Perturbative Configuration Interaction Research Articles

Simulation of Vibrational Circular Dichroism Spectra Using Second-Order Møller-Plesset Perturbation Theory and Configuration Interaction Doubles.

We present the first single-reference calculations of the atomic axial tensors (AATs) with wave function-based methods including dynamic electron correlation effects using second-order Møller-Plesset perturbation theory (MP2) and configuration interaction doubles (CID). Our implementation involves computing the overlap of numerical derivatives of the correlated wave functions with respect to both nuclear displacement coordinates and the external magnetic field. Out test set included three small molecules, including the axially chiral hydrogen molecule dimer and (P)-hydrogen peroxide, and the achiral H2O. For our molecular test set, we observed deviations of the AATs for MP2 and CID from that of the Hartree-Fock (HF) method upward of 49%, varying with the choice of basis set. For (P)-hydrogen peroxide, electron correlation effects on the vibrational circular dichroism (VCD) rotatory strengths and corresponding spectra were particularly significant, with maximum deviations of the rotatory strengths of 62 and 49% for MP2 and CID, respectively, using our largest basis set. The inclusion of dynamic electron correlation to the computation of the AATs can have a significant impact on the resulting rotatory strengths and VCD spectra.

Relativistic theoretical calculations of singly and doubly energy levels, lifetimes, wavelengths, weighted oscillator strengths and radiative rates for Helium-Like Ions with [formula omitted]

We provide accurate energy levels for the lowest singly excited 70 levels among 1snl(n≤6,l≤(n−1)) configurations and the lowest doubly excited 250 levels arising from the K-vacancy 2ln′l′(n′≤6,l′≤(n′−1)) configurations of helium-like ions with Z=5−9. Wavelengths, weighted oscillator strengths and transition rates for electric-multipole (dipole (E1), quadrupole (E2)) and magnetic-multipole (dipole (M1), quadrupole (M2)) are also calculated. The lifetimes determinations are reported for all the calculated levels. The calculations were performed using the Relativistic Configuration Interaction (RCI) method implemented in the Flexible Atomic Code (FAC). For comparative purposes, the second set of calculations was obtained with other packages of programs for relativistic atomic structure calculations (AMBiT) based on a method combining many-body perturbation theory and configuration interaction (CI). Additionally, the Breit interaction and leading quantum electrodynamics effects (QED) are included. Our results are compared with other available theories reported in the literature as well as the data taken from NIST online database. A good agreement between them has been found. We signal that our calculations for the doubly excited levels are made for the first time and they provide accurate and complete atomic data on these ions. Our results can contribute to the NIST database by essentially extending the data for doubly excited states.

Formation of carnosine - an ab initio study

Formation of carnosine from histidine and b-alanine is studied by ab initio MO-LCAO-SCF method followed by the perturbative configuration interaction (MP2) in vacuo. After the full geometry optimization at the SCF level, the molecular properties were evaluated and followed by the vibrational-rotational analysis. Consequently, the energy, entropy and free energy were evaluated for the reactants and products of the reaction histidine + beta-alanine = carnosine + H2O and finally the equilibrium constant was enumerated.

Nucleus–electron correlation revising molecular bonding fingerprints from the exact wavefunction factorization

We present a novel theory and implementation for computing coupled electronic and quantal nuclear subsystems on a single potential energy surface, moving beyond the standard Born-Oppenheimer (BO) separation of nuclei and electrons. We formulate an exact self-consistent nucleus-electron embedding potential from the single product molecular wavefunction and demonstrate that the fundamental behavior of the correlated nucleus-electron can be computed for mean-field electrons that are responsive to a quantal anharmonic vibration of selected nuclei in a discrete variable representation. Geometric gauge choices are discussed and necessary for formulating energy invariant biorthogonal electronic equations. Our method is further applied to characterize vibrationally averaged molecular bonding properties of molecular energetics, bond lengths, and protonic and electron densities. Moreover, post-Hartree-Fock electron correlation can be conveniently computed on the basis of nucleus-electron coupled molecular orbitals, as demonstrated for correlated models of second-order Møllet-Plesset perturbation and full configuration interaction theories. Our approach not only accurately quantifies non-classical nucleus-electron couplings for revising molecular bonding properties but also provides an alternative time-independent approach for deploying non-BO molecular quantum chemistry.

