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.

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 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.

Relations between the aromaticity and magnetic dipole transitions in the electronic spectra of hetero[8]circulenes.

Magnetically induced current densities have been calculated at the second-order Møller-Plesset perturbation theory (MP2) level for seven hetero[8]circulenes and their dicationic and dianionic forms. Calculations of the magnetic dipole transition moments have also been carried out at the algebraic diagrammatic construction (ADC(2)) and the second-order approximate coupled-cluster (CC2) levels. The calculations show that the degree of aromaticity and the size of the magnetic dipole transition moment of the lowest magnetic-dipole allowed excited state are related. We show that neutral hetero[8]circulenes are weakly antiaromatic when the first excited state with a large magnetic dipole transition moment of 10-16 a.u. lies at high energies (∼2.8-3.5 eV). For the dications, this transition often lies at much lower energies. Hetero[8]circulene dications with large magnetic dipole transition moments are strongly antiaromatic. The lowest excited states of the hetero[8]circulene dianions have very small magnetic dipole transition moments implying that they are aromatic.

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.

Magnetic response properties of gaudiene - a cavernous and aromatic carbocage.

A spherical and cavernous carbocage molecule exhibiting faces with larger ring sizes than regular fullerenes is a suitable species for investigating how molecular magnetic properties depend on the structure of the molecular framework. The studied all-carbon gaudiene (C72) is a highly symmetrical molecule with three- and four-fold faces formed by twelve membered rings. Here, we attempt to unravel the magnetic response properties of C72 by performing magnetic shielding and current density calculations with the external magnetic field applied in different directions. The obtained results indicate that the induced current density flows mainly along the chemical bonds that are largely perpendicular to the magnetic field direction. However, the overall current strength for different directions of the magnetic field is nearly isotropic differing by only 10% indicating that C72 can to some extent be considered to be a spherical aromatic molecule, whose current density and magnetic shielding are ideally completely isotropic. The induced magnetic field is found to exhibit long-range shielding cones in the field direction with a small deshielding region located perpendicularly to the field outside the molecule. The magnetic shielding is isotropic inside the molecular framework of C72, whereas an orientation-dependent magnetic response appears mainly at the exterior of the molecular cage.

A divide and conquer real-space approach for all-electron molecular electrostatic potentials and interaction energies.

A computational scheme to perform accurate numerical calculations of electrostatic potentials and interaction energies for molecular systems has been developed and implemented. Molecular electron and energy densities are divided into overlapping atom-centered atomic contributions and a three-dimensional molecular remainder. The steep nuclear cusps are included in the atom-centered functions making the three-dimensional remainder smooth enough to be accurately represented with a tractable amount of grid points. The one-dimensional radial functions of the atom-centered contributions as well as the three-dimensional remainder are expanded using finite element functions. The electrostatic potential is calculated by integrating the Coulomb potential for each separate density contribution, using our tensorial finite element method for the three-dimensional remainder. We also provide algorithms to compute accurate electron-electron and electron-nuclear interactions numerically using the proposed partitioning. The methods have been tested on all-electron densities of 18 reasonable large molecules containing elements up to Zn. The accuracy of the calculated Coulomb interaction energies is in the range of 10(-3) to 10(-6) E(h) when using an equidistant grid with a step length of 0.05 a(0).

The direct approach to gravitation and electrostatics method for periodic systems.

The direct approach to gravitation and electrostatics (DAGE) algorithm is an accurate, efficient, and flexible method for calculating electrostatic potentials. In this paper, we show that the algorithm can be easily extended to consider systems with many different kinds of periodicities, such as crystal lattices, surfaces, or wires. The accuracy and performance are nearly the same for periodic and aperiodic systems. The electrostatic potential for semiperiodic systems, namely defects in crystal lattices, can be obtained by combining periodic and aperiodic calculations. The method has been applied to an ionic model system mimicking NaCl, and to a corresponding covalent model system.

Universal method for computation of electrostatic potentials.

A computational approach to determine electrostatic interaction and gravitational potentials by performing direct numerical integration is presented. The potential is expanded using finite-element functions of arbitrary order. The method does not involve any solutions of systems of linear equations. The potential is instead obtained as a sum of differential contributions. Thus, no boundary conditions for the potential are needed. It is computationally efficient and well suited for parallel computers, since the innermost loops constitute matrix multiplications and the outer ones can be used as parallel indices. Without using prescreening or other computational tricks to speed up the calculation, the algorithm scales as N4/3 where N denotes the grid size.

The quest for beryllium peroxides.

There is no experimental proof documented in the literature for the existence of any beryllium peroxide compound. All recent pertinent preparative attempts described in this work, using a range of beryllium salts with various peroxides as reagents under mild conditions, were equally unsuccessful. (1)H and (9)Be NMR investigations of aqueous solutions containing beryllium salts and hydrogen peroxide in a broad pH range also gave no definite evidence for the presence of peroxoberyllates as components of the manifold equilibria in such solutions. Quantum chemical calculations have therefore been carried out to delineate the energetics and structures of various beryllium peroxide model compounds. Standard Hartree-Fock and density functional methods were employed at various levels of sophistication. The series of prototypes considered consists of [BeOH](+), Be(OH)(2), Be(OH)(OOH), Be(OOH)(2), [Be(O(2))(2)](2-), [BeO(2)(OH(2))(2)], and [Be(2)(O(2))(2)(OH(2))(4)] (all in the gas phase). Surprisingly, the triatomic cation [BeOH](+) has been found to have a linear structure. All the Be-O(peroxide) bonds are found to be rather long, suggesting weaker bonding compared to the Be-O bonds in aquo, hydroxo, or oxo complexes. Hydrogen peroxide or anions derived therefrom are therefore not able to compete successfully with water (hydroxide anions) in aqueous solution. In the mononuclear beryllium peroxide molecules, the peroxide groups form chelating units at tetrahedrally 4-coordinate metal atoms. The binuclear compound [Be(2)(O(2))(2)(OH(2))(4)] has a puckered six-membered-ring structure, close to the standard chair conformation. A significant lengthening of the O-O bonds upon coordination to the Be(2+) centers has been calculated, but it is unlikely that the polarization of the peroxide group by the high positive charge density at Be(2+) is significant to cause an intrinsic instability of beryllium peroxides. All structures represent distinct local minima on the potential energy surface and are predicted to be (meta)stable species in nonaqueous media. The field of aluminum peroxides is a similar gray area on the map of metal and metalloid peroxides and is reminiscent of the well-established "diagonal-relation" of Be and Al in the periodic table of the elements.

The aromatic character of magnesium porphyrins

The aromaticity of magnesium porphyrins have been studied by calculating the nuclear magnetic shieldings in selected points outside the molecules. The strength of the induced ring currents for a given magnetic field have been obtained by using the aromatic-ring-current-shielding (ARCS) method. Nucleus-independent chemical shift (NICS) calculations provide additional information about the current routes in the multiple-ring systems. The total aromatic pathway of magnesium porphyrins must be considered as a superposition of several (4n + 2) pi-electron Huckel pathways. We found that all beta-unsaturated pyrrolic rings have local ring currents the strength of which is 70-90% of the current strength for the pyrrole molecule. The present study also shows that the 18pi-[16]annulene aromatic pathway does not exist in magnesium porphyrins until all four pyrrolic units are saturated in the beta-position.