Multiconfigurational Second-order Perturbation Theory Research Articles

Lagrangian of extended multiconfigurational self-consistent field second-order quasidegenerate perturbation theory combined with reference interaction site model self-consistent field constraint spatial electron density.

Lagrangians of the state-averaged multiconfigurational self-consistent field (SA-MCSCF) and multistate extended second-order quasidegenerate perturbation theory (MS-XMCQDPT2) coupled with the reference interaction site model self-consistent field constraint spatial electron density are defined. In addition, variational equations were derived to calculate the excitation energies of the target molecules dissolved in various solvents. The theory was applied to a phenol molecule in various solutions, and the gradients and Hessian matrices were calculated to evaluate the absorption spectral lines, including the broadening bandwidth. Numerical calculations revealed fine structures in any solvent surroundings. The main intramolecular vibrational modes related to such fine structures were stretching vibrations of the aromatic ring and the oxygen atom of the phenol molecule. The present theory plays an important role in predicting the structure of potential energy surfaces, such as Hessian matrices for various solvent types, during the photoexcitation process.

Reconciling TD-DFT and CASPT2 electronic structure methods for describing the photophysics of DNA.

Time-dependent density functional theory (TD-DFT) and multiconfigurational second-order perturbation theory (CASPT2) are two of the most widely used methods to investigate photoinduced dynamics in DNA-based systems. These methods sometimes give diverse dynamics in physiological environments usually modeled by quantum mechanics/molecular mechanics (QM/MM) protocol. In this work, we demonstrate for the uridine test case that the underlying topology of the potential energy surfaces of electronic states involved in photoinduced relaxation is similar in both electronic structure methods. This is verified by analyzing surface-hopping dynamics performed at the QM/MM level on aqueous solvated uridine at TD-DFT and CASPT2 levels. By constraining the dynamics to remain on state we observe similar fluctuations in energy and relaxation lifetimes in surface-hopping dynamics in both TD-DFT and experimentally validated CASPT2 methods. This finding calls for a systematic comparison of the ES potential energy surfaces of DNA and RNA nucleosides at the single- and multi-reference levels of theory. The anomalous long excited state lifetime at the TD-DFT level is explained by trapping due to the tendency of TD-DFT in QM/MM schemes with electrostatic embedding to underestimate the energy of the state leading to a wrong energetic order. A study of the FC energetics suggests that improving the description of the surrounding environment through polarizable embedding or by the expansion of QM layer with hydrogen-bonded waters helps restore the correct state order at TD-DFT level. Thus by combining TDDFT with an accurate modeling of the environment, TD-DFT is positioned as the standout protocol to model photoinduced dynamics in DNA-based aggregates and multimers.

Spin-orbit coupling of electrons on separate lanthanide atoms of Pr2O2 and its singly charged cation.

Although it plays a critical role in the photophysics and catalysis of lanthanides, spin-orbit coupling of electrons on individual lanthanide atoms in small clusters is not well understood. The major objective of this work is to probe such coupling of the praseodymium (Pr) 4f and 6s electrons in Pr2O2 and Pr2O2+. The approach combines mass-analyzed threshold ionization spectroscopy and spin-orbit multiconfiguration second-order quasi-degenerate perturbation theory. The energies of six ionization transitions are precisely measured; the adiabatic ionization energy of the neutral cluster is 38 045 (5) cm-1. Most of the electronic states involved in these transitions are identified as spin-orbit coupled states consisting of two or more electron spins. The electron configurations of these states are 4f46s2 for the neutral cluster and 4f46s for the singly charged cation, both in planar rhombus-type structures. The spin-orbit splitting due to the coupling of the electrons on the separate Pratoms is on the order of hundreds of wavenumbers.

Iron(II) Complexes with Porphyrin and Tetrabenzoporphyrin: CASSCF/MCQDPT2 Study of the Electronic Structures and UV-Vis Spectra by sTD-DFT.