Configuration–Interaction Perturbation Theory Calculations of Pu II

Configuration–interaction perturbation theory (CI–PT) is applied to calculations of low-energy states of Pu II. This ion is quite challenging due to a large number of possible determinants arising from seven valence electrons and strong relativistic effects. The CI–PT calculations agree with experiments for the energies and g-factors for many low-energy states that allowed positive identification of the theoretical levels. Isotope shifts were also used to aid in identification, and, in case of the odd states, fitting with three independent parameters was used to match theoretical isotope shifts to the experimental values with good accuracy. The CI–PT approach tested here on the Pu II ion can be generally used to calculate properties of many complex atoms, including U I that can find application in fundamental and applied science.

Analytic gradients for state-averaged multiconfiguration pair-density functional theory.

Analytic gradients are important for efficient calculations of stationary points on potential energy surfaces, for interpreting spectroscopic observations, and for efficient direct dynamics simulations. For excited electronic states, as are involved in UV-Vis spectroscopy and photochemistry, analytic gradients are readily available and often affordable for calculations using a state-averaged complete active space self-consistent-field (SA-CASSCF) wave function. However, in most cases, a post-SA-CASSCF step is necessary for quantitative accuracy, and such calculations are often too expensive if carried out by perturbation theory or configuration interaction. In this work, we present the analytic gradients for multiconfiguration pair-density functional theory based on SA-CASSCF wave functions, which is a more affordable alternative. A test set of molecules has been studied with this method, and the stationary geometries and energetics are compared to values in the literature as obtained by other methods. Excited-state geometries computed with state-averaged pair-density functional theory have similar accuracy to those from complete active space perturbation theory at the second-order.

Hydrogen-bond Network of Water and Irradiation Effects

Results obtained in nonempirical simulations of neutral and positively charged (H2O)n water clusters with n up to 20 in the ground and excited electronic states carried out with the use of the second order Moller–Plesset perturbation theory and configuration interaction method with single and double excitations form the basis for the analysis of diverse processes promoted by the irradiation of water specimens with near and mid-range ultraviolet light with an emphasis on production of radical particles. Ionization of local H‑bonded domains results in the formation of hydronium cations and hydroxyl radicals. Concurrently, the electronic excitation and the ionization followed by the recombination of cations with hydrated electrons are shown to cause the appearance of hydrogen atoms and OH radicals.

Understanding CH-Stretching Raman Optical Activity in Ala-Ala Dipeptides.

Raman optical activity (ROA) becomes a standard method to monitor peptide conformation. However, the signal in the CH-stretching region is particularly difficult to measure and interpret. In order to understand the structural information contained in this part of the spectrum, data obtained on a custom-made ROA spectrometer have been analyzed for the model Ala-Ala molecule, with the help of molecular dynamics (MD) and density functional theory computations. The Ala-Ala enantiomers provided the "mirror image" spectra, which proves that the signal can be reliably measured, in spite of a rather low ROA/Raman intensity ratio (∼2 × 10-5). The theoretical modeling indicated that the most intense ROA bands can be attributed to locally asymmetric CH3 and αCH vibrations, whereas symmetric methyl CH-stretching modes contribute less. A simplified model made it possible to estimate the contribution of local chirality of the two alanine residues to the resultant ROA pattern. In spite of a significant frequency shift (over 100 cm-1) because of the anharmonic corrections, the harmonic level was able to explain the main spectral features. The anharmonic corrections were treated by second-order perturbation and limited vibrational configuration interaction procedures. This allowed for assignment of some weaker spectral features because of the combination and overtone vibrations. The results show that the peptide CH-stretching ROA signal contains rich structural information, reflecting also the peptide environment. The experimental data, however, need to be deciphered by relatively complex and time-consuming spectral simulations.

Machine Learning Configuration Interaction.

We propose the concept of machine learning configuration interaction (MLCI) whereby an artificial neural network is trained on-the-fly to predict important new configurations in an iterative selected configuration interaction procedure. We demonstrate that the neural network can discriminate between important and unimportant configurations, that it has not been trained on, much better than by chance. MLCI is then used to find compact wave functions for carbon monoxide at both stretched and equilibrium geometries. We also consider the multireference problem of the water molecule with elongated bonds. Results are contrasted with those from other ways of selecting configurations: first-order perturbation, random selection, and Monte Carlo configuration interaction. Compared with these other serial calculations, this prototype MLCI is competitive in its accuracy, converges in significantly fewer iterations than the stochastic approaches, and requires less time for the higher-accuracy computations.

