Accurate Dissociation of Chemical Bonds Using DFT-in-DFT Embedding Theory with External Orbital Orthogonality.

Our recent density functional theory (DFT)-in-DFT embedding protocol, which enforces intersubsystem (or external orbital) orthogonality, is used for the first time to investigate covalent bond dissociation and is shown to do so accurately. Full potential energy curves for the dissociation of a H-O bond in H2O and the C-C bond in H3C-CH3 have been constructed using the new embedding method, as have the challenging ionic bonds in LiH and LiF, and were found to match the reference Kohn-Sham (KS)-DFT curves to at least one part in 106. The added constraint of external orbital orthogonality allows for the formulation of an embedding protocol that does not rely on approximate kinetic energy functionals for the evaluation of the so-called nonadditive kinetic potential, does not introduce compensatory potentials, and does not require a total system calculation at any stage. The present work extends the demonstrated applicability of the external orthogonality variant of embedding theory by more than a factor of 2 to the interaction strength range of strong single bonds. In particular, it is demonstrated that homolytic cleavage of both covalent and ionic bonds into radicals can be accomplished.

Density differences in embedding theory with external orbital orthogonality.

First results on electron densities and energies for a number of molecular complexes with different interaction strengths (ranging from ca. 0.3 to 40 kcal/mol), obtained using our recently introduced DFT-in-DFT embedding equations (i.e., Kohn-Sham equations with constrained electron density (KSCED) and external orbital orthogonality (ext orth), KSCED(x, ext orth), where x denotes the single particle support: monomer (m); supermolecular (s); or extended monomer (e)) are compared with densities from supermolecular Kohn-Sham (KS)-DFT calculations and traditional DFT-in-DFT results. Because our methodology does not rely on error-prone potentials that are not present in supermolecular KS-DFT calculations, it allows DFT-in-DFT calculations to achieve much higher accuracy than previous protocols of DFT-in-DFT that employed such potentials. It is shown that whereas conventional DFT-in-DFT embedding theory leads to errors in the electron density at the boundary between subsystems, the situation is remedied when orbital orthogonality between subsystems (i.e., external orthogonality) is enforced. Our approach reproduces KS-DFT total energies at least to the seventh decimal place (and exactly at most geometries) for the tested systems. Potential energy curves (PECs) of the separation of some of the tested systems into fragments are calculated. PECs, obtained with the new equations, using the usual Kohn-Sham equations with constrained electron density and supermolecular basis expansion [KSCED(s, ext orth, v(T) = 0), where v(T) is the nonadditive kinetic potential] were found to be virtually identical to those from conventional KS-DFT; equilibrium distances and interaction energies were reproduced to all reported digits for both local density approximation (LDA) and generalized gradient approximation (GGA) functionals. As an additional approximation, an alternative one-particle space (to the common monomer or supermolecular spaces) in which KS orbitals of a subsystem are expanded is introduced. This expansion, which we refer to as the extended monomer expansion [e.g., KSCED(e)], includes basis functions centered on atom(s) of the complementary subsystem in the interfacial region. Density differences and PECs obtained with the new equations and new one-particle space [i.e., KSCED(e, ext orth, v(T) = 0)] were closely related to those obtained from KSCED(s, ext orth, v(T) = 0). The new approach does not require any supermolecular calculations.

GVVPT2 multireference perturbation theory description of diatomic scandium, chromium, and manganese.