The geometry and electronic structures of iron(II) complexes with porphyrin (FeP) and tetrabenzoporphyrin (FeTBP) in ground and low-lying excited electronic states are determined by DFT (PBE0/def2-TZVP) calculations and the complete active space self-consistent field (CASSCF) method, followed by the multiconfigurational quasi-degenerate second-order perturbation theory (MCQDPT2) approach to determine the dynamic electron correlation. The minima on the potential energy surfaces (PESs) of the ground (3A2g) and low-lying, high-spin (5A1g) electronic states correspond to the planar structures of FeP and FeTBP with D4h symmetry. According to the results of the MCQDPT2 calculations, the wave functions of the 3A2g and 5A1g electronic states are single determinant. The electronic absorption (UV-Vis) spectra of FeP and FeTBP are simulated within the framework of the simplified time-dependent density functional theory (sTDDFT) approach with the use of the long-range corrected CAM-B3LYP function. The most intensive bands of the UV-Vis spectra of FeP and FeTBP occur in the Soret near-UV region of 370-390 nm.

Electronic states and transitions of PrO and PrO+ probed by threshold ionization spectroscopy and spin-orbit multiconfiguration perturbation theory.

The precise ionization energy of praseodymium oxide (PrO) seeded in supersonic molecular beams is measured with mass-analyzed threshold ionization (MATI) spectroscopy. A total of 33 spin-orbit (SO) states of PrO and 23 SO states of PrO+ are predicted by second-order multiconfigurational quasi-degenerate perturbation (MCQDPT2) theory. Electronic transitions from four low-energy SO levels of the neutral molecule to the ground state of the singly charged cation are identified by combining the MATI spectroscopic measurements with the MCQDPT2 calculations. The precise ionization energy is used to reassess the ionization energies and the reaction enthalpies of the Pr+ O → PrO+ + e- chemi-ionization reaction reported in the literature. An empirical formula that uses atomic electronic parameters is proposed to predict the ionization energies of lanthanide monoxides, and the empirical calculations match well with available precise experimental measurements.

Toward Simulation of Fe(II) Low-Spin → High-Spin Photoswitching by Synergistic Spin-Vibronic Dynamics.

A new theoretical approach is presented and applied for the simulation of Fe(II) low-spin (LS, singlet, t2g6eg0) → high-spin (HS, quintet, t2g4eg2) photoswitching dynamics of the octahedral model complex [Fe(NCH)6]2+. The utilized synergistic methodology heavily exploits the strengths of complementary electronic structure and spin-vibronic dynamics methods. Specifically, we perform 3D quantum dynamics (QD) and full-dimensional trajectory surface hopping (TSH, in conjunction with a linear vibronic coupling model), with the modes for QD selected by TSH. We follow a hybrid approach which is based on the application of time-dependent density functional theory (TD-DFT) excited-state potential energy surfaces (PESs) and multiconfigurational second-order perturbation theory (CASPT2) spin–orbit couplings (SOCs). Our method delivers accurate singlet–triplet–quintet intersystem crossing (ISC) dynamics, as assessed by comparison to our recent high-level ab initio simulations and related time-resolved experimental data. Furthermore, we investigate the capability of our simulations to identify the location of ISCs. Finally, we assess the approximation of constant SOCs (calculated at the Franck–Condon geometry), whose validity has central importance for the combination of TD-DFT PESs and CASPT2 SOCs. This efficient methodology will have a key role in simulating LS → HS dynamics for more complicated cases, involving higher density of states and varying electronic character, as well as the analysis of ultrafast experiments.

Excited states of lutetium oxide and its singly charged cation.

Vibronic spectra of lutetium oxide (LuO) seeded in supersonic molecule beams are investigated with mass-analyzed threshold ionization (MATI) spectroscopy and second-order multiconfigurational quasi-degenerate perturbation (MCQDPT2) theory. Six states of LuO and four states of LuO+ are located by the MCQDPT2 calculations, and an a3Π(LuO+) ← C2Σ+ (LuΟ) transition is observed by the MATI measurement. The vibronic spectra show abnormal vibrational intervals for both the neural and cation excited states, and the abnormality is attributed to vibrational perturbations induced by interactions with neighboring states.

Metal-to-Ligand Charge-Transfer Spectrum of a Ru-Bipyridine-Sensitized TiO2 Cluster from Embedded Multiconfigurational Excited-State Theory.