Ab initio description of highly correlated states in defects for realizing quantum bits

Coupled localized electron spins hosted by defects in semiconductors implement quantum bits with the potential to revolutionize nanoscale sensors and quantum information processing. The present understanding of optical means of spin state manipulation and read-out calls for quantitative theoretical description of the active states, built-up from correlated electrons in a bath of extended electron states. Hitherto we propose a first-principles scheme based on many body perturbation theory and configuration interaction and address two room temperature point defect qubits, the nitrogen vacancy in diamond and the divacancy in silicon carbide. We provide a complete quantitative description of the electronic structure and analyze the crossings and local minima of the energy surface of triplet and singlet states. Our numerical results not only extend the knowledge of the spin-dependent optical cycle of these defects, but also demonstrate the potential of our method for quantitative theoretical studies of point defect qubits.

Psi4NumPy: An Interactive Quantum Chemistry Programming Environment for Reference Implementations and Rapid Development.

Psi4NumPy demonstrates the use of efficient computational kernels from the open-source Psi4 program through the popular NumPy library for linear algebra in Python to facilitate the rapid development of clear, understandable Python computer code for new quantum chemical methods, while maintaining a relatively low execution time. Using these tools, reference implementations have been created for a number of methods, including self-consistent field (SCF), SCF response, many-body perturbation theory, coupled-cluster theory, configuration interaction, and symmetry-adapted perturbation theory. Furthermore, several reference codes have been integrated into Jupyter notebooks, allowing background, underlying theory, and formula information to be associated with the implementation. Psi4NumPy tools and associated reference implementations can lower the barrier for future development of quantum chemistry methods. These implementations also demonstrate the power of the hybrid C++/Python programming approach employed by the Psi4 program.

Different approaches to the coupled-cluster method and related ways of solving the coupled-cluster equations

ABSTRACTThe coupled-cluster (CC) method is one of the most efficient approaches to describe electron correlation effects in atoms and molecules. The method can be related to other earlier and more conventional methods for an approximate evaluation of the correlation energy like perturbation theory or configuration interaction method. The relations are usually used to suggest possible ways of solving the CC equations. The most popular iterative schemes for obtaining the cluster amplitudes are based on perturbative Jacobi-type procedures but also other algorithms are known from the literature. All of them are characterised by different convergence properties. In the paper, we try to study the efficiency of the basic iterative schemes used in the CC calculations.

Radical O–O coupling reaction in diferrate-mediated water oxidation studied using multireference wave function theory

The O-O (oxygen-oxygen) bond formation is widely recognized as a key step of the catalytic reaction of dioxygen evolution from water. Recently, the water oxidation catalyzed by potassium ferrate (K2FeO4) was investigated on the basis of experimental kinetic isotope effect analysis assisted by density functional calculations, revealing the intramolecular oxo-coupling mechanism within a di-iron(vi) intermediate, or diferrate [Sarma et al., J. Am. Chem. Soc., 2012, 134, 15371]. Here, we report a detailed examination of this diferrate-mediated O-O bond formation using scalable multireference electronic structure theory. High-dimensional correlated many-electron wave functions beyond the one-electron picture were computed using the ab initio density matrix renormalization group (DMRG) method along the O-O bond formation pathway. The necessity of using large active space arises from the description of complex electronic interactions and varying redox states both associated with two-center antiferromagnetic multivalent iron-oxo coupling. Dynamic correlation effects on top of the active space DMRG wave functions were additively accounted for by complete active space second-order perturbation (CASPT2) and multireference configuration interaction (MRCI) based methods, which were recently introduced by our group. These multireference methods were capable of handling the double shell effects in the extended active space treatment. The calculations with an active space of 36 electrons in 32 orbitals, which is far over conventional limitation, provide a quantitatively reliable prediction of potential energy profiles and confirmed the viability of the direct oxo coupling. The bonding nature of Fe-O and dual bonding character of O-O are discussed using natural orbitals.

