-conversion (kIC) and intersystem-crossing (kISC) processes within the adiabatic and Franck-Condon (FC) approximations is proposed. The applicability of the method is demonstrated by calculation of kIC and kISC for a set of organic and organometallic compounds with experimentally known spectroscopic properties. The studied molecules were pyrromethene-567 dye, psoralene, hetero[8]circulenes, free-base porphyrin, naphthalene, and larger polyacenes. We also studied fac-Alq3 and fac-Ir(ppy)3, which are important molecules in organic light emitting diodes (OLEDs). The excitation energies were calculated at the multi-configuration quasi-degenerate second-order perturbation theory (XMC-QDPT2) level, which is found to yield excitation energies in good agreement with experimental data. Spin-orbit coupling matrix elements, non-adiabatic coupling matrix elements, Huang-Rhys factors, and vibrational energies were calculated at the time-dependent density functional theory (TDDFT) and complete active space self-consistent field (CASSCF) levels. The computed fluorescence quantum yields for the pyrromethene-567 dye, psoralene, hetero[8]circulenes, fac-Alq3 and fac-Ir(ppy)3 agree well with experimental data, whereas for the free-base porphyrin, naphthalene, and the polyacenes, the obtained quantum yields significantly differ from the experimental values, because the FC and adiabatic approximations are not accurate for these molecules.

The computational and experimental investigations of photophysical and spectroscopic properties of BF2 dipyrromethene complexes.

The electronic excited states of BF2 dipyrromethene (2BrDPM, DPMI, DPMII, PM567 and 4PhDPM) complexes were investigated using the extended multi-configuration quasi-degenerate at the second order of perturbation theory (XMCQDPT2) and the second-order approximate coupled-cluster (CC2) methods. The excitation energies calculated by CC2 are significantly overestimated by 0.42-0.59 eV because of the substantial contributions of double excitation levels to excited states (>10%). However, the calculated XMCQDPT2 excitation energies agree well with experimental ones within the accuracy 0.11-0.20eV. The very low lasing efficiency (7.8-8.4%) of 4PhDPM compound was explained by the T1→T4 and T1→T5 reabsorptions at XMCQDPT2 level of theory. The molecular photonics of pyrromethenes are studied using a combination of the first-principle and semi-empirical calculations. The main mechanism for the deactivation of the energy of the first singlet excited electronic state is the radiative electronic transition for DPMI, DPMII, PM567 and 4PhDPM compounds. Also, the main mechanism for the quenching of fluorescence in considered complexes (except DPMII compound) is the internal conversion. The processes of the internal conversion and intersystem crossing compete with each other in DPMII compound. The measured and calculated fluorescence quantum yields agree well for all considered molecules.

Theoretical investigation of fluorescence properties of EDTA and DTPA substituted tetraphenylporphyrin molecules.

The matrix elements of spin-orbit coupling operator (H(SO)) and non-adiabatic coupling operator (Ω) for the H(2)ATPP-EDTA and H(2)ATPP-DTPA molecules were calculated using INDO method. Rate constants of internal conversion and of intersystem crossing were calculated using the values of matrix elements of H(SO) and Ω operators and excitation energies both calculated with the ADC(2) and TDDFT methods and obtained from experimental data. Results of calculations show that the probability of radiationless deactivation in internal conversion channel is greater than the probability of radiationless transition in intersystem crossing channel for considered molecules. Obtained theoretical values of fluorescence quantum yield have good agreement with their experimental values.

Electronic absorption spectrum of monoamine tetraphenylporphyrin with the complexon of ethylenediaminetetraacetic acid as substitute.

In the framework of density functional theory the equilibrium geometry of the ground electronic state of monoamine tetraphenylporphyrin with the complexon of ethylenediaminetetraacetic acid was found using B3LYP functional and 6-31G(d,p) basis set. Electronic absorption spectrum of this molecule in ethanol solution was measured in the range of 300-600nm and interpreted using the PCM/TDDFT method (with the B3LYP, CAMB3LYP, M06-2X functionals) with 6-31G(d,p) and 6-31++G(d,p) basis sets. The observed and calculated line positions and intensities are well agreed.

Calculation of rovibrational energy states for water vapor using the symmetric top approximation in the Pade form.

Considering the water vapor molecule for ka > or = J/2 >> 1 as a symmetric top, the simple analytical Pade form for vibrational rotational energy levels was proposed. The rotational spectroscopic parameters for ground and 010 vibrational states of H2O molecule in the framework of this model have been obtained with good prediction. The absorption coefficient of water vapor in the spectral range 725-925 cm(-1) has been calculated for 1000-6000 K temperatures taking into account the transitions to high-excited states up to J < or = 35 and J < or = 30 for the 000 and 010 vibrational states, respectively. It is shown that the prominent role of transitions to high-excited states is in 8-12 microm atmospheric transparency window.