With relatively simple model spaces derived from valence bond models, a straightforward zero-order Hamiltonian, and the use of moderate-sized Dunning-type correlation consistent basis sets (cc-pVTZ, aug-cc-pVTZ, and cc-pVQZ), the second order generalized Van Vleck perturbation theory (GVVPT2) method is shown to produce potential energy curves (PECs) and spectroscopic constants close to experimental results for both ground and low-lying excited electronic states of Sc(2), Cr(2) and Mn(2). In spite of multiple quasidegeneracies (particularly for the cases of Sc(2) and Mn(2)), the GVVPT2 PECs are smooth with no discontinuities. Since these molecules have been identified as ones that widely used perturbative methods are inadequate for describing well, due to intruder state problems, unless shift parameters are introduced that can obfuscate the physics, this study suggests that the conclusion about the inadequacy of multireference perturbation theory be re-evaluated. The ground state of Sc(2) is predicted to be X(5)∑(u)(-), and its spectroscopic constants are close to the ones at the MRCISD level. Near equilibrium geometries, the 1(3)∑(u)(-) electronic state of Sc(2) is found to be less stable than the quintet ground state by 0.23 eV. The Cr(2) PEC has several features of the Rydberg-Klein-Rees (RKR) experimental curve (e.g., the pronounced shelf at elongated bond lengths), although the predicted bond length is slightly long (R(e) = 1.80 Å with cc-pVQZ compared to the experimental value of 1.68 Å). The X(1)∑(g)(+) ground state of Mn(2) is predicted to be a van der Waals molecule with a long bond length, R(e), of 3.83 Å using a cc-pVQZ basis set (experimental value = 3.40 Å) and a binding energy, D(e), of only 0.05 eV (experimental value = 0.1 eV). We obtained R(e) = 3.40 Å and D(e) = 0.09 eV at the complete basis set (CBS) limit for ground state Mn(2). Low lying excited state curves have also been characterized for all three cases (Cr(2), Mn(2), and Sc(2)) and show similar mathematical robustness as the ground states. These results suggest that the GVVPT2 multireference perturbation theory method is more broadly applicable than previously documented.

GVVPT2 energy gradient using a Lagrangian formulation.

A Lagrangian based approach was used to obtain analytic formulas for GVVPT2 energy nuclear gradients. The formalism can use either complete or incomplete model (or reference) spaces, and is limited, in this regard, only by the capabilities of the MCSCF program. An efficient means of evaluating the gradient equations is described. Demonstrative calculations were performed and compared with finite difference calculations on several molecules and show that the GVVPT2 gradients are accurate. Of particular interest, the suggested formalism can straightforwardly use state-averaged MCSCF descriptions of the reference space in which the states have arbitrary weights. This capability is demonstrated by some calculations on the ground and first excited singlet states of LiH, including calculations near an avoided crossing. The accuracy and usefulness of the GVVPT2 method and its gradient are highlighted by comparing the geometry of the near-C(2v) minimum on the conical intersection seam between the 1 (1)A(1) and 2 (1)A(1) surfaces of O(3) with values that were calculated at the multireference configuration interaction, including single and double excitations (MRCISD), level of theory.

Theoretical study of the photodissociation of Li(2)+ in one-color intense laser fields.

A theoretical treatment of the photodissociation of the molecular ion Li(2) (+) in one-color intense laser fields, using the time-dependent wave packet approach in a Floquet Born-Oppenheimer representation, is presented. Six electronic states 1,2 (2)Σ(g)(+), 1,2 (2)Σ(u)(+), 1 (2)Π(g), and 1 (2)Π(u) are of relevance in this simulation and have been included. The dependences of the fragmental dissociation probabilities and kinetic energy release (KER) spectra on pulse width, peak intensity, polarization angle, wavelength, and initial vibrational level are analyzed to interpret the influence of control parameters of the external field. Three main dissociation channels, 1 (2)Σ(g)(+) (m = -1), 2 (2)Σ(g)(+) (m = -2), and 2 (2)Σ(u)(+) (m = -3), are seen to dominate the dissociation processes under a wide variety of laser conditions and give rise to well separated groups of KER features. Different dissociation mechanisms for the involved Floquet channels are discussed.

Ground and low-lying excited electronic states of [3,3'] bidiazirinylidene (C2N4).