Multireference explicitly correlated F12 theories

We review our recent developments in multireference explicitly correlated F12 theories (explicitly correlated internally contracted multireference perturbation and multireference configuration interaction theories) that achieve near-basis-set-limit accuracy of the underlying multireference electron correlation methods with basis sets of medium size. The applicability of the multireference F12 theories is the same as that of their non-F12 counterpart, and therefore it is a computational tool with predictive accuracy for complicated electronic structures with strong correlation. A comparison with the earlier developments by others is also discussed.

Direct determination of exciton couplings from subsystem time-dependent density-functional theory within the Tamm–Dancoff approximation

In subsystem time-dependent density functional theory (TDDFT) [J. Neugebauer, J. Chem. Phys. 126, 134116 (2007)] localized excitations are used to calculate delocalized excitations in large chromophore aggregates. We have extended this formalism to allow for the Tamm-Dancoff approximation (TDA). The resulting response equations have a form similar to a perturbative configuration interaction singles (CIS) approach. Thus, the inter-subsystem matrix elements in subsystem TDA can, in contrast to the full subsystem-TDDFT case, directly be interpreted as exciton coupling matrix elements. Here, we present the underlying theory of subsystem TDDFT within the TDA as well as first applications. Since for some classes of pigments, such as linear polyenes and carotenoids, TDA has been reported to perform better than full TDDFT, we also report applications of this formalism to exciton couplings in dimers of such pigments and in mixed bacteriochlorophyll-carotenoid systems. The improved description of the exciton couplings can be traced back to a more balanced description of the involved local excitations.

Which Ab Initio Wave Function Methods Are Adequate for Quantitative Calculations of the Energies of Biradicals? The Performance of Coupled-Cluster and Multi-Reference Methods Along a Single-Bond Dissociation Coordinate.

We examine the accuracy of single-reference and multireference correlated wave function methods for predicting accurate energies and potential energy curves of biradicals. The biradicals considered are intermediate species along the bond dissociation coordinates for breaking the F-F bond in F2, the O-O bond in H2O2, and the C-C bond in CH3CH3. We apply a host of single-reference and multireference approximations in a consistent way to the same cases to provide a better assessment of their relative accuracies than was previously possible. The most accurate method studied is coupled cluster theory with all connected excitations through quadruples, CCSDTQ. Without explicit quadruple excitations, the most accurate potential energy curves are obtained by the single-reference RCCSDt method, followed, in order of decreasing accuracy, by UCCSDT, RCCSDT, UCCSDt, seven multireference methods, including perturbation theory, configuration interaction, and coupled-cluster methods (with MRCI+Q being the best and Mk-MR-CCSD the least accurate), four CCSD(T) methods, and then CCSD.

An ab Initio Investigation of Fluorobromo Carbene

Fluorobromo carbene, an important halogenated carbene in the stratospheric ozone depletion, has long been received considerable interest. However, the energy, structure, and dynamics of even the lowest excited states have not been well understood. In this paper, we performed a detail ab initio study on CFBr using complete active space second-order perturbation (CASPT2) and multireference configuration interaction (MRCI) method. We investigated the effect of basis set on the CASPT2 results of the ground X(1)A' state and the first excited singlet A(1)A" state. The potential energy surface (PES) of the A(1)A" state along C-Br bond distance was carefully examined at CASPT2/cc-pV5Z level, by optimizing C-F bond and F-C-Br angle at every C-Br bond length in contrast to fix them at the equilibrium values. On the basis of the PES, a reliable barrier height of the A(1)A" state was obtained from CASPT2 and MRCI+Q calculations with different basis sets, considering the scalar relativistic effect, spin-orbit coupling, and core-valence correlation. Finally, we carried out the first theoretical study on higher excited state with energy up to 7 eV. The present calculated results were compared with previous experimental and theoretical results where available. Our results will add some understanding and shed more light on the structure and dynamics of electronic states of CFBr radical.

