The Role of Triplet States in the Photodissociation of a Platinum Azide Complex by a Density Matrix Renormalization Group Method

Platinum azide complexes are appealing anticancer photochemotherapy drug candidates because they release cytotoxic azide radicals upon light irradiation. Here we present a density matrix renormalization group self-consistent field (DMRG-SCF) study of the azide photodissociation mechanism of trans,trans,trans-[Pt(N3)2(OH)2(NH3)2], including spin–orbit coupling. We find a complex interplay of singlet and triplet electronic excited states that falls into three different dissociation channels at well-separated energies. These channels can be accessed either via direct excitation into barrierless dissociative states or via intermediate doorway states from which the system undergoes non-radiative internal conversion and intersystem crossing. The high density of states, particularly of spin-mixed states, is key to aid non-radiative population transfer and enhance photodissociation along the lowest electronic excited states.

These calculation have been performed with the TURBOMOLE 7.0 11 program package.
Using the above molecular structure, multiconfigurational density matrix renormalisation group-self consistent field (DMRG-SCF) 12,13 calculations have been carried out with an active orbital space consisting of 26 electrons in 19 orbitals. The comprising orbitals are depicted in Fig. S1. The number of renormalised block states (m) has been set to 500. To estimate the effect of m on the accuracy of the calculation, we also performed a single-point calculation of singlet states with m = 1000 at the equilibrium structure, but the excitation energies differed only slightly from those obtained with m = 500 (see Table S3): hence, for performance reasons we settled for a value of m = 500 for the remaining calculations.
To validate the results further, we performed multiconfigurational calculations that include dynamic correlation, namely quasi-degenerate n-electron valence based second-order perturbation theory calculations based on our DMRG-SCF reference wavefunction with m = 500 (DMRG-QD-NEVPT2). 14-17 Due to a very large computational cost, only three lowest singlet state energies at the Franck-Condon structure were computed. The results are presented in Table S4.
These calculations employed the all-electron ANO-RCC valence quadruple-zeta polarised (ANO-RCC-VQZP) basis set 18 for Pt and its more compact triple-zeta pendant, ANO-RCC-VTZP, for remaining atoms. Two-electron integrals were calculated with the atomic compact S2 Cholesky decomposition (CD) approach 19-21 with a decomposition threshold of 10 −4 a. u., and the second-order scalar-relativistic Douglas-Kroll-Hess one-electron Hamiltonian [22][23][24] was used to account for scalar relativistic effects.
The DMRG-SCF calculations have been performed in a state-average manner, averaging separately over the different spin states, i. e. as two separate state-average calculations averaging over 16 singlet and 10 triplet states, respectively. Out of these states, only 10 lowest singlet and 9 triplet states were considered due to intruder state problems with higher excited states and since higher-lying excited states are not relevant for the excitation near the absorption maximum anyway. Spin-orbit couplings were calculated with the SO-MPSSI 25,26 approach. All multiconfigurational calculations were performed with the OpenMOLCAS 27 program package and its interface to the QCMaquis DMRG program. 28 Figure S1: Active orbitals employed for DMRG-SCF calculations of the Pt complex discussed in this work. The plus or minus signs in the orbital description denote bonding and antibonding interaction of the orbitals.
S4 Table S1: Spin-free excitation energies, oscillator strengths and characters of the lowest singlet and triplet excited states of complex 1. The excited state characters are obtained from the natural transition orbitals (NTOs) for each state: orbital contributions in parentheses denote a small contribution, plus or minus signs denote bonding or antibonding interaction, respectively. The bright states are highlighted in bold.
State ∆E/eV f Character  T1  T2  T3  T4  T5  T6  T7  T8  T9   T1   T2   T3   T4   T5   T6   T7   T8 T1  T2  T3  T4  T5  T6  T7  T8  T9   T1   T2   T3   T4   T5   T6   T7   T8 T1  T2  T3  T4  T5  T6  T7  T8  T9   T1   T2   T3   T4   T5   T6   T7   T8   While the electronic energies between the respective states differ of up to 5 × 10 −3 a. u., the absolute difference between excitation energies (i. e. energy differences of the excited states to the respective ground state) is smaller than 0.1 eV for all states.  Table S4 shows the energies of three lowest singlet states of complex 1 at the equilibrium structure calculated with DMRG-QD-NEVPT2. Compared to DMRG-SCF results, the relative energy of S 1 is red-shifted by 0.30 eV and that of S 2 by 0.23 eV. We assume that a similar shift should be expected also for higher excited singlet states, and thus the inclusion of dynamic correlation should improve the agreement with the experiment by a similar amount.