Timo Fleig

The generalized active space concept for the relativistic treatment of electron correlation. III. Large-scale configuration interaction and multiconfiguration self-consistent-field four-component methods with application to UO2

We present an implementation for large-scale relativistic electronic structure calculations including spin-dependent contributions and electron correlation in a fully variational procedure. The modular implementation of the double group configuration interaction (CI) program into a multiconfiguration self-consistent-field (MCSCF) code allows for the treatment of large CI expansions in both the spinor optimization step and the post-MCSCF dynamic electron correlation step. As an illustration of the potential of the new code, we calculate the spectroscopic properties of the UO2 molecule where we study the ground state and a few excited states in vertical and adiabatic calculations.

Large-scale parallel configuration interaction. II. Two- and four-component double-group general active space implementation with application to BiH.

We present a parallel implementation of a large-scale relativistic double-group configuration interaction (CI) program. It is applicable with a large variety of two- and four-component Hamiltonians. The parallel algorithm is based on a distributed data model in combination with a static load balancing scheme. The excellent scalability of our parallelization scheme is demonstrated in large-scale four-component multireference CI (MRCI) benchmark tests on two of the most common computer architectures, and we also discuss hardware-dependent aspects with respect to possible speedup limitations. With the new code we have been able to calculate accurate spectroscopic properties for the ground state and the first excited state of the BiH molecule using extensive basis sets. We focused, in particular, on an accurate description of the splitting of these two states which is caused by spin-orbit coupling. Our largest parallel MRCI calculation thereby comprised an expansion length of 2.7x10(9) Slater determinants.

A direct relativistic four-component multiconfiguration self-consistent-field method for molecules

A new direct relativistic four-component Kramers-restricted multiconfiguration self-consistent-field (KR-MCSCF) code for molecules has been implemented. The program is based upon Kramers-paired spinors and a full implementation of the binary double groups (D(2h)(*) and subgroups). The underlying quaternion algebra for one-electron operators was extended to treat two-electron integrals and density matrices in an efficient and nonredundant way. The iterative procedure is direct with respect to both configurational and spinor variational parameters; this permits the use of large configuration expansions and many basis functions. The relativistic minimum-maximum principle is implemented in a second-order restricted-step optimization algorithm, which provides sharp and well-controlled convergence. This paper focuses on the necessary modifications of nonrelativistic MCSCF methodology to obtain a fully variational KR-MCSCF implementation. The general implementation also allows for the use of molecular integrals from a two-component relativistic Hamiltonian as, for example, the Douglas-Kroll-Hess variants. Several sample applications concern the determination of spectroscopic properties of heavy-element atoms and molecules, demonstrating the influence of spin-orbit coupling in MCSCF approaches to such systems and showing the potential of the new method.

A relativistic 4-component general-order multi-reference coupled cluster method: initial implementation and application to HBr

We present the initial implementation of a determinant-based general-order coupled cluster method which fully accounts for relativistic effects within the four-component framework. The method opens the way for the treatment of multi-reference problems through a state-selective expansion of the model space. The evaluation of the coupled cluster vector function is carried out via relativistic configuration interaction expansions. The implementation is based on a large-scale configuration interaction technique, which may efficiently treat long determinant expansions of more than 108 terms. We demonstrate the capabilities of the new method in calculations of complete potential energy curves of the HBr molecule. The inclusion of spin–orbit interaction and higher excitations than coupled cluster double excitations, either by multi-reference model spaces or the inclusion of full iterative triple excitations, lead to highly accurate results for spectral constants of HBr.

Large-scale parallel configuration interaction. I. Nonrelativistic and scalar-relativistic general active space implementation with application to (Rb–Ba)+

We present a parallel implementation of a string-driven general active space configuration interaction program for nonrelativistic and scalar-relativistic electronic-structure calculations. The code has been modularly incorporated in the DIRAC quantum chemistry program package. The implementation is based on the message passing interface and a distributed data model in order to efficiently exploit key features of various modern computer architectures. We exemplify the nearly linear scalability of our parallel code in large-scale multireference configuration interaction (MRCI) calculations, and we discuss the parallel speedup with respect to machine-dependent aspects. The largest sample MRCI calculation includes 1.5x10(9) Slater determinants. Using the new code we determine for the first time the full short-range electronic potentials and spectroscopic constants for the ground state and for eight low-lying excited states of the weakly bound molecular system (Rb-Ba)+ with the spin-orbit-free Dirac formalism and using extensive uncontracted basis sets. The time required to compute to full convergence these electronic states for (Rb-Ba)+ in a single-point MRCI calculation correlating 18 electrons and using 16 cores was reduced from more than 10 days to less than 1 day.