Automated evaluation of matrix elements between contracted wavefunctions: A Mathematica version of the FRODO program

A symbolic program performing the Formal Reduction of Density Operators (FRODO), formerly developed in the MuPAD computer algebra system with the purpose of evaluating the matrix elements of the electronic Hamiltonian between internally contracted functions in a complete active space (CAS) scheme, has been rewritten in Mathematica. New version : A program summaryProgram title: FRODOCatalogue identifier: ADV Y _v2_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADVY_v2_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 3878No. of bytes in distributed program, including test data, etc.: 170729Distribution format: tar.gzProgramming language: MathematicaComputer: Any computer on which the Mathematica computer algebra system can be installedOperating system: LinuxClassification: 5Catalogue identifier of previous version: ADV Y _v1_0Journal reference of previous version: Comput. Phys. Comm. 171(2005)63Does the new version supersede the previous version?: NoNature of problem. In order to improve on the CAS-SCF wavefunction one can resort to multireference perturbation theory or configuration interaction based on internally contracted functions (ICFs) which are obtained by application of the excitation operators to the reference CAS-SCF wavefunction. The previous formulation of such matrix elements in the MuPAD computer algebra system, has been rewritten using Mathematica.Solution method: The method adopted consists in successively eliminating all occurrences of inactive orbital indices (core and virtual) from the products of excitation operators which appear in the definition of the ICFs and in the electronic Hamiltonian expressed in the second quantization formalism.Reasons for new version: Some years ago we published in this journal a couple of papers [1, 2] hereafter to be referred to as papers I and II, respectively dedicated to the automated evaluation of the matrix elements of the molecular electronic Hamiltonian between internally contracted functions [3] (ICFs). In paper II the program FRODO (after Formal Reduction Of Density Operators) was presented with the purpose of providing working formulas for each occurrence of the ICFs. The original FRODO program was written in the MuPAD computer algebra system [4] and was actively used in our group for the generation of the matrix elements to be employed in the third-order n-electron valence state perturbation theory (NEVPT) [5–8] as well as in the internally contracted configuration interaction (IC-CI) [9].We present a new version of the program FRODO written in the Mathematica system [10]. The reason for the rewriting of the program lies in the fact that, on the one hand, MuPAD does not seem to be any longer available as a stand-alone system and, on the other hand, Mathematica, due to its ubiquitousness, appears to be increasingly the computer algebra system most widely used nowadays.Restrictions: The program is limited to no more than doubly excited ICFs.Running time: The examples described in the Readme file take a few seconds to run.

Singlet–triplet excitation energies of naphthyl cations: High level composite method calculations suggest a singlet ground state

Singlet–triplet excitation energies (ES–T) were calculated for the phenyl, 1-naphthyl, and 2-naphthyl cations using a broad range of model chemistries, including semiempirical, Hartree–Fock, density functional, Moller–Plesset perturbation, composite, coupled cluster, and quadratic configuration interaction methods and various basis sets. Substantial model chemistry dependent ES–T results were obtained for all three cations with correspondingly minimal basis set size effects. G4/G4MP2 composite method well-to-well (and adiabatic) ES–T for the phenyl, 1-naphthyl, and 2-naphthyl cations are 101.9/102.3 (101.7/102.0), 20.4/18.8 (19.3/17.8), and 21.6/21.4 (20.8/20.7)kJ/mol, respectively. All composite methods predict a substantially positive ES–T for the 1- and 2-naphthyl cations, and are in both quantitative and qualitative disagreement with many other model chemistries (particularly density functionals such as B3LYP) in estimating both the magnitude and sign of the singlet–triplet excitation energy for the 1- and 2-naphthyl cations. Composite method approaches suggest both the 1- and 2-naphthyl cations are ground state singlets with sufficiently large ES–T such that the population of the corresponding triplet state should be negligible, and thereby non-observable, where experimental conditions operate under thermodynamic control.

Isomerization energies of tetrahedranes to 1,3-cyclobutadienes: A challenge for theoretical methods

The gas phase (298.15 K, 1 atm) isomerization energies (Δ isom E (g)) of various tetra-substituted (hydro, chloro, bromo, methyl, ethynyl, cyano, tert-butyl, and tetrakis(trimethylsilyl)) tetrahedranes to their corresponding 1,3-cyclobutadienes were investigated with a broad range of model chemistries (Hartree–Fock, density functional, Moller–Plesset perturbation, composite, coupled cluster, and quadratic configuration interaction methods) and Pople-/Ahlrichs-/Dunning-type basis sets. Substantial model chemistry dependent Δ isom E (g) variability was found for all tetrahedrane/1,3-cyclobutadiene derivatives. Basis set influences on Δ isom E (g) variability were modest and less influential than the choice of model chemistry. Several density functionals previously found to provide excellent Δ isom E (g) prediction performance for a broad range of small and large organic compounds demonstrated poor capability when applied to the tetrahedrane/1,3-cyclobutadiene isomerizations.