The second-order generalized Van Vleck perturbation theory (GVVPT2) variant of multireference perturbation theory was used to investigate the ground and low-lying excited electronic states of [3,3'] bidiazirinylidene (C(2)N(4)). C(2)N(4) is arguably the simplest molecule with multiple CN(2) rings. Equilibrium geometries and adiabatic energy differences of the 1(1)A(g) ground state and 2 (1)A(g), 1(1)B(1g), 1(3)B(1g), 1(1)B(2g), 1(3)B(2g), 1(1)B(3g), 1(3)B(3g), 1(1)B(2u), 1(3)B(2u), 1(1)B(3u), and 1(3)B(3u) excited states of D(2h) symmetry were obtained. In addition, vertical excitation energies to and emission energies from the excited states were obtained. The 1(1)A(g) optimized geometry and harmonic frequencies for the CN(2) rings in C(2)N(4) are similar to those for the related difluorodiazirine molecule: R(CN), R(NN) bonds and the angleNCN angle are 0.012 and 0.006 A longer and 0.8 degrees smaller than that for the ring in F(2)CN(2). The NN stretch frequencies are 1470 and 1562 cm(-1), and CN stretches are 993 and 995 cm(-1). The similarity between the GVVPT2 results of C(2)N(4) and F(2)CN(2) suggests that C(2)N(4) might be sufficiently stable to be synthesized. The lowest-energy spin- and electric dipole-allowed vertical excitation, to the 1(1)B(2u) state, is predicted to occur in the visible (2.30 eV, 538.9 nm).

Multireference generalized Van Vleck perturbation theory (GVVPT2) study of the NCO + HCNO reaction: insight into intermediates.

Possible mechanisms for the NCO + HCNO reaction, previously studied using single reference methods, have been revisited using the second-order generalized Van Vleck perturbation theory (GVVPT2) variant of multireference perturbation theory. Large scale GVVPT2 calculations, with 25 active orbitals, demonstrate that the electronic structures of the ground states of all eight previously identified plausible doublet spin intermediates of this reaction are substantially multiconfigurational with maximum configuration amplitudes not larger than 0.87. Moreover, comparison of GVVPT2 results with underlying MCSCF calculations demonstrates a pronounced effect of dynamic correlation on the configurational structure. GVVPT2 calculations of vertical excitation energies of the intermediates showed that all the intermediates, except one, have significant excitation energies to both the same and other spatial symmetries as the ground states. The relative GVVPT2 energies of the intermediates were found to be consistent with earlier calculations, including the prediction of a negative temperature dependence of the rate constant, and support available experimental observations.

Embedding theory for excited states.

Using the technique of Perdew and Levy [Phys. Rev. B 31, 6264 (1985)], it is shown that both the density function theory (DFT)-in-DFT and wave function theory (WFT)-in-DFT embedding approaches are formally correct in studying not only the ground state but also a subset of the excited states of the total system. Without further approximations, the DFT-in-DFT embedding approach results in a pair of coupled Euler-Lagrange equations. In contrast to DFT-in-DFT, the WFT-in-DFT approach is shown to ensure a systematic description of excited states if such states are mainly related to excitations within the embedded subsystem. Possible ways for the practical realization of the WFT-in-DFT approach for studying excited states are briefly discussed.

Configuration-driven unitary group approach for generalized Van Vleck variant multireference perturbation theory.

A new, efficient, configuration-driven algorithm utilizing the unitary group approach (UGA) was developed and implemented for the generalized van Vleck perturbation theory (GVVPT) variant of multireference perturbation theory. The computational speed has been improved by 1 or 2 orders of magnitude compared to the previous implementation based on the Table-CI technique. It is shown that the reformulation is applicable to both the second-order (GVVPT2) and third-order (GVVPT3) approximations. Calculations on model problems and on a chemically realistic description of cyclobutadiene are used to illustrate the performance of the method. The calculations on cyclobutadiene, using over 2.3 billion CSFs, provide results on geometric parameters and the barrier height of the automerization reaction in good agreement with established high accuracy results.