Understanding optical properties of the dye molecule in dye-sensitized solar cells (DSSCs) from first-principles quantum mechanics can contribute to improving the efficiency of such devices. While density functional theory (DFT) and time-dependent DFT have been pivotal in simulating optoelectronic properties of photoanodes used in DSSCs at the atomic scale, questions remain regarding DFT's adequacy and accuracy to furnish critical information needed to understand the various excited-state processes involved. Here, we simulate the absorption spectra of a dye-sensitized solar cell analogue, comprised of a Ru-bipyridine (Ru-bpy) dye molecule and a small TiO2 cluster via DFT and via an accurate embedded correlated wavefunction (CW) theory. We generated CW spectra for the adsorbed Ru-bpy dye via a recently introduced capped density functional embedding theory or capped-DFET (to generate the embedding potential that accounts for the interaction of the molecule and the TiO2 cluster). We then combined capped-DFET with the accurate but expensive multiconfigurational complete active space second-order perturbation theory (CASPT2)-embedded CASPT2. Because the CW theory is conducted on only a portion of the total system in the presence of an embedding potential that describes that portion's interaction with its environment, we efficiently obtain CW-quality predictions that reflect local properties of the entire system. Specifically, for example, with capped-DFET and embedded CW theory, we can simulate accurately a plethora of metal-to-ligand charge-transfer excited properties at a manageable computational cost. Here, we predict detailed electronic spectra within the visible region, featuring the lowest three singlet and triplet excited states, along with predictions of the singlets' lifetimes. We illustrated these results using a Jablonski diagram that show the relative energy position of the singlet and longer-lived triplet excited states and analyzed and proposed relaxation paths for the excited state corresponding to the most intense but short-lived absorption (interconversion, intersystem crossing, fluorescence, and phosphorescence) that may lead to longer-lived excited states necessary for efficient charge separation required to generate current in solar cells.

Molecular Structure, Thermodynamic and Spectral Characteristics of Metal-Free and Nickel Complex of Tetrakis(1,2,5-thiadiazolo)porphyrazine.

The Knudsen effusion method with mass spectrometric control of the vapor composition was used to study the possibility of a congruent transition to the gas phase and to estimate the enthalpy of sublimation of metal-free tetrakis(1,2,5-thiadiazolo)porphyrazine and its nickel complex (H2TTDPz and NiTTDPz, respectively). The geometrical and electronic structure of H2TTDPz and NiTTDPz in ground and low-lying excited electronic states were determined by DFT calculations. The electronic structure of NiTTDPz was studied by the complete active space (CASSCF) method, following accounting dynamic correlation by multiconfigurational quasi-degenerate second-order perturbation theory (MCQDPT2). A geometrical structure of D2h and D4h symmetry was obtained for H2TTDPz and NiTTDPz, respectively. According to data obtained by the MCQDPT2 method, the nickel complex possesses the ground state 1A1g, and the wave function of the ground state has the form of a single determinant. Electronic absorption and vibrational (IR and resonance Raman) spectra of H2TTDPz and NiTTDPz were studied experimentally and simulated theoretically.

A SA-CASSCF and MS-CASPT2 study on the electronic structure of nitrosobenzene and its relation to its dissociation dynamics.

The photodissociation channels of nitrosobenzene (PhNO) induced by a 255 nm photolytic wavelength have been studied using the complete active space self-consistent method and the multistate second-order multiconfigurational perturbation theory. It is found that there exists a triplet route for photodissociation of the molecule. The reaction mechanism consists of a complex cascade of nonadiabatic electronic transitions involving triple and double conical intersections as well as intersystem crossing. Several of the relevant states (S2, S4, and S5 states) correspond to double excitations. It is worth noting that the last step of the photodissociation implies an internal conversion process. The experimentally observed velocity pattern of the NO fragment is a signature of such a conical intersection.

Theory of polarization-averaged core-level molecular-frame photoelectron angular distributions: I. A full-potential method and its application to dissociating carbon monoxide dication