Instability of the Al42- “All-Metal Aromatic” Ion and Its Implications

Al42 - is a prototype structural unit of a new class of all-metal aromatic molecules. Without stabilizing counterions this species is unstable with respect to electron autodetachment in the gas phase. We estimated the height of the repulsive Coulomb barrier to approximately 2.7 eV and calculated a lifetime of 9 fs. This is a short lifetime: The only way to study the isolated dianion experimentally is to use electron scattering techniques. Investigations of the validity of bound-state quantum chemical calculations on the isolated species show that the results suffer from significant admixture of continuum states to the bound-state wave function depending on the basis set. Calculations of molecular properties can therefore give essentially arbitrary results for this ill-defined system, as is demonstrated for the energy and nuclear magnetic shieldings. This substantiates that results from calculations on the isolated dianion should be approached with caution.

Electronic and Vibrational Spectroscopy of 1‐Methylthymine and its Water Clusters: The Dark State Survives Hydration

Electronic and vibrational gas phase spectra of 1-methylthymine (1MT) and 1-methyluracil (1MU) and their clusters with water are presented. Mass selective IR/UV double resonance spectra confirm the formation of pyrimidine-water clusters and are compared to calculated vibrational spectra obtained from ab initio calculations. In contrast to Y. He, C. Wu, W. Kong; J. Phys. Chem. A, 2004, 108, 94 we are able to detect 1MT/1MU and their water clusters via resonant two-photon delayed ionization under careful control of the applied water-vapor pressure. The long-living dark electronic state of 1MT and 1MU detected by delayed ionization, survives hydration and the photostability of 1MT/1MU cannot be attributed solely to hydration. Oxygen coexpansions and crossed-beam experiments indicate that the triplet state population is probably small compared to the (1)n pi* and/or hot electronic ground state population. Ab initio theory shows that solvation of 1MT by water does not lead to a substantial modification of the electronic relaxation and quenching of the (1)n pi* state. Relaxation pathways via (1)pi pi*(1)-n pi*(1) and (1)pi pi*-S(0) conical intersections and barriers have been identified, but are not significantly altered by hydration.

Electron electric dipole moment and hyperfine interaction constants for ThO

Abstract A recently implemented relativistic four-component configuration interaction approach to study P - and T -odd interaction constants in atoms and molecules is employed to determine the electron electric dipole moment effective electric field in the Ω = 1 first excited state of the ThO molecule. We obtain a value of E eff = 75.2 GV cm with an estimated error bar of 3% and 10% smaller than a previously reported result (Skripnikov et al., 2013). Using the same wavefunction model we obtain an excitation energy of T v Ω = 1 = 5410 ( cm - 1 ), in accord with the experimental value within 2%. In addition, we report the implementation of the magnetic hyperfine interaction constant A | | as an expectation value, resulting in A | | = - 1339 (MHz) for the Ω = 1 state in ThO. The smaller effective electric field increases the previously determined upper bound (Baron et al., 2014) on the electron electric dipole moment to | d e | 9.7 × 10 - 29 e xa0cm and thus mildly mitigates constraints to possible extensions of the Standard Model of particle physics.

Spectroscopic and electric properties of the LiCs molecule: a coupled cluster study including higher excitations

Aimed at obtaining complete and highly accurate potential energy surfaces for molecules containing heavy elements, we present a new general-order coupled cluster method which can be applied in the framework of the spin-free Dirac formalism. As an initial application we present a systematic study of electron correlation and relativistic effects on the spectroscopic and electric properties of the LiCs molecule in its electronic ground state. In particular, we closely investigate the importance of excitations higher than coupled cluster doubles, spin-free and spin-dependent relativistic effects and the correlation of outer-core electrons on the equilibrium bond length, the harmonic vibrational frequency, the dissociation energy, the dipole moment and the static electric dipole polarizability. We demonstrate that our new implementation allows for highly accurate calculations not only in the bonding region but also along the complete potential curve. The quality of our results is demonstrated by a vibrational analysis where an almost complete set of vibrational levels has been calculated accurately.

Two- and four-component relativistic generalized-active-space coupled cluster method: Implementation and application to BiH

A string-based coupled-cluster method of general excitation rank and with optimal scaling which accounts for special relativity within the four-component framework is presented. The method opens the way for the treatment of multi-reference problems through an active-space inspired single-reference based state-selective expansion of the model space. The evaluation of the coupled-cluster vector function is implemented by considering contractions of elementary second-quantized operators without setting up the amplitude equations explicitly. The capabilities of the new method are demonstrated in application to the electronic ground state of the bismuth monohydride molecule. In these calculations simulated multi-reference expansions with both doubles and triples excitations into the external space as well as the regular coupled-cluster hierarchy up to full quadruples excitations are compared. The importance of atomic outer core-correlation for obtaining accurate results is shown. Comparison to the non-relativistic framework is performed throughout to illustrate the additional work of the transition to the four-component relativistic framework both in implementation and application. Furthermore, an evaluation of the highest order scaling for general-order expansions is presented.