Theoretical study of electronic states of N22+in an intense radiation field.

The Floquet states of N(2) (2+) created by the interactions of the six lowest singlet (1 (1)Sigma(g) (+), 1 (1)Delta(g), 2 (1)Sigma(g) (+), 1 (1)Pi(u), 1 (1)Pi(g), and 1 (1)Sigma(u) (-)) states of the dication with intense (0.4 x 10(13) Wcm(2)) radiation have been studied using the recently developed multireference configuration interaction method with single and double excitations (MRCISD)-based approach. The adiabatic Floquet state coinciding near its minimum with the initial X (1)Sigma(g) (+) ground state and asymptotically correlating with A (1)Pi(u) (m = -1), i.e., with one less photon in the dressed state, is expected to be metastable, as is the ground state in the absence of a field, but to support up to the v(max) = 12 quasibound vibrational level in comparison with v(max) = 11 in the parent field-free X (1)Sigma(g) (+) ground state. The tunneling lifetimes of the highest vibrational levels in this adiabatic Floquet state are predicted to be several orders longer than those in the parent field-free state. Analysis of the complete basis set limit extrapolated MRCISD potential energy curve of the field-free X (1)Sigma(g) (+) state of N(2) (2+) calculated in the present work (R(e) = 1.130 A, omega(e) = 2011 cm(-1), omega(e)x(e) = 26.1 cm(-1)) is in good agreement with spectroscopic experimental data. Calculations on the field-free A (1)Pi(u) state (T(e) = 12 106 cm(-1), R(e) = 1.252 A, omega(e) = 1438 cm(-1), omega(e)x(e) = 23.5 cm(-1)) generally support earlier theoretical work and do not support reported experimental values.

Multireference configuration interaction based electronic Floquet states for molecules in an intense radiation field: theory and application to Li(2)+.

A multireference configuration interaction (CI) method which includes single and double excitations based description of adiabatic Floquet states for the electronic structure of a molecule in an intense laser field is introduced. Using a variant of a recently introduced configuration state function (CSF) based Table-CI methodology, it is shown that the multiple states of several irreducible representations required for a good description of low-lying Floquet states can be obtained using modifications of computational molecular electronic structure techniques. In particular, formulas for all components of the transition dipole moment matrix elements within the CSF-based Table-CI method are derived and presented. Moreover, the flexibility of the recently introduced macroconfiguration description of model and external configuration spaces is shown to lead to multiple potential energy surfaces of sufficiently uniform quality to allow construction of useful Floquet states. The formalism and computer programs developed are demonstrated on Li(2) (+) in a 0.9 x 10(12) W/cm(2) field. In analogy with Na(2) (+), the 1,2 (2)Sigma(g) (+), 1,2 (2)Sigma(u) (+), 1 (2)Pi(g), and 1 (2)Pi(u) states are of relevance, although the pattern of couplings is shown to be more complex. A hitherto unnoticed metastable state, which correlates asymptotically with 2 (2)Sigma(u) (+), is described.

Multireference spin-adapted variant of density functional theory.

A new Kohn-Sham formalism is developed for studying the lowest molecular electronic states of given space and spin symmetry whose densities are represented by weighted sums of several reference configurations. Unlike standard spin-density functional theory, the new formalism uses total spin conserving spin-density operators and spin-invariant density matrices so that the method is fully spin-adapted and solves the so-called spin-symmetry dilemma. The formalism permits the use of an arbitrary set of reference (noninteracting) configurations with any number of open shells. It is shown that the requirement of degeneracy of the total noninteracting energies of the reference configurations (or configuration state functions) is equivalent to the stationary condition of the exact energy relative to the weights of the configurations (or configuration state functions). Consequently, at any molecular geometry, the weights can be determined by minimization of the energy, and, for given reference weights, the Kohn-Sham orbitals can be determined. From this viewpoint, the developed theory can be interpreted as an analog of the multiconfiguration self-consistent field approach within density functional theory.