We present a theoretical study of the polarization-averaged molecular-frame photoelectron angular distributions (PA-MFPADs) emitted from the 1s orbital of oxygen atoms of dissociating dicationic carbon monoxide CO2+. Due to the polarization average, the contribution of the direct wave of the photoelectron, which represents the largest contribution to the MFPADs, is removed, so that the PA-MFPADs clearly show the details of the scattering image of the photoelectron. As a result, it is necessary to employ an accurate theory for the theoretical analysis of the continuum state. In this study, we apply a full-potential multiple scattering theory, where the space is partitioned into Voronoi polyhedra and truncated spheres, to take into account the electron charge density outside the physical atomic spheres. We do not use the spherical harmonic expansion of the cell shape functions to avoid divergence problems. The potentials in the scattering cells are computed using the multiconfigurational second-order perturbation theory restricted active space method to take into account the influence of the core hole in the electron charge density in the final state, so that a realistic relaxation can be achieved. We show that the full-potential treatment plays an important role in the PA-MFPADs at a photoelectron kinetic energy of 100 eV. In contrast, the PA-MFPADs are not sensitive to any type of major excited states in the Auger final state. We also study the dynamics of the CO2+ dissociation. We find that the PA-MFPADs dramatically change their shape as a function of the C–O bond length.

A new interpretation of the absorption and the dual fluorescence of Prodan in solution.

Remarkable interest is associated with the interpretation of the Prodan fluorescent spectrum. A sequential hybrid Quantum Mechanics/Molecular Mechanics method was used to establish that the fluorescent emission occurs from two different excited states, resulting in a broad asymmetric emission spectrum. The absorption spectra in several solvents were measured and calculated using different theoretical models presenting excellent agreement. All theoretical models [semiempirical, time dependent density functional theory and and second-order multiconfigurational perturbation theory] agree that the first observed band at the absorption spectrum in solution is composed of three electronic excitations very close in energy. Then, the electronic excitation around 340 nm-360 nm may populate the first three excited states (π-π*Lb, n-π*, and π-π*La). The ground state S0 and the first three excited states were analyzed using multi-configurational calculations. The corresponding equilibrium geometries are all planar in vacuum. Considering the solvent effects in the electronic structure of the solute and in the solvent relaxation around the solute, it was identified that these three excited states can change the relative order depending on the solvent polarity, and following the minimum path energy, internal conversions may occur. A consistent explanation of the experimental data is obtained with the conclusive interpretation that the two bands observed in the fluorescent spectrum of Prodan, in several solvents, are due to the emission from two independent states. Our results indicate that these are the n-π* S2 state with a small dipole moment at a lower emission energy and the π-π*Lb S1 state with large dipole moment at a higher emission energy.

CAS Calculation of the Excited States of the Methylthio Neutral Radical and Its Ions.

The complete active space (CASSCF) and the multiconfiguration second-order perturbation theory (CASPT2) calculations with 6-311++G(3df,3pd) gauss basis sets are performed for several electronic states of the methylthio neutral radical and its cation and anion. Twenty-two electronic states are optimized in the Cs point group. Through the vertical promotion calculations, the absorption spectral is simulated for the neutral radical. Furthermore, through the energy comparison between the neutral radical and relative ions, the ionization energy and the electronic absorption energy are understood adiabatically.

Quantum and Quantum-Classical Studies of the Photoisomerization of a Retinal Chromophore Model.

We report an in-depth analysis of the photo-induced isomerization of the 2-cis-penta-2,4-dieniminium cation: a minimal model of the 11-cis retinal protonated Schiff base chromophore of the dim-light photoreceptor rhodopsin. Based on recently developed three-dimensional potentials parametrized on ab initio multi-state multi-configurational second-order perturbation theory data, we perform quantum-dynamical studies. In addition, simulations based on various quantum-classical methods, among which Tully surface hopping and the coupled-trajectory approach derived from the exact factorization, allow us to validate their performance against vibronic wavepacket propagation and, therefore, a purely quantum treatment. Quantum-dynamics results uncover qualitative differences with respect to the two-dimensional Hahn-Stock potentials, widely used as model potentials for the isomerization of the same chromophore, due to the increased dimensionality and three-mode correlation. Quantum-classical simulations show, instead, that three-dimensional model potentials are capable of capturing a number of features revealed by atomistic simulations and experimental observations. In particular, a recently reported vibrational phase relationship between double-bond torsion and hydrogen-out-of-plane modes critical for rhodopsin isomerization efficiency is correctly reproduced.

Peculiarities of electronic structure and chemical bonding in iron and cobalt metal complexes of porphyrazine and tetra(1,2,5-thiadiazole)porphyrazine

The geometrical and electronic structures of iron and cobalt metal complexes of porphyrazine and tetra(1,2,5-thiadiazole)porphyrazine in ground and low-lying excited electronic states were determined by DFT calculations and the complete active space (CASSCF) method with following accounting dynamic correlation by multiconfigurational quasidegenerate second-order perturbation theory (MCQDPT2). A geometrical structure of D[Formula: see text] symmetry has been obtained for all four complexes. According to data obtained by the MCQDPT2 method, the complexes of cobalt and iron possess the ground states 2A[Formula: see text] and 3A[Formula: see text], respectively, and wave functions of the ground states have the form of a single determinant. It is shown that the crystal field theory (CFT) can be used to describe the sequence of electronic states of the investigated complexes. The nature of the bonds between metal atoms and nitrogen atoms has been described using the analysis of the electron density distribution in the frame of Bader’s quantum theory of atoms in molecule (QTAIM).

A Theoretical Study on the Excited States of the KCCH Radical

Based on the C2v symmetry, the low-lying electronic states of the KCCH radical was studied in the complete active pace self-consistent field (CASSCF) and multi-configurational second-order perturbation theory (CASPT2) methods. For the low-lying electronic states of KCCH, the calculated harmonic vibrational modes are in agreement with theoretical reports. Moreover, the electron transitions of KCCH, from X1Σ+ to 21Σ+, 11Π, 21Π, 11Σ-, 13Σ+, 13Π, 23Π and 13Σ-, are predicted at 5.43, 5.59, 7.87, 5.50, 5.15, 5.73, 5.53 and 6.82 eV, respectively. The CASSCF/CASPT2 potential energy curves (PECs) were calculated for K+-loss dissociation from the 13Σ+, 23Σ+,13Π ,21Σ, 11Π and 21Π states. Analyses of electron transition and dissociation curves show the ionic properties in the metal–ligand bond for KCCH. The dissociation energy of the KCCH (X1Σ+)→CCH-(11Σ)+K+(S0) is 4.423 eV at the CASSCF/CASPT2 level.

Can the symmetrical Dewar pyridine be observed experimentally? A theoretical study

ABSTRACTIn this work we study the possibility of the photochemical formation of the symmetrical Dewar pyridine (1-azabicyclo-[2,2,0]-hexa-2,5-diene), by applying the complete active space self-consistent field method and the multiconfigurational second-order perturbation theory to explore the corresponding ground and excited state potential energy surfaces. According to our theoretical calculations there are three possible paths that can be followed, one is a biphotonic process which involves irradiating pyridine in its ground state with a 358 nm laser guiding the system to an intersystem crossing S1/T1/S0 of triple character whereby deactivation to the ground state, S0, Dewar minimum occurs, the second one, which is a ground state thermal reaction involves the use of a far-Infra-Red laser where planar pyridine is vibrationally excited to a very high vibrational level whose energy is comparable to that of the ground state transition structure, S0(TS), connecting the symmetrical S0 Dewar pyridine and the ground state of planar pyridine. The third process is also a biphotonic one involving excitation of planar pyridine with an energy which is in the limits of its ionisation potential. In this case there is a theoretically accessible S1/S0 Conical Intersection which leads directly to the ground state of the symmetrical Dewar pyridine.

Efficient Implementation of the Second-Order Quasidegenerate Perturbation Theory with Density-Fitting and Cholesky Decomposition Approximations: Is It Possible To Use Hartree-Fock Orbitals for a Multiconfigurational Perturbation Theory?

The high cost of common multireference second-order perturbation theory (MRPT2) methods compared with the single-reference variant (MP2) arises from the expensive complete active space self-consistent field (CASSCF) orbital optimization step. Furthermore, the use of conventional four-index electron repulsion integrals (ERIs) prevents their application to larger molecular systems due to expensive I/O procedures. To address these bottlenecks of the multiconfigurational second-order quasidegenerate perturbation theory (MC-QDPT2), an efficient implementation of QDPT2 with the density-fitting (DF) and Cholesky decomposition (CD) approximations, denoted by DF-QDPT2 and CD-QDPT2, is reported. For the DF/CD-QDPT2 methods, the Hose-Kaldor approach is used. The DF-QDPT2 method, with the cc-pwCVTZ basis set, dramatically reduces the computational cost compared to conventional multiconfigurational QDPT2 (MC-QDPT2, from the Gamess 2017.R2 package), with a more than 122-fold reduction for the largest member of the diradical test set considered. The DF approximation enables substantially accelerated energies to be obtained for the QDPT2 approach due to the significantly reduced I/O time. The performance of the DF-QDPT2 and CD-QDPT2 methods is compared with that of CASSCF, the multireference second-order perturbation theory (MRMP2), MC-QDPT2, and CASSCF-based second-order perturbation theory (CASPT2) methods for singlet-triplet energy splitting (EST) in O2 and C2 molecules and for the dissociation energy of F2. For the O2 and C2 molecules, the performance of the DF-QDPT2 and CD-QDPT2 methods is significantly better than that of CASSCF, MRMP2, MC-QDPT2, and CASPT2; while for the F2 case, the results of DF-QDPT2, CD-QDPT2, MRMP2, MC-QDPT2, and CASPT2 are similar and remarkably better than that of CASSCF, which fails dramatically. Moreover, the DF-QDPT2, CASSCF, CASPT2, and MRCI+Q methods are applied to potential energy curves (PECs) for N2, CH4, and F2 molecules. Our results demonstrate that the performance of DF-QDPT2 is substantially better than that of CASSCF and is comparable with that of CASPT2 for the molecules considered. Overall, the present application results demonstrate that the DF-QDPT2 and CD-QDPT2 methods are very promising for electronically challenging molecular systems suffering from (quasi)degeneracy problems, where the single-reference methods cannot provide an accurate electronic description, but the DF-QDPT2 and CD-QDPT2 methods can do so at significantly reduced computational costs.

Q y and Q x Absorption Bands for Bacteriochlorophyll a Molecules from LH2 and LH3.

Light-harvesting systems 2 and 3 (LH2 and LH3) act as antennas for the initial light capture by photosynthetic purple bacteria, thus initiating the conversion of solar energy into chemical energy. The main absorbers are carotenoids and bacteriochlorophylls (BChls), which harvest different parts of the solar spectrum. The first two optical transitions in BChl produce the Q y and Q x absorption bands. The large size of BChl molecules has prevented accurate computational determination of the electronic structures for the relevant states, until we recently succeeded in obtaining the excitation energies and transition dipole moments of the first (Q y) transition for all BChls in LH2 and LH3 using multi-state multiconfigurational second-order perturbation theory calculations. In this work, we go one step further, compute the corresponding values for the Q x transition, in line with previous work [ J. Am. Chem. Soc . 2017 , 139 , 7558 - 7567 ], and compare and assess our data against excitation energies obtained through time-dependent density functional theory methods. Interestingly, we find that the two transitions respond differently to BChls' geometrical factors, such as the macrocycle ring curvature and the dihedral torsion of the acetyl moiety. These findings will aid the unraveling of structure-function relationships for absorption and energy transfer processes in purple bacteria, and once again this demonstrates the viability of multireference quantum chemical methods as computational tools for the photophysics of biomolecules.

Assessment of MC-PDFT Excitation Energies for a Set of QM/MM Models of Rhodopsins.

A methodology for the automatic production of quantum mechanical/molecular mechanical (QM/MM) models of retinal-binding rhodopsin proteins and subsequent prediction of their spectroscopic properties has been proposed recently by some of the authors. The technology employed for the evaluation of the excitation energies is called Automatic Rhodopsin Modeling (ARM), and it involves the use of the complete active space self-consistent field (CASSCF) method followed by a multiconfiguration second-order perturbation theory (in particular, CASPT2) calculation of external correlation energies. Although it was shown that ARM is capable of successfully reproducing and predicting spectroscopic property trends in chromophore-embedding protein sets, practical applications of such technology are limited by the high computational costs of the multiconfiguration perturbation theory calculations. In the present work we benchmark the more affordable multiconfiguration pair-density functional theory (MC-PDFT) method whose accuracy has been recently validated for retinal chromophores in the gas phase, indicating that MC-PDFT could potentially be used to analyze large (e.g., few hundreds) sets of rhodopsin proteins. Here, we test this theory for a set of rhodopsin QM/MM models whose experimental absorption maxima (λ a max) have been measured. The results indicate that MC-PDFT may be employed to calculate λ a max values for this important class of photoresponsive